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Development of a Small Cruising-type AUV and Training of Constant Altitude Swimming
by Taku Suto, Member Tamaki Ura,_ Member
Summary A small cruising-type test-bed vehicle named “Manta-Ceresia” is developed to ensure performance of various control architectures for Autonomous Underwater Vehicles (AUVs). Although it is so compact (13 kg in weight) that one researcher can carry and handle the vehicle, it is equipped with sensors and actuators required for prototype AUVs. Pairs of elevators and thrusters make it possible to move in 3 dimensional space. It is realized to swim along walls of a pool keeping constant distance automatically making use of 6 channels of range finder. Taking advantage of these characteristics, adaptive controller which requires comparatively long swimming for adjustment can be examined in a small pool. The performance of the constant-altitude-controller utilizing neural-network, which can accumulate experience by adaptation, is examined with this robot. Switching structure of neural networks is introduced to keep experience which is apt to be forgotten through additional learning. It is demon strated by the developed test-bed vehicle that introduced switching system represents underwater terrain more precisely and the controller is adjusted appropriately.
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Fig. 1 Picture of small cruising-type underwater robot “Manta-Ceresia” DISCLAIMER
Portions of this document may be illegible in electronic image products. Images are produced from the best available original document p y 1- © k afvff ©flSK 207
Table 1 Specification of the robot —Axis of Range Finders asu t-'Xy Kd#7 t LJ—%% £M Manta-Ceresia A* 489 mm A* 634 mm 196 mm ESS* i3.8 e*wtsx 1.5 m
1 m/sec Thruster /Unit 2B#SS30 S'
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ATK, CtlNN k FwdNN K 1 a.-9;F^y hV-^3 y hn-y^ffiv^-Cndf-y h K*6fl£JilI]Sli'Jtofi :T- Z©#e#^Ufm*K#RL^C:k^ 7 ^iRSLfco £©t—7 Geometric d- y h frCL*3»k'©Mje**tr)A. %9#&8M#(D#AR:j: r7-7©^I'£fi1ofcft#A k, ?6»##±©^B D CkA*T@^RK:mL^3y 80 -7% k^-R®$5##±©@Bd}C lc#U"C Geometric d- y 1 k**T@ 5. 7 - ? ®S-fTo fcS-6-©|sS©lE^©l±^6ia 10 E atf.010 i±±^6f-7^U»V) 4. n^-y HCct-E.SSSEffrogto B±©f-7 B ©#e. i8#©&a#B±©f-f c ©# 2$TW#L*:o^y T'@/\-F9j:7K:3#TaE'<& %D#t#*®y7h7^7»@#U. ±#^XzA©# ^UTt^.lo®y77K:%&®*g*t&6©K, -a.-? §®^EESrfj5o 20m, fi5m, #$ 1.5m® y h 7 - d' i±i@^#m©$m@E j: 0 #a##*igEk 6AAK ^7-4rf h$08© flat terrain + rugged terrain: A X 5 ic*ffk:EeL7ko n*> 1 K 6m 110 cm (DmMttvmLxjjmmmnfmD #*.*, otKyh®K*#®##^id*--a-9/k^yh 7-^%%mLA]>"ha-9K:j:-3Tg|%IL, f®## »WE75. tt^^-;ydfld&%D@AWf+A-C$0, 4-0©%K KB^-nay^ d- 5 ^xHgE-fbg-&f%B^td&ai'fbg-wr 10 too 1000 10000 learning times 5> fflT, ffl D#^.##1±BI 9 K5x5il5 15K Geometric 3.'yh9-?##&9]D#a.&j:3R:, &dt2o®^'yh flat terrain: B(#2) 7-^ De& & J: 3 K^gLA. 0.1 - 10000 learning times rugged terrain: C (#1) 0.1 - Fig. 8 Underwater structure 0.01 - 10000 learning times Fig. 10 Convergence of learning of geometric Fig. 9 Switching system for modularized network networks p # 7 h ©Hf& t fcfi&Mfragm 211 ^T< 3©T,f ft?fhlO#S©$##Eot)Tig w 0.2 5 0.1 — with switch without switch Training times Fig. 13 Control with switching structure after 6 times Fig. 12 Transition of error of altitude of training 212 #1181# G&B0—SBT&&. fTc-CV^V). # # 3t # 5. *s m 1) ##, mm^%5@^:##m&0A:*0g#m #*jB0M%m%, #9@m#x#y>4fs;7A, ^##K*3 it 5 n df y h ©SljfflW^©^ (1989), pp. 203-207 ^0AAK, V7h9^7M%%^0&^/J#g#oiKy 2) ESE, m* : SBBUECX y h ©EiR 10M%SfT-3teo ;©n*7 h ttBfrllk LT©^* gitlfi 1 (f 02: 7t7-Ftf^ta>iD-7 /!#? &%/J\ 0R#^*0%A), 8$^#^#^%, Vol.174, (1993), pp. 917-924 HO^WtCfe^TgUWCSIltlff^fT'J c k»i"eS6o 3) Ura, T.: Free swimming vehicle PTEROA for mSrfflviT, '> 5 a t/—-y 3 y-e^ESii-T^t: —3,— deep sea survey, Proc. of ROV ’ 89, San Diego, (1989), pp. 263-268 -7 0#ie*^o^y hCKv^Tbm^JKfzk^^CkAi 4) : gBXEH- i-7H'>1321 n m^%De^#*0#AKi!), m#0/<7 -?yxf A0M%k#*a0Bmm/\0a% ->0#%&frV), ^tU^Ml&Ltz^ > 1 n-9*igllW 8$:)#%###^:#, vol.169, (1991), pp. 477-496 5) #*, K*E#$fL&c:k^gfL, %l#*gm0%AA:. $# ms (e©i: 77-ff-f>'y$MT09m:), B*m /j\#0KfTmf% ht? yo#y h vol. 162, (1987), pp. 117-124 a, cfL&TKgii^tv^ u^L, f0*#, 6) 5#am, mm, ##**: -a-y/p^y t v- 7Kza#*m0am0i^E (e©2: ##a@0 - *T EI S # * fj* B.A.A.P Balasuriya** za # # #** E# # #* II I E # st*** Visual Feedback Navigation for Cable Tracking by Autonomous Underwater Vehicles by Motoyuki Takai, Member B.A.A.P Balasuriya Wan Chung Lam, Member Tamaki Ura, Member Yoji Kuroda, Member Summary This paper proposes and demonstrates a cable tracking system based on a visual feedback navigation as an application for the environmental survey using AUVs (Autonomous Underwater Vehicles). The proposed cable tracking system consists of three levels of controllers : (1) The higher level controller decides the AUVs' steering mode which includes a mode to search the cable in case that the vehicle loses it. ( 2 ) The middle level controller generates target values to realize the steering determined in (1) by fusing vision data and other sensing data. ( 3 ) The lower level controller generates control commands for the actuators according to the target values. This paper also addresses the vision processing techniques including Hough transformation and the transformation from two dimensions to three dimensions which are necessary for the steering decision in(1 land the target generation in( 2 ). The proposed system is implemented on an actual AUV named the “Twin-Burger 2”. The perfor mance of the system was examined though trials carried out at Lake Biwa on October 1996. The vehicle navigated for about fifteen minutes without losing the cable although the cable was sporadically veiled in waterweed and transparency of water was not good. It is shown that the vehicle implemented the proposed cable tracking system can be a practical and general platform for environmental survey in the predetermined area. i. m w ##SB, AuvK#Lta#mm#smAf&kR h (AUV: Autonomous Underwater etc, Vehicle) B, hya-AommefrcT#*/*'. &. CO*:*) AUV B, , is#m&oa C y M-aeaKKmu, Auvaief^mAczo'y-yn/t 5 y 7 K'lrigii 5 C k B# L <, LBL (Long base ALT, -line) ¥ SSBL (Super short base-line) ti. k' ©Hhinfiv' kaftayTFfjLTkLT, ** *** 9, gams## JSESS 9 ¥ l U 10 B ¥l&9¥5M15B ff 5 tz ft KiffiIAiii4i©fg®!SK 13 ti THiiS-fTo feo 214 mm# -y/l/CmE&frS) 2. AUV <7)77 K7X7H§ji k#ftW-2--7*;v5rS*7fcS-B-©SaSi£- 2.1 £wm %^5. 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AITV ©»A##mAG (%'D) disturbances T5 L4©5£ H k U H frZ AA’ ET5 LfcSS HF ©, Force & Rate, Modd PSA Controller deadzon -^Target Point Detected Line(A-A') Fig. 5 Swaying and Yawing Targets Plan View Fig. 6 PSA Controller 217 rze<0, Xe<0 or §@R#E#gtffd-a^6, ad?yh© — KlXer ify \P U\—\ *-Xe>On 0, Xe>0 kSr*fB^^3t©ki-%. y-yvp« 0 otherwise ^*5,-?tf'C|6]A^'TEBSrh-, ## • fz«<0, %.<0, t,<0 w (6 ) K2.0m, 4.5mT*,5.mi&K:Km%&L, y-y^i± — KlXe if 1 m = i *■ Xe > 0, Xe>0, Xe > 0 k i:5HC3av##iT,-CVr.%. lo otherwise T@3>ha-9-r$SPSA3>ha-9r%m-r'5 %,=«] + % 7-i-p/fy^">'T>'SrTablel©j:^l:^*5. B#@ Surg ing ©*kKB#@S &, X9X^©%#S-#AT%kkt 5. m fsn C Yawing $!] # E S' # /k tk 0.2[m/s] k i$t 3« Fig.7K^T Heaving SBPEdo ty<5 gSKStt CCD is f 7 ©Bft-’f’II I: ds ^ T # ft/k @###4: o #©^%a t#A L, 1.25 [m] k 5 . -y - y t -S y h © Twin-Burger 27)i;^SL> IlIiilMkSnllfflifitC — PT*tt, Surging ©T^TKESilStt 0[m/s] k L, Sway A##KT It -3 fc0 ing do X Zf Yawing © B IS fit If /ID (i S' f: tl tb S fP Twin-Burger 2 K, 0.05[m], 3 [deg] k 6 « * /k AUV a^y - y;PimfT^ lmlkmEI#]a^»v^j:^Ey&/kK'E, 10, 30, 50, 70, 90, 110#©%S-C^:5lRl&aE3-&&. C k 5. n di y h B#m%#l 80 S©/NB i2o^*ry-y;p*!%^,T@»t^*^Ka y$/a>-%^ 7y%/k»E»±t-FE»fzy%. nd?y h k#Ak©B#&a6^kA;W#T$&o Twin- j: &m#%me#d3 z #mm& Fig. g- Buger 2 ©### Sr ftSI Surging 7? 1% ia^6 3E^f. ©**aa t f js i f & ^ Fig. 3 CgSLfc, Hpixel] k 6[deg] S-fflViT^T„ r\y Tr8D, ##B©EA#@&^K%0f4(74^A:2mK:ZD Surging, Yawing 7J|n]©§iJi@Sr, ^A-hTTrlnlKW D ftt} & &T©Mv#MCdsviTli, HBra©7--?MaRasy: Git/i 2*KiD Heaving ^|ui©$iJ@PSr, HE^HT 5 k kS'fiJUL, ^|g©/\ Vttftbtl-fc ISC X 0 Swaying ^luIOSiJffllSrfT-5 o 7 (x, o) ©meEc do Twin-Burger 2 tt, Rolling k Pitching S'icG E H C X 6t©kf 3. (r, 0) ©$#@ 3.2 8BKS#D/k g^.%7kAK:, aReK-y-y/ya# c Auv miS EBBih 5T —TVHizktpKdoViT ®Btt©iW v1 it y?7*200g'a^ 520#Ka^T(r[plxrel], g[deg]) 3, y-y;pi±m#mErKv^y 1±, d3dsj=f (50, 770)Sr%R:S%;L»a^, y-y;y ia#@:*K:aga&giT,.5 i ^ E##f $^#T# c k »< m%cy^6. y-y;p«mm AUV©gr#Srag#'fk^-%^»l:. y-y^ElmCTkE (724[pixel]x7az[pixel]) ©f'DKKM^. (W, 7W) k* #2fL6#*BK:&5;:kaig$L!,>as, e>KJ]xstf, V ftffliJEdo t>T2E_ta$ D ©HE Table 1 Gains in PSA Controller K1 z2 Surge [N/(m/s)] 50 800 Sway [N/m] 110 300 Heave [N/m] 200 1000 Yaw [Nm/rad] 40 100 Fig. 7 The Twin-Burger 2 218 181 •§■ Vision Processing J. 0.5 ■ Steering Mode -" Searching 'in.. nn XIIBXmi ~~ Traeking cendi 3g -•+--— Wa °0 100 200 300 400 500 600 700 800 900 1000 Time[sj Fig. 8-3 Experimental Results (Target and State) Fig. 8-1 Experimental Results (Vision Processing and Steering Mode) Auv kti&o —Jj Surging is J: If Heaving ©SJfll 520#$TK:^^T«7-7/P A60[m]oE# 0#^(, 200#, 520#WKK:ot)T«, 7-7/P Twin-Burger 2 7 — 7/1/1 M.% o X 7 — 7/P@ 8re-FK:#frfakkt,K:, 7-7/pe%^.LR(f7- 6. # W Xitr£tt, SffEStpDdly HcBB®SEe^3A7 ZZkfciV, L, ESSffl^o EEL, giSii^75Xi£©JISlXfiXfco CftK:### y-f, j3ZifB#*%sa#-?'T@3 7t'0-7k»a Time [s] PSA 3 > h n-7©#A&e-3A:.*%Xa7-7/P0@ Fig. 8-2 Experimental Results (Control Command) $ y h — ~?)V\z. J: O XSilfe # % X IK 1) mm, #m, /i\&, min, a# rma-y-yA- b ? y ^ >y@&mm*#j# (f ® 2 SSNamCA#N: f-7;i/ b 7 y 4f >/#{$)J, B*)#iB#^^#, Tgg#4:o%Ky h»mv^->--y/ym%m^K:amL#E Vol. 175, pp. 219-226, (1994). 2) mo#*, rnmr^fb/pmis^n^vbom^k &f5S%. y-y;i/K:j:cT#@m#3aK:mS #W#BWRJ, Vol. 178, pp. 657 -665, (1995.12). 2fL%. H±, y i TARLA AUV TT-;l/7>"Od;7 bj #B8 ~7 % —A h & 9 tho as^essitiRj, m«im, PP. 113-118, (1997.2). m »' 4) B. A. A. P Balasuriya and T. Ura, ’’Vision Based Tracking for Unmanned Underwater Vehicles”, Proc. of SICE’ 96, (1996.7). m»6^6oT*,o. 5) B. A. A. P Balasuriya and T. Ura, ’’Vision Based Object Following for Underwater Vehicles”, @*6#^#:%*, Vol. 180, pp. 663-668, (1996.11). Hh^/aLSfo 6) ###,#*, r#$LfT#m*o^yh®3)^Ch7 #%*, Vol. 180, pp. 677-684, (1996.11). 7) W. C. Lam and T. Ura, "Non-Linear Controller with Switched Control Law for Tracking Control of Non-Cruising AUV”, Proc. of AUV ’96 pp. 78 Bern -85, (1996.6). 8) T. Fujii, T. Ura and Y. Kuroda, ’’Development of a Versatile Test-Bed ’Twin-Burger ’toward In telligent Behaviors of Autonomous Underwater Vehicles”, Proc. of OCEANS ’93, Vol. 1, pp. 186- 191, Victoria, (1993). 221 2-10 7 Ab 7 —9 &WI1I 7 — h' 0 2# % # tr iEi Preliminary Estimation Tool of Propulsive Performance for High Speed Craft based on Artificial Neural Networks by Taketsune Matsumura, Member Tamaki Ura, Member Summary In preliminary designs of high speed craft, it is often that main engines, reduction gears, and propellers are specified referring to accumulated trial data of actual craft, which is usually converted to design charts. These stern components should satisfy the requirements of both propulsive perfor mance and practicable stern arrangement. The design knowhow of compromise between these requirements builds up by collecting the trial data. This paper proposes a trial database system for high speed craft, which consists of a collection of trial data, mapping neural networks (what we call a memory model) , and a descriptive neural network. The memory model, whose input is a design condition (length, displacement, target speed) , and outputs are the required horse power and the standard propeller specification, is generated by learning of the trial data. The descriptive neural network, which denotes the frequency of actual craft with the similar design condition, indicates the designer how conservative the given design condition is. The proposed database system is based on the trial data of 36 craft. The constructed neural networks set standard for the stern components, quickly estimate the propulsive performance, and reduce the number of iteration of the design spiral. When additional trial data is available, it is easy to modify the constructed networks, taking advantage of learning ability of neural network. l. (i D A tc 0#w CFD##r#&ff p l.i A#*: 20-50 m 20—40 kts 0#iSa# BBLTB, &fn k 0 0###, warn, L%_kr, 0.5—l.l@@0a##&*/f-1-&&0T&a#, Z0# ISff- § ^i 11 % tz tb c # # K a g ft r - -v k £ -5 X v > 3o i.2 a c k (m), Et (kts), BHP(PS) k LT7 E S 9 BHP/W/r), BHP/J ¥58 9 IF 1 H 10 H Fig.l j; o $36 %0 b 9 -f ^T E t 222 mm-# 225 200 a 175 6 150 1 125 ts < 100 75 50 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 Fn r = 0.83 Fig. 1 Cadm of high speed craft 100 125 150 175 200 225 a'&9©/? Estimation by Niwa chart Fig. 2 Correlation between Actual Cadm & Estimation by Niwa chart * o, amemf-©##?#; < #m 2 an: w a. Fig. 2 - TRIAL DATABASE SYSTEM - i— NEURAL NETWORKS . X- MEMORY MODEL ^03^" KS"^wA#^@k^#@k©itR% C^. ©B C Manning Net 0 (1) SPEED POWER CHARACTERISTIC T^L-C^aas, j=cTi±20%j^±©K^at*,9, C Mapping Net ) (2) STANDARD PROPELLER DESIGN POINT r « 0.83 C Descriptive Net 0 (3) FREQUENCY OF ACTUAL CRAFT WITH Learning THE SIMILAR DESIGN CONDITION a c kamm±#L <, a#imm##ekam COLLECTION OF __ TRIAL DATA 0§mB&BB&W&a#LA:_k-r, %*7mA%»Kj:a &S&L%9, ff-hmg@k0fBMt#^L-Cjsh, (3)m#(m*©ma, 7i A*^m^t#iii-&a#^kfa. ##K# #^©Km-#*e@i±, #%a#m#»§s#A©#emeUkUT, ^##»5#©§W(f-7%gK:, %*fa kLT®f-7^-xa;#gK*»aa:, s/%f A©#s@g7it#@Kf a. 7 )V^y 17-?( 1°) ©KH £fBfSfa^E i. V, XEfWIB ##, ^#Ti±/\-Ff4"f>'jl6mK:Za#Bya-t7 4--rL-D yfEoS^lES^raST*, 5SiEto»:9-* 2*##R^*#kLTt^aat, f©#m##K:MLTH $'to#e,a^^#7'-7"<-xi/XTA©#ie&M» Appendix l(A.l) K, S$tS$#tt^MLTti Appendix a. %*faS/XTA©#^(±Fig.3E#7j:^E, h? 2(A.2) Kf #Lf kL#g&asf #, — a —y h 7 — 7 -Y7;i/f-f&k, y h<'»Ej:aB«t7;K ©^tf/l/CRLT# Appendix 3(A.3)Kf ©#g& y h<"'a^a^9ao. it. ASr#efa7k»E, 2. h7-r7Arf?-^^<-7.'>XTA<7)S@ #f-Ejs^af-f-fyx/<'f9;Fti^*L, 2.i ^sSUmticfcttSTV-f >x/Hv;u %#ETa. %E, f©##M#$r-3L-y;pfyh7- "FRmR©#^-, ±5B©as#*at@w@m*#^e; 223 (3) &*#Bg-?'fyy7Vy7yx0m*, 7 h y-4^Af ±#B#±A^ < &8I#*:&&. oi9, EH±©S^»:>5>WEJf>7D^7@eE —i^SIEk-&So (1) Z0j:^K:, ya^7SB0RSK±8(M, #5m%©ag &, #m%#±®s$kii6m5m±o (2) mam'D*#^LT*mo77y7>&^ #$©/iK'f>'b (ff-ffil#, tf-B® k -4@©7f y 7"&yif ^ >x/<^f 7;i/0—mk L, g$c, KMf3±a0/f7y7##t#H:&A 2: k tc»& (Fig.4#M). tc L T ff to ti 6 V* 5'# v v ^^Th^-fy^y-yK^v^a, *#, #*a, #h #K#Ram0#&B7o/<7gB*;mBT, e me, &tm#R;%k ©%&:####*%&& (1) *m##(A.i#^), sm#@##(A.2#LTv^CkK:»&. KiD, naa, BbkE:/o^7@ 2.2 Mtrmmmiffl Trim & Stability Check Preferable Trim Condition Intact & Damage Stability Balance OK Speed Power Curve Main Engine Specification Neural Network Propeller Specification Model Basic Design Accomplished | Reduction Gear Ratio Fig. 4 Design procedure of high speed craft Fig. 5 Memory model of present trial database system 224 181# k0@A m#@^%0 60K@m(L7W5^ yT/;FX&B, cmmcT, y%f %O-10##T#^7a^ y F 9-7 : y F A0A#»# Descriptive ^=6'=216 0A$mmL-CV^.# Neural Network #KBLTa;=6 0m%a^mv^T^=M' kLt. Cadm Mapping Neural Network Fig. 8 8, zme,0#af-7»6kK##g$lFA|»# *-y F©m#fi0#SHT, #@@m« 8,6406 = 20,000% Mn -» 432 7sT v ~7~C'h6c Table 1 C-a-n >P^0|g^-)ffi k — 3. — n y©[li{B$'7ir'4"0@8 Fn-Rn VH$■—"O Rn* -► k L, M, 'Propeller Design Point k 0@g, %^0**0## K $ 6 ^ 0—1 ©m# &&-?-[ Mapping Neural Network C k#W#k»a„ S 6 f ;kC138 Fig. 6 Neural networks for present trial database #$ y F 9-9 0m##K:*f system 225 3.2 mm^TMztnizmtZ'v h ±TR#*f4=k@K:D, y b K, y b 0#@ k 1.2 m #@0IRme*&Fig.9-12K:^fA*, BA^*,AB& ®36%Ob7-f7;Ff-f$-&kCfr^. If C^, fl0.95, 0.93, 0.97, 0.97 kL-n±ioo%±*mAm^img&Rof-f & k»o-CV)&. #KC^»K:MLTa, Fig. 2 k Fig. 12 $r BA AB%If Cm* 0@0#G lt#f6k, #f-f^-%y%TA(Df8MIW9#f + - filf jl.5—16, 28—55, 0.50—1.25, &tf50—220 KR%L, #/r0-l #C7° Fn -zL-9;F^.yb9-^®# f—f@-7^z, u, K»6^#0mQ»im«m#Ae@#-e& o , * k LT# (FA, B?, M,) ^6 +#a*#S2) $£»MSeTi>Z z k*5>, ^ift-CttS-Mig^SS#tt #AL»w^kkL7^6. @L, ma^gSKf-fA^a & z k t#a. <=,#.&. Fig. 13 Kyo-tvfif-f > b0#:#^y b 7- Table 1 Weight and threshhold values of D. N. N. W0(1)= 0.800 KD = Mn hl(l) = 5.400 W0(2)= 2.500 1(2) = Fn hl(2) = -2.000 W0(3)= 0.004 1(3) = Rn hl(3) = -1.400 witi.i) 1 = 1 1 = 2 1 = 3 i = 1 3.868 -38.657 -17,705 h2(l) = -7.026 i = 2 -37.490 -0.948 -25.683 h2(2) = 0.245 i = 3 -8.811 -4.723 7.898 h2(3) = 4.748 Fn i = 4 -4.949 -0.199 3.974 h2(4) = 0.361 W2(i.i) 1 = 1 1 = 2 1 = 3 .1 = 4 Fig. 7 Distribution of trial data (M„, Ft, R%) i = 1 -50.909 45.562 74.515 -80.819 h3(l) = -46.521 Mn = 5.5 Mn = 6.0 Mn — 6.5 Mn - 7.0 Mn = 8.0 e 3 60 80 100 120 40 60 80 100 120 40 60 SO 100 120 40 60 80 100 120 40 60 80 100 120 Fn * 100 Fn * 100 Fn * 100 Fn * 100 Fn * 100 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Output of Descriptive Network Fig. 8 Descriptive Neural Network 1.4 r = 0.95 r = 0.97 0 5 10 15 20 Network output Network output Fig. 9 Cerrelation between Actual Bf and network Fig. 11 Correlation between Actual AR and network output output Cadm O 150 r = 0.93 r = 0.97 50 75 100 125 150 175 200 225 20 30 40 50 60 Network output Network output Fig. 12 Correlation between Actual Cadm and network Fig. 10 Correlation between Actual 8* and network output output 7 Horn LXG&kkk, to E 7° □ ^ 7$ < &5l®|iW;£>$ k k %>o Fig. 14 E Cadm ©¥B* 7 h V- 7 ©tH^lS^A?^ am##E»5EdlfC31^k6 f. 36* L(i )# #. a#, LTV1< AR t$Elf-%© k»%E%cTC^.©#l±±#T6. EK-WXKM. Eoft-T Cadm (DM t> ±Wi~ 6. (3)ARA^#<»5E%W(#E1.0j^±), C.^© a:, m©aa-fk, :&3HkE #7 < » 6*l=l^mmftoE*A 6 fret) k ^ 6 y b K, % E t -I.-?y h ij/B 227 Bp* mapping 8* mapping AR mapping Descriptive net Fn * 100 Fn *100 Fn * 100 Fn * 100 Output of ^ ^ Output of 55 0.5 Output of ^ ® ® Output of * ® Bp* mapping net 5* mapping net AR mapping net descriptive net Fig. 13 Propeller design point mapping neural network Table 4 K, 3-v ymoftnaffiAk-^ — u „ HftKiH Fig. 13 ®.t/Fig. 14 CO -ylV^y J-9-7 ©ifi/fblg* C J: D, 513 &$R9, ## fUf, mi##Kj:9, McMLTH h7-?#BT#a;:kB996a:'T&&. Table 2 Table 3 K, C^. y h KMLT B 228 181# AR = 0.6 AR = 0.8 AR = 1.0 AR = 1.2 Descriptive Net Fn*100 50 75 100 125 150 175 200 0.0 1.0 Output of Cadm mapping net Output of descriptive net Fig. 14 Speed power {Cadm) mapping neural network 4. m m m **:, Fig. 15KKC«d.0fBM&'^L-Ct f/!/ K: j: 5 A &, 3t#"'""<.4xi.x:.) ®% ■So Cadm 0^##. y b Cll AR y b (A-E) Table 5 0 SLfco y A, B, D, ~BlXI E K©BSt 0, c % c t A* y h v—>; 229 & tiS*C js»5KIRS* B//P*(PS) ©fiSBiStt, * y h y h 7 - 7 © $ fL & . 15%J%FSK:W:i|%&^Tw&a!, CjgTIi 3%T$6. @@ Table 4 Weight and threshhold values of Cadm Dpi m), SHB»Jt AR ©JfSBgElHCTfc, A, B, M. N. N. %^ERTHef±#»©K^a*±i;-cv^a*, CRT# W0(1)= 0.800 1(0 = Mn hl(l) = 5.400 ffLffb, 3%, 2%, 5%k»-pTV^. Fig.l6K#*©K W0(2)= 2.500 1(2) = Fn hi (2) = -2.000 W0(3)= 0.004 1(3) = Rn hi (3) = -1.400 W0(4)= 2.667 1(4) = AR hl(4) = -2.333 wia.i) i = i 1 = 2 1 = 3 1=4 i = 1 -5.704 -1.734 3.290 2.216 52(1) = 0.521 Table 2 Weight and threshhold values of B* and 5* i = 2 1.464 0.013 -3.407 2.134 52(2) = -2.750 i = 3 5.005 0.143 0.294 -1.789 52(3) = 1.151 M. N. N. i = 4 0.714 -0.526 -1.338 -1.271 52(4) = -0.757 i = 5 -4.486 -0.554 -2.429 3.424 52(5) = -2.598 W0(1)= 0.800 Mn hl(l) = 5.400 W2(iJ) i = i 1 = 2 1 = 3 j =4 .1-5 W0(2)= 2.500 Fn hl(2) = -2.000 i = 1 -3.255 -2.473 -3.831 -3.166 -1.717 53(1) = 5.790 W0(3)= 0.004 s i c Rn hl(3) = -1.400 Wl(i,i) 1 = 1 1 = 2 1 = 3 i = 1 -3.636 5.971 5.696 52(1) = 7.871 i = 2 0.376 -3.642 -3.824 52(2) = -2.419 i = 3 0.905 4.425 0.920 52(3) = -1.077 Cadm i = 4 1.244 9.783 2.299 52(4) = -3.940 W2(U) j = l 1 = 2 1 = 3 1 = 4 i = 1 -5.569 -3.358 -2.792 -1.156 53(1) = 6.613 i = 2 -7.069 -2.154 2.259 -4.750 53(2) = 6.200 ® 150 (i = 1 for Bp* i = 2 for 6 *) Table 3 Weight and threshhold values of AR M.N. N. -1 100 W0(1)= 0.800 1(1) = Mn 51(1)= 5.400 W0(2)= 2.500 1(2) = Fn 51(2) = -2.000 r = 0.93 W0(3)= 0.004 1(3) = Rn 51(3) = -1.400 Wl(ij) 1 = 1 1=2 1 = 3 i = 1 -5.205 0.933 4.941 52(1) = -2.786 50 75 100 125 150 175 200 225 \ = 2 -3.411 8.833 5.980 52(2) = 1.199 i = 3 5.294 -11.988 -12.012 52(3) = -3.005 Network output i = 4 1.274 -7.370 -0.565 52(4) = -3.126 W2(U) 1 = 1 1=2 1 = 3 J* = 4 Fig. 15 Correlation between Actual Cadm and network i = 1 5.164 -8.790 -6.685 -3.028 53(1) = 7.437 output for non-learned craft Tale 5 Comparison of actual trial data of non-learned craft and the estimated by present database systen Design Condition D.N.N. B p* 6 ^ AR Cadm* Mn Fn* Rn* Output Actual Estimated Actual Estimated Actual Estimated Actual Estimated A 5.73 1.17 330.1 0.00 7.80 5.74 31.68 28.79 1.20 1.22 159 147 B 5.07 0.97 194.1 0.00 9.41 10.08 36.68 36.71 0.75 1.21 140 122 C 6.33 1.17 308.8 0.95 5.75 5.69 28.93 28.81 0.94 0.89 184 179 D 6.93 1.02 263.6 0.03 6.55 6.30 33.83 30.08 0.70 0.69 158 142 E 7.53 0.77 356.1 0.00 8.48 9.91 33.85 38.27 0.90 0.99 137 139 Design Condition Graph BHP* (PS) Np* (rpm) Dp (m) L (m) A (t) V* (kts) Symbol Actual Estimated Actual Estimated Actual Estimated A 22.50 61.90 33.89 o 3820 4155 1193 842 0.90 1.16 B 17.90 45.20 25.05 A 1425 1637 1107 1106 0.83 0.83 C 21.55 40.47 33.10 ▲ 2320 2388 1064 1037 0.90 0.92 D 21.31 29.81 28.57 □ 1415 1577 1074 979 0.90 0.88 E 31.25 73.40 26.32 • 2335 2299 882 1039 1.01 0.97 230 mm-#- 5000 TRIAL DATA ESTIMATION %©l%k^9 F 9-96#^?# 5. A O ------B A ------4000 to # C A ------D □ ------E # ------— lra, ^#i%#±#©B#m^#emc- 3000 ~v)V^v h7-^KM1-5#a@S)W%S^rfc*D, m < 33lifpL$>if£to $fc, *im"e##KLtz&W$M, 2000 *#^a±K=#mm(#)mm - »6ifk:mTmA©#iemt: J; 0##T#7z6©T$0, %KUlTARE«%meE3tK: Sl^to # # 5t E Vk (kts) 1) #m-#:^MiKK#m#(20), m©## Vol. 30 (1977), pp. 78-86 Fig. 16 Estimated speed power curves and actual trial 2) /M&ES, mom#: #mmk#m, mmmmiz data for non-learned craft mm## (1989), pp. 75-118 3) g*mmm#as: ## 5. |p Em mm), B^mm#m&@ dose) 9-x(2)3o^-h/Emi@immmeK:ok)T, m m, Vol. 51, No. 7 (1978), pp. 39-63 s) m±^)rmmmwK#K:m±*^)T@fmgy F9T7/Ff-^©@mK:#BL, 9 -xdo)iso F>mmmm "t&e", mm, voi. 53, No. 587 (1980), pp. 9-24 -^.-9,p^.yF9 6) Mmgm@#:mmmgBK Mmmm##B%/i/, — 9 4-fEfflLT, —f"<~ No. 019-4 (1993), pp. 47-48 7) msmmm#: #mm@B^, Mmmm«##e. A,, Aii, *aa, &tfXo No. 021-10 (1993), pp. 48-49 8 ) fEBWt- : HiSEE#, (1971) 9 ) #R5m:*-#me©-EM-md3), mo## %o-c, Vol. 47, No. 2 (1994), pp. 51-53 m^AK^v^T, *me#±0g$hEm±og^o/f7 10) ati%j5:3^^^3-XAk#@, gm ##©#§g 4 (1991), pp. 51-77 #ifF*©lR^^#»e#^W#Ek U^k. 11) ##' ^ ^ - 9 ;p^. y h #@# K#^yh&me@-e-CW5#R:j:0, #FmKa* %©K*k%#R##, B#mm###3i:#, Vol. 171 (1992), pp. 587-593 EM-W##%»© 0a^*Rl:%l 6 12) msmmm#:#mm@B*, M@mmm#*6A/, T#, ##e0Sg/<7>x-f AE#rg&«,%^-C, No. 032-7 (1996), pp. 66-67 ErHEK©$###cbtt*), H 13) Rammm#: grmmg B*, M@mm%#m g. A,, k T, T t K»&k V^9 No. 032-7 (1996), pp. 68-69 14) Mmmmm#:m@m#B^, Mmmmm#B('A„ f©#, -a- No. 019-4 (1993), pp. 49-50 9;E^.yF?-9©#@##K:Z0, f-f/t-XBBC is) #m?*ep = f^g%MnW34mrnt-f-9> 9 “CUSTOMS 1101”, mm, Vol. 53, No. 5o 591 (1980), pp. 55-63 i6) zmmm^r: mmm ‘t-*-^ 2” ©es, mm, SfcibU, f~? SSSEIfiityBOK^SS/cA 5, $#m Vol. 54, No. 601 (1981), pp. 50-66 TarLZrf—?/<—%S/XfAB, -a—9;>4"yF7 — Appendix ^KJ:6E%t7',y»#K.-Cj30, &RK:j:T)T#k,fLA A. 1 fcOB^KmibL-C^-Cwt. mEPBTktaaeWkf #-a©#K*ammd v m/\- F f ^ T >mm-r F 9 231 5.0 4.0 ., 3.0 g ■ 5 b d a c 0.6 - a'_TYPE CP ° 2.0 a 0.69 43.5 b 0.77 43.8 1.0 <» 0.4 c 0.81 42.9 0.0 d 0.78 40.6 4.5 5.0 5.5 6.0 LCB %LWL from AE B/d Fig. A-2 Csw of typical high speed craft AE 1 5 6 8 9 FP Station r - kc-ii , 4) Fig. A-l Cp curves of typical high speed craft 4h9iaeB-7?n%,<7/-f k#^@Bt#OMK:me*l dW4f»>O.40#i*38#KK-l')TB L^6m*m*BP.>o.35m± LTv^0tC:0)#Oj|6mK:j:5##yn^7 2##mK j: 9 t#A#ttlc3@ < e# #4i%#*"A*mA0—ok#4.64t%.$4:B, »A^m B, k M. OM&k SJ(JLP) 14, Fig. A-2 K^-r«Cj|&ac 4 Z-ftZiS-m #%g4tTV^%#, A/B At@@Kd\$ < &144L14, B/ai t I$St, 4.0-6.5 0gwM»#mcm)Tf aa#@#&&Mi=& a# c« 14, mwut B/<^ $ 9 4iTW %. K#M14 —#, #m%$ 9 i4^m%$k f4ucyo^< h7>1hAOf-y-f 9 # 4i». a%@ amm (4i*a7* d —tf A 0HT14, 14kAB^'fbL»Vik#4.64L6. %^#K:e;mL-cwa®Tem%$9TKML-c(4, a.2 @0oAeT-^k#4.64t%. *%, @Rg*KNL-C a#0 h ylxthAXf —>#6@t®#&14 B«>0.4 k 6, a#Oh9>f-A^^-y®||6m#Kl414imm9» 6kh9>1hAA^*^+%0-#^'T^O, hy^thAmiC fmr#^A4t-ri39, y h$-aL-c#jg^e,mtfaiL-ct^^#T&6#t#im &E# 14±ME—^ k » 9, %%mmg^k LT14E zK@# (h7>ihA@g^) Klte!ILA##@#^k# ffbif, @jR#*Ki44om#^®B#4 9 , 4.641%. %^T4:aae®SRB2%7cRK:gj(.&0^ amr&9, k#^@iRB,K:l}-14-C#4.6 ^*"A)±k#4_64i%. %oT*%$9gl4Fl.lC±% 41%.%^-C^rBJ#^ BAP 14#*#*%- mmA!hmk#a.6it, Bailey<*", 19-#*", Cf, r„ mm##&?, it#@ && % k L, $ & E A.i c« & yo^9##%$9oicML-n4, $*, #Ai-& k#E*^0«K*gfi5. LAiL2.imTa-t4:#K, yo^yggoa^KKLT BHP=-z k C«d. # h o, k #K*1K: £., £„ M„ A£ ©M&k LT, L, ^©AAKSy-JE-TSSS Lv^i±j*% U k LT, £= mm, y2 (h-o,)'T-#tGfL&ai2#S,E &, £ e#/J\ ^ 6 gf gm* < # a. (#%K:«@/J\) k#a@Hk wSomt^fb^ta. @L# r kc-VT-VR-VH(Fn)-Vo(AR) , r \ T^a<>©kfa. msawmK: # n a t a z k, & /w*"c#?T#9igLeM*&m,', ^ k ^ g,, o A. 3. A.3 -a-7A^-y h’7-^<7>18® ^zL-?/P$y # m £ s* # x\ = wj = w°Ii + h\ (7) Bilge Hulls, Second Symposium on Small Fast Warships and Security Vessels No. 18 RINA Xi=f(uf) {n> 2) (8) (1982), pp. 239-252 /(«) = l/(l+exp (-«)) (9) A 6) fmm- : SfiWi$EBM<19>, mm Vol. 56, No. 621 iic, uf: H w HIS z # @ © — j. — n y ©IHtli, (1983), pp. 62-73 tyg™ 1 : S » —1 ESS/ #g@—zz. —□ % If SI z # a 7) ARs# • AiEffia:: /j\g#mm©*m*m©*# g©-a.-nyv X©s-B'SS, )!?:inli!#|c-a m, No. 75 (m?), pp. 36-si A8) am@#-##:-:i-7/R&yhCi5#WK© mm#j@-*#m?©$mw©mm-, aAitm# z'#g©—i —n y©m^i, /,: AA, w°: AtlfrbAtiM #H;%W, Vol. 166 (1989), pp. 503-511 C^a-ny^®g^fS, h\ : AtlM ~Sf V V^Sn II ^ ffl I ^ IE zm /j\ # ^ B* r** Development of the Hull Inspection Robot (RTV-SHIP) by Yoshihisa Nakata, Member Masatake Otsuka Hiroomi Ozawa, Member Makoto Konosu Summary Recently, demands for increased safe operation and ocean environment protection, especially preventing oil pollution in the sea are remarkable as the international tendency. On the other hand, the trend of the shipping world indicates clearly a strong demands to reduce the cost for operations and maintenance of ships. From the viewpoint of survey and inspection of ship hull structure, the improve ment of reliability of inspection, safety of work and reduction of costs for inspections are one of the most required subjects today. In order to correspond to the social requirements for surveys and inspections of hull structures, the authors are studying and developing the new monitoring system by the underwater RTV robot (MITSUI RTV-SHIP). The advantages of the RTV-SHIP are as follows : 1) All the tank walls can be inspected and easily recorded on video tapes. 2) All the operations can be controlled on the upper deck by minimum operators. 3) All the surveys can be performed on voyage. The basic tests of RTV-SHIP with regard to positioning in the tank, measurement of plate thickness and large diflection of panels were carryed out and satisfactory results were obtained. The utility of the RTV-SHIP was proved in this study and further tests for the actual ships are now planned with the aim of realizing this system. The RTV-SHIP is expected to make a major contribution to the safe operations and ocean environment protection. i. at w f h (RTV) t©st-aFeB©;s9 =k v ffl©*tpTi/trn*> h, RTV-SHIP c c % & s c, m# ** S#ai8(#) / * h n . yx f JHH38 ¥BSc 9 ¥ 1 H 10 B CT©g*%©lul±K: t 6 t ©T& -So 234 2. 2.1 Hffggfl #:yxf A©N%g#&TBE#f. y7fi©g#k&«, AM©emkg©IEa$&(ffMg# #©gE-fbE^fS^aiR##ATj3D, 2:tL^©fMt **6f E#W^#©^A#k%#%ti@Aa c: kang# »yxf az:k. 2) A#a*?-^@ti.az:m*#B©7ya-©c E, @R*E#±T©#$##%hT# EfaCk. Fig. 1 General View of the RTV-SHIP C%a#aA#C#m# *»a», $&E, m*-m@a;-#k»-3Tmmit*# AKWR-r#a & 0 k%8#LTw&. (1) S31$:HtbS 4-ig©mm%©mmtm6KRT ’iUi, 7>7fiEioHSnrf (s) n¥-y 7-f/^-T*m±©^^m#mKK%LTv^. 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K-A *VX?X5- V Fig. 5 Outline Drawing of the Vehicle afiMSS^oiKy b (RTV-SHIP) 237 t#@#PPI&^Tt-y-KyD7y^ #$±5= (6) CPU EE #&f-7®mmiR», try^-a @^x©t — 7 ®^S$.tirS3fitEtf$|J'C$i 5 = 3.3 *-<1/ —>a >©^>$ 3.3.1 ftW« (1) a#©am #:adly Fi/XTA-^%*#&B±K:%AL0fm®m KKRIKf 3. (2) f-7AA $$tl*©7>'7[WK£ffiotiBtiSb, 6B h'JA : ±9 0 5@m*at®%&®7 >7B#y-y * CPU EE ^ A®-75 = Controllable Axes of the Vehicle 3.3.2 #:ndl'y FyxTAhTFIE®j:3K:2~3:&&l*akU Ttf—y a y%:fT^o ya^y#75mmT (1) &3*g# iff ow@#mt-*-fkLTm*ikgWTK:em?T^ e,iKT$T, fmagfr^XA-Xicfr^^A© 6. maiaiEKRH.Skgf, 3*eAl.5kgf T$6. K#^©XyX7ii, BI^Bao&OTlEW&Kl.S kgf, mg#RlkgfT$5. »®T'7y4"yh3^'txrHK3gA^@<*f^*, (2) b"—7;k^^i/—7 tf—7;y^-/*-®#*# gKc^ywt##®#9|»f&e-7/k gK^^-C^R#aLV7A^*Ki-%Ckt#%L, *6# ^^i/-7E^t, y-y^-tv-7 mgm^ioo m, ?&±-& a@^5oo m®e#t 600m t LTV)50 ##LT&aw. (3) 3.3.3 CiL5©EEti:, nzKy h*#;%fF*iiS-if 5/i6®S* E#T*,5. a#k, f-7fmmu7t#, ey^T-y^amu-nE (4) ^»#e*ku-c@mi-5t®k 2«Rtmsu-c^5. $%cpu#m f@Bmay-%/My-xk&&T&%3#, #&e* a#KMLTas%»%gi-#*T, f©#Tey^-y-y 1-fUf Axa-y^BOtz^ —a?TS % j: ^ E»^T kCPUf-7®3tf-^%D, ffL&±y-7kUT@ 5 „ (s) y-y-wmm ±13 e -7 V vx «, iiSBflifffl'J ti 17 ■V it &k ft 5 h % © ©x \ 7°n7T^9 —0#%#gT$3. tf—A©X4fy>l± 4-m, @ % Z-RA *-*A±T, 0.9°/1.8°/3.6° Xy y y©wffl^T 360"AMEt»f:c-C ^ff$fL,**#*r®E*ta@ucPUK:ai*i-6. * 238 Baaa&gansas mm# 4. )(OcBR&CPUEA^T5^m»l:K:ML-C, iO## 4.1 anttflBKB . (*) eomm*# (LxBxD=55mX (2) ±gEB#H9KK 8mX3m) K:j3l,)T, B9#@gk Fig.9aya7y^9-0&*#T*,%. Z:0R&l±* #©f@»#©±KX/ V::H / (VefVir^l —-X ' \ T: : :^::: ■; e~»n,aa:; * ' A ' T : : "! :::. : :,:: Fig. 7 Measured Data of the Tank Walls 111 Tin mm TTT iii i i i 11 n i i i ; ii i iii t*— ^ /utiS Fig. 8 Analyzed Data of the Vehicle Position Fig. 9 Measured Data of Large Deflections #^02 (066D a m0#Ylim&lW:B0iK#im#*7-@i-7 4^7 '-7 <^0#9#l/?a '2IW2(411##%$#$ '91^ w x a? # # >7 ? <¥ "2$!# Ta#2^. #*3 9if 217 $*i:^a0i@*MHa%^0#* #@*8 'f(1^^2)%B@0Yly/3* °2gi@#>(4 '10 V ^ % 21 (? 9 ^ #^-@-W%2)l $ B# % q>#p0#g$»a*^c(:Y%#7'<70#[mi (6) ommoT ;2##^3#w*8Ra:3m8#& 24-*% %#mMm0#mii mg^% '?22g %mm0*OTamgms0#%M#w: 'i%g^Yi l-B:+^m#3(K0gmm#@^0^#g %/$5#^(4B3 4 6#a,W#$###13&ia0@*^4^>/ '#%sm 'OTztmmmmww# (z) °^vgmk??2 2_f.ar#-EH-^^@% m m %@^m-i«yi%##0W'f/<^ 'ogi#Jk$y? "2 $1^% 0Mi= ? 2 2%? 2 2 4- Y 3- 4 °2(4iTfg@6?^*0#mi##%^mm(i%###$# 'mmg# '3?90^»0#9% s '%(?? 2^»*i#a^m(4i#0^wam;?#30 '«2(qmmm*0YiY/;:$: (E) 6EZ %Bfl0 (dIHS-AXd) 4 ^iFcuMZBS### 241 2-12 A Study on Unified Automatic Control System for Longitudinal Motion of Jetfoil Based on Optimal Servo Theory by Hiroyuki Yamato*, Member Takeo Koyama*, Member Akira Fushimi*, Member Sang-hyun Kim**, Member Summary Current Jetfoil control has been made by platform and contour mode selection and by manual input of fore-foil depth according to sea conditions by human operator, which cause overload and may be difficult for operators. This requires the further automation in the control system. In this paper, authors propose unified automatic control system (ACS) which is based on optimal servo theory and eliminates human operation in ACS. The reference input signal in the servo system was modified to the sea conditions to achieve unification of platforming and contouring. First, optimal servo system (OSS) was designed to keep the fore and aft foil depths in waves to find that the sole OSS was still sluggish. Therefore, authors added proportional and differential element in inner feedback loop in addition to the modification of reference input. The MOSS+MRI, which represents modified optimal servo system (MOSS) and modification of reference input (MRI), was confirmed the good control performance in the wide range of waves through simulation. may be impossible. 1. Introduction In this paper, authors propose the unified automatic Jetfoil is essentially configured to provide good ride control system for eliminating human operation in ACS quality and speed performance since it is free from based on the optimal servo theory. In the optimal servo water, and the control system is efficient to stable or to system, the reference input is used as the signal to augment stability of the vehicle* 1,~* 4'. follow and this may suitably be deformed to platform The present automatic control system (ACS) of Jet ing and contouring according to the sea conditions. foil is designed by optimal feedback gain theory which First, optimal servo system (OSS) to keep fore and use inertial and ultrasonic sensor signals. And this aft foil depth in waves is designed. And the modified includes platform and contour mode selection and optimal servo system (MOSS) which has proportional manual input of fore-foil depth by human operator. and differential element in inner feedback loop is The Jetfoil copes with the wide range of waves by designed to improve control performance. And also the human operation in ACS. modification of reference input (MRI) is performed to The platforming is the normal foilborne mode of Jetfoil achieve unification of platforming and contouring. and regulates heave and pitch motion. This gives the Finally the MOSS + MRI, which consists of MOSS and best ride quality in wave heights up to strut length. MRI, is proposed as the unified ACS of Jetfoil. But among long and high swells, the Jetfoil needs 2. Jetfoil contouring the wave. In this case, contour mode is selected in ACS to avoid cresting and broaching. This 2.1 Configuration* 3''* 41 contour mode is keeping fore foil depth in waves'1''14'. The configuration of Jetfoil which becomes simula However, an suitable mode selection and manual tion model in this paper is shown in Fig. 2-1. input of foil depth may be difficult and overload for The principal dimension of Jetfoil is shown in Table operators. Especially very poor visibility or night, this 2-1. But the detailed fore and aft foil and strut type are not open to public, the type of foil and strut is deter mined by authors in this paper. And flaps were * Dept, of Naval Architecture and Ocean Engi equipped in fore and aft foil to control the motion. neering, University of Tokyo. 2. 2 Coordinate system and equation of motion ** Graduate Student, Dept, of Naval Architecture and Ocean Engineering, University of Tokyo. The coordinate system is shown in Fig. 2-2. Authors origin at the center of gravity and positive direction of Received 10th Jan. 1997 translation and rotation are in the direction of the Read at the Spring meeting 15th May 1997 arrows in Fig. 2-2. 242 Journal of The Society of Naval Architects of Japan, Vol. 181 Fig. 2-3 The flap deflection Wave Automatic Control System Selection Fig. 2-1 Three view of the Jetfoil • Platform Mode Control |----- • Contour Mode Control Control Input Table 2-1 The principal dimension of Jetfoil Sensor Signal Length over all Loa 27.4 m Plant( Jetfoil ) Model Breadth B 9.5 m Wave drift (hull borne) d 5.2 m Fig. 3-1 The concept of current Jetfoil controller drift(foil borne) d 1.7 m Displacement Disp. 115 Lt Mrotal Force __ Mlirl Heave Force i M,surge Force 6 = (2.3) Depth (hull borne) 12.8 m Ivy Depth (foil borne) 15.5 m where z '■ have acceleration Ship Speed ^ship.speed 43 kn z '■ heave velocity Fore/Aft Foil Type NACA631-412 z : heave displacement Fore/Aft Foil Type NACA66-006 6 : pitch angle acceleration 8 : pitch angle velocity 8 : pitch angle X : total surge force Z : total heave force Pitch Angle m ." mass of hull Mrotai Force ’■ total force moment around y axis lyy '■ moment of inertia around y axis 2.3 Flap-controIt5H6) The flap-control is used to control Jetfoil motion in this paper. The configuration of flap-control is shown in Fig. 2-3. In case of flap-control, lift is shown by Fig. 2-2 The coordinate system Foiluft =-^P‘V2‘^Cl + 8 j• Sfou (2.4) where S: flap deflection angle The longitudinal equation of motion is given by 1) Surge motion 3. Automatic control system of Jetfoil 3.1 Current Jetfoil controller 111-'21 Detailed design method of current Jetfoil controller is Hulhc Foil * = -z8 + L+ not clearly states in references. The concept of Jetfoil controller is shown in Fig. 3-1. , Strut* Hullth (2.1) In this paper, platform mode and contour mode con trol system of Jetfoil are designed by tuning weight 2) Heave motion function in optimal regulator. And we define Zm (relative distance bow and wave), dZ (heave velocity) , Ftullweie Foilb-, 8 (pitch angle) , d8 (pitch angle velocity) as state = £9 + L+ m m variable of Jetfoil. The configuration of ACS of Jetfoil Stmtbuoy | Foiluft by optimal regulator is shown in Fig. 3-2. + ( . ) m 2 2 This optimal regulator controller was used as a base 3) Pitch motion controller to be referenced as present one. The primary A Study on Unified Automatic Control System for Longitudinal Motion of Jetfoil Based on Optimal Servo Theory 243 Automatic Control System Modification of Optimal Servo System Reference Input Desired Zrb Error signal Calculation of Error signal Plant( Jetfoil ) Model Desired Fore/Aft Fig. 3-2 ACS of Jetfoil by optimal regulator Foil Depth Fig. 3-3 The concept of proposed ACS of Jetfoil problem of current Jetfoil controller may be considered that the contour mode does not work so well, since using only fore foil depth. In particular, it becomes serious in head sea. 3. 2 Proposed ACS of Jetfoil in this paper In this paper, authors propose ACS of Jetfoil which is based on optimal servo theory for keeping fore and aft A--[i ?] M”J we % Mil foil depths in waves. The features of this ACS may be (4.4) considered as follows : And in infinite time, x{t) and u(t) become xs, us which 1) The reference input in optimal servo system can is given as be modified to the sea conditions. 2) The unified ACS of Jetfoil which has no platform From the previous results, we can define dx(t), Su(t) as and contour mode selection and manual input of fore dx(t)~x(t) — xs depth may be realized by using reference input. du(t) — u(t) — us (4.6) 3) Improvement of performance of contouring to Let wave profile, since using fore and aft foil depths in ACS. &c.(f)=[&r(fy 5u(<)T]T- And the concept of proposed ACS of Jetfoil in this Equation (4.3) can be written paper is shown in Fig. 3-3. 8Xe(t) = AeSxe(t) + Bev(t) + Ded(t) . . 4. Optimal Servo Theory (7)~ai) y(t)—r=CeSxe(t) Consequently, we can suggest that the control prob Optimal servo theory is one of the method to design lem of y{t)~^r as replace the control problem of linear multi-input-output optimal tracking system. It $xe(t)—>Q as f-*o° which may be achieved by using is common to associate an integral compensator with optimal regulator theory. Namely, if the performance the given plant and to apply a stabilizing control law to index may be expressed as the resulting augmented system. And the optimal regu lator problem is extensively used for the stabilization. Je=fa (||&re(f)|||.+]|r(f)||*«)aif (4.8) In this chapter, the abstract of optimal servo theory where and modified optimal servo theory is explained. Qe(n+ m x n + m). = n + m X n + m) > 0 4.1 Mathematical formulation Re(mXm)=Re{mXm)> 0 The linearized equation of motion written in state The control problem of y(t)^>r can be replaced the equation form are optimal regulator problem for minimizing equation x(t)=Ax(t) + Bu(t) + d(t) : A(nXn), B(nXm) (4.8). y{t)=Cx{t) : C{pxn) The solution to equation (4.8) is given as (4.1) v(t) = ~Fe8x e(t) (4.9) where, ,r(0) = -ro, d(t) is disturbance, m=p and plant is where controllable and observable Fe = Rl1BePe (4.10) Here, we consider servo system that output y(t) tracks Pe=PI>Q satisfies Riccati equation reference input r(=#=0) in infinite time. In this case, Substituting feedback form of state variable x(t) and control input of servo system becomes constant value ye(t)=i—y(t), equation (4.9) is given as for infinite time and also satisfies limii(<)=0. M) = -[f K^Jc^^-Fxifi + Kir-yit)) If we can use v(t)=u(t) (4.2) (4.11) as new control input, the equation (4.1) is given as From integration of equation (4.11), we can get Xe(t) = AeXe(t) + Bev(t) + Ded(t) , . control input as g(f)=C.a.(f) ^ u(t) = — Fx(t) + K£ ye{t)dt + Fx(0) (4.12) where 244 Journal of The Society of Naval Architects of Japan. Vol. 181 where initial condition is .r(0) = 0 x(t) = Ax(t) + Bu(t) : A(4X4), £(4x2) . , This provides the control law. The block diagram of y{t)=Cx{t) '. C(2X4) optimal servo system (OSS) is shown in Fig. 4-1. z 0 0 1 0 z 4. 2 Modified optimal servo system Q 0 0 0 1 Q In simulation, OSS was found sluggish. To improve z -0.80 -94.65 -4.74 15.94 z performance of OSS, authors tried tuning of weight 0 -0.001 -0.39 -0.019 -2.20 e function in OSS. But this needs excessive deploy of flaps. 0 0 Therefore, it is not theoretical, authors attempt to add o o ra/i + proportional and derivative element in inner feedback -7.141 -20.567 LdJ loop of optimal servo system to improve control perfor 0.637 -0.767 mance. This modified optimal servo system (MOSS) is shown in Fig. 4-2. 2 [Z/Ziri -13 0 01 8 (5.2) 5. Design of Unified Automatic Control System Izafi Ll 5.8 0 0J i 5.1 State equation 6 The longitudinal equations of motion are where 8/ : fore-foil flap deflection angle Sa : aft-foil flap deflection angle Disturbance Zff : heave motion in fore-foil Servo Compensator Stabilization Compensator Zaf : heave motion in aft-foil Reference Input lYe^« 5. 2 Reference input x=Ax+Bu+d The reference input is a error signal between desired foil depths and actual foil depths in waves. This refer ence input is equal to the necessary heave displacement in position of fore and aft foil for keeping desired foil depths. And this reference input is deformed to cope Fig. 4-1 Optimal servo system (OSS) with sea state. The reference input in waves is shown in Fig. 5-1. Disturbance Servo Compensator Stabilization Compensator Reference Input lYe^tV x = Ax+Bu+d- Fig. 4-2 Modified optimal servo system (MOSS) Fig. 5-1 The reference input in waves Disturbance Servo Compensator Stabi lization Compensator Modifying Error signal Desired Error signal | 1 Reference I Input foil depth x=Ax+Bu Foil depth in wave Zff, Zaf l di, 9, de Observer Distance from jerfoil to wave Fig. 5-2 MOSS + MRI A Study on Unified Automatic Control System for Longitudinal Motion of Jetfoil Based on Optimal Servo Theory 245 5.3 MOSS+MRI 6. Simulation The MOSS + MRI, which consists of MOSS and modification of reference input (MRI), is designed to 6.1 Simulation tool improve control performance and to achieve unification In simulation, we used MATRIXx design tool which of platforming and contouring. The MOSS + MRI is had been developed by Integrated System Incorporated shown in Fig. 5-2. Authors propose the MOSS + MRI as (ISI)(12). The simulation model of Jetfoil which was unified automatic control system (ACS) of Jetfoil in constructed by MATRIXx is shown in Fig. 61. this paper. 6.2 ACS And also, state variables, which are estimated by The ACS which is shown in Table 6-1 was simulated observer is used, because of all state variables of plant in this paper. can not be observable in general. In simulation, the control-limit of ACS is defined as 5.4 Modification of reference input broaching and cresting. In ACS of current Jetfoil, fundamentally, the contour And also, authors use dominant wave component of mode is selected for long and high wave height, and the irregular waves to estimate control performance of platform mode is selected for short and low wave ACS. Namely, the criterion to estimate ACS becomes height <1H4). whether ACS is effective or not in dominant wave of Authors refer to these operation in modification of irregular waves. The Pierson-Moskowitz (PM) spec reference input. In this paper, authors use gain and low trum of irregular waves with each significant wave -pass filter in modification of reference input. The aim height is shown in Fig. 6-2. of using gain is to reduce reference input for platform 6. 3 Simulation results of ACS ing. The example of gain is shown in Fig. 5-3. In case In simulation, Jetfoil speed is 20 m/s. of low wave height, the gain becomes small and reduces 1) Platform and contour mode control reference input to strengthen platforming. The control-limit of platform and contour mode The low-pass filter is used to cut high frequency compo control in regular waves and dominant wave of irregu nent from reference input for platforming. The cut-off lar waves is shown in Fig. 6-3. frequency of low-pass filter is determined by dynamic Fig. 6-3 shows that platform and Contour mode control characteristics of plant and characteristics of encounter is satisfied by platform and contour mode selection in waves. In case of cut-off frequency 0.5 rad/sec, 1.0 rad/ following sea, but it is not satisfied by platform and sec, 1.5 rad/sec, the modification of reference input by low-pass filter is shown in Fig.5-3. Table 6-1 Automatic control system of Jetfoil ACS of Jetfoil System Purpose Contouring Keeping constant heave height Platforming I Platform Optimal regulator Contour Optimal regulator Keeping foil depth in wave Platforming 0.5 1.0 1.5 Wave Height OSS Optimal servo Keeping foil depth in wave Cut-off frequency of low-; To improve control performance MOSS Modified optimal servo against OSS Fig. 5-3 The concept of modification of reference Modified optimal servo and To unification of platforming and MOSS+MRI input Modification of Reference Input contouring in MOSS JETFOIL 3A7A rrrfESD Continuous WAVE PROFILE iiJ WAVE DATA ill Continuous Continuous Fig. 6-1 Simulation model 246 Journal of The Society of Naval Architects of Japan, Vol. 181 Encounter Ffequency(rad/sec) Fig. 6-4 Control-limit of OSS and MOSS Heave Acc. in FP(Max. & Min.) in Wave Height 1.0m Frequency (radfeec) Fig. 6-2 Pierson-Moskowitz (PM) spectrum • - Dominant Wave(Follow Encounter Frequency (rad/sec) Fig. 6-5 Heave acceleration Encounter Frequency(rad/sec) Fig. 6-3 Control-limit of platform and contour mode control contour mode selection in head sea. This result Encounter Frequency!rad/sec) confirms necessity of control system which is improved performance of keeping fore and aft foil depths in Fig. 6-6 Control-limit of MOSS + MRI and MOSS waves. 2) OSS and MOSS The control-limit of OSS and MOSS is shown in Fig. ing is strengthened by modification of reference input. 6~4. And the control-limit of MOSS + MRI and MOSS is Fig. 6-4 shows that OSS and MOSS are more effective shown in Fig. 6-6. than platform and contour mode control in the wide Fig. 6-6 shows that the control-limit of MOSS + MRI range of waves. It is because OSS and MOSS may be becomes narrow against MOSS by modification of refer improved performance of keeping foil depth in waves ence input. And MOSS + MRI is more effective than by using fore and aft foil depths in ACS. platform and contour mode control in wide range of And also, Fig. 6-4 shows that control-limit of MOSS is waves, even if it has no platform and contour mode wider than OSS and is satisfied with in following and selection in ACS. head sea. These result confirms validity of MOSS. But MOSS+MRI is not sufficient in head sea. This 3) MOSS + MRI result confirms the necessity of more effective The heave acceleration is investigated in terms of modification of reference input, in terms of ride quality ride quality. The max-min heave acceleration of plat and range of control-limit. form mode control, MOSS and MOSS + MRI is shown in 4) Simulation result Fig. 6-5. Fig. 6-7 shows the simulation result of MOSS in Fig. 6-5 shows that ride quality of MOSS+MRI is much regular wave (wave height 1 m, encounter frequency 5. better than MOSS. This result confirms that platform 4 rad/sec). And Fig. 6-8 shows the simulation result of A Study on Unified Automatic Control System for Longitudinal Motion of Jetfoil Based on Optimal Servo Theory 947 fled optimal Se.^-e Sy - n n fri n n n n i 1 n n n n i n n n n inn jjjjj Fig. 6-7 Simulation result of MOSS in regular wave Fig. 6-8 Simulation result of MOSS in regular wave MOSS in regular wave (wave height 2.5 m, encounter 4) Weist, W. R. and Mitchell, W. I.: “The Auto frequency 1.0 rad/sec). These result shows that MOSS matic Control System for Boeing Commercial is achieved unification of platforming and contouring, “JETFOIL””, IEEE, NAECON, pp. 366-375(1976) 5) Ira, H. Abbott and Albert, E. Von Doenhoff : even if it has no platform and contour mode selection in THEORY OF WING SECTION, Dover Publica ACS. tion, New York 7. Conclusions 6) John, D. Anderson : Fundamentals of Aer odynamics, McGRAW-HILL In this paper, authors develop unified ACS of Jetfoil 7) Pak, P. S. and Suzuki, Y. and Fujii, K.: ’’Synthe to eliminate human operation in ACS. And the validity sis of Multivariable Linear Optimal Servo-Sys of the proposed system was confirmed by simulation. tem Incorporating Integral-Type Controllers” , Transactions of the Society of Instrument and 1) The unified ACS was effective in the wide range Control Engineers, Vol. 10, No. 1, pp. 1-5 (1974), of waves without mode selection in ACS. (in Japanese) 2) The design method of reference input in optimal 8) Takeda, T. and Kitamori, T.: “A Design Method servo system was proposed. The unified ACS could of Linear Multi-Input-Output Tracking Sys provide better ride quality, however, worse control- tems”, Transactions of the Society of Instrument limit. and Control Engineers, Vol. 14, No. 4, pp. 13-18 In this regard, effective modification on reference (1978), (in Japanese) 9) Fujii, T. and Mizushima, N.: “A New Approach input or tuning is necessary. And, in general, heave to LQ Design —Application to the Design of displacement and foil depth measurement system Optimal Servo Systems —”, Transactions of the becomes essential concern for the actual application of Society of Instrument and Control Engineers, this system. Vol. 23, No.2, pp. 129-135 (1987), (in Japanese) 10) keda, M. and Suda, N.: “Synthesis of Optimal References Servosystems ”, Transactions of the Society of 1) Saito, Y. and Kuroi, A.: “Active Control System Instrument and Control Engineers, Vol. 24, No. 1, of Hydrofoils ”, Prediction of Seakeeping Qual pp. 40-46 (1988), (in Japanese) ities of High-Speed Craft, The 6th Symposium of 11) Fujii, T. and Simomura, T.: “Generalization of The Society of Naval Architects of Japan, pp. 74 ILQ Method for the Design of Optimal Servo -110 (1989), (in Japanese) Systems ”, Transactions of the Institute of Sys 2) Saito, Y. and Ikebuchi, T.: “Fully Submerged tems, Control and Information Engineers, Vol. 24, Hydrofoil Craft”, Prediction of Seakeeping Qual No. 1, pp. 40-46 (1988), (in Japanese) ities of High-Speed Craft, The 7th Marine 12) Integrated System Incorporated : MATRIXx Dynamics Symposium of The Society of Naval V 4.0, ISI (1994) Architects of Japan, pp. 107-141 (1990), (in 13) Kim, S. H.: “A Study on Longitudinal Motion Japanese) Control System of Jetfoil to cope with Sea- 3) Imamura, H. and Saito, Y. et al.: “Automatic state”, A master’s degree thesis (in Japanese), Control System for Jetfoil ”, KAWASAKI TECH Dept, of Naval Architecture and Ocean Engineer NICAL REVIEW, Vol. 107, pp. 1-8 (1991), (in ing, University of Tokyo. (1996) Japanese) 249 2-13 Ejl IF * * S* E* g W # Bj* i» f Hi # fi* Basic Studies on Accuracy Management System Based on Estimating of Weld Deformations by Toshiharu Nomoto, Member Shoji Takechi, Member Kazuhiro Aoyama, Member Summary Accuracy management of products is one of the most important issues in industries. There are two significant ways for accuracy management. One way is accuracy control by measuring products in assembling stage. The other way is “accuracy planning ” that is accuracy management in production design stage. Authors have already reported about the former, and the latter is discussed in this paper. Authors have been engaged in development of SODAS for shipbuilding CIM. Therefore authors developed accuracy planning system considered weld deformation based on SODAS. For accuracy planning, it is important to estimate deformation. Authors practice modeling of weld deformation of products and make it possible to estimate easily welding deformation. By using them, the accuracy management system by estimating of weld deformations is implemented. $ it i> © g ftf t'• MW t S' & tz ft c h, 1. * W 1.1 *#%<©## on%#a?K, ShWit FBfff©Dn jf (quality of design) J me##, k F§S® ©nnK (quality of conformance) J CASH Sit52)c F%^#J ? 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C©^B#ti, #^©A^mt:j#fS, k ti ti—R L T 1^6 o (2) *l5tiii* Fig. 12 Example of Weld Deformation Estimation Fig. 13 Weld Deformation Estimation 259 Fig. 14 Example of Estimation due to Inverse Method Fig. 15 Weld Deformation Estimation due to Inverse Method -c, soDAs $ e,K:, FEM i±iooo#c@:AL-c^$fT/-cv)&o FEMgf-#fO6(DE3^@a0fLa-kt ;:©#i©m#mma>6, ^*-mAm©*ari±?%L ©t»©FEMg|-#(±, #$f 0.4mm, ISfitJ^I^K 0.5mm@S©Ett*L em© e@ar# 5 ma#6fi7k. C©mifL*«. ##B©A)RA#K:Mi-& D. ^L^k-&©#m$rl|g| ZfUi#3g#»#.l#ias fTc%±E0#lTki: 1 ^#©^k»c-n,^AAT*»3k#^.6fi&o 5.2.2 m^mi©^#?m©mfm Fig. 14( 1)j: 3 # f V 7©ffTa© f ©%&%:, 1 f A@IAO% C2 0MTK, ^K^*%mg#g©m K, ^B©#akit'<6kmfmtta#<, #4©##© &©%%#%&$*% c:k eft. n©^|6]©gE B?-aof!lri±, 20 mm Tt!), #@© 1.0X10'cal/cm k—#T& % klS^f %. 6. tk W &. C 0/J\7o y 7 0&&mma, SODAS ©#@iK&©a 6.1 ttsb @e%a^T%KS*cTV)6 k75o .COi/cry ?(0&a JlJfk ii^:< ©iMK*4 7n y^&SIffS Fig. 14 ia±. »K, ^ie©mmE^Ac-cet,^6##©mm^m@R 0C5to Fig. 14(2 )~( 6)0— H©0-Ci4:, *±0®A K^m#KL%as?TA#&fT$;:k&avLTi,)5. ^© &**L7k. I^TK, ^#3t©*g#tgRLT^fo mf¥ K % -3 T, ms [Sj © ^i^T® & fr 5 «? Sr ^ L tz II ifl (i)*aea#mt#«&m',>T3tg7&%&K:, m Fig. 15 Tt 6. ArTgL, Fig. 15l:j3V^-C#*iF^XH2.0 mT&D,FEM*#K:j3^%*7^$#ta:, 7>7^*©- k^gamcLt. e©^*Kmaism^ie$-, gmc 260 mm-# 6wa#m#®#gea@*T&a#m=#'@L, f OT&5<:ka!#%fWf, ZfL&0%B6#gL^5ig L7k. mm (2) *@#mr^, $ z: ka*mg (EE##: T*>o, 06555303) 0%m^SkM:W»Z:ktfj'KL, E#KL* S f % z: k aims? $ 6 z: k L fo tc o S # £ E (3) ±^(2)@a:AK:«, 1) : Ififfiftiii/XTA©#*-, 5Z2ka%BT$9, (1995) 6 z: ka*S 2) a##m (1984) gT&&Z:k&HmK:L2:. 3) s* • Wi-U • : mm-UteisvzmmtDrn&tg (4) tf- 6,, #178# (1995), pp. 725-737 4) #immzfmmi#*sm, B*m«^E*%fiF (1975 ) %3RLa:o (5) ±S0#AK*cfV)T, SODAS &/<-:% C&B? R4 CAE ^X f A 0##-)#% CIM 0 7k * 0R A&*#La:. ehsmM8a#%#y%TA0##G(to9)- g 6.2 #&<7Dl!E *)S*8###%# 178 # (1995), pp. 749-762 6) a#-##-##5 (i JI !#### 32 ## 2 # (1992), pp. 83-91 7) ±b • fam • e • s* • blu : nmmmsL EM B lij fn SB** Development of Computer Aided Design and Manufacturing System for Advanced Composite Marine Structures (4 th Report : Investigation of Computer Aided Manufacturing System in Fitability) by Takeshi Takatoya, Member Isao Kimpara, Member Kazuro Kageyama, Member Summary The present paper aims at developing a computer aided design and manufacturing system for advanced composite marine structures, that is, shell structures in which stiffness and strength for out- plane pressure and light-weight are achieved by making efficient use of advanced composite materials. In the previous reports, some specialized prototypes of CAD/CAE system for laminated materials were developed by means of object oriented language. It showed that the developed system is effective in designing and analyzing laminated panels. In this report, specifications of the system are discussed in the point of developing an effective system. Based on the specifications, two points are important in the systems aided for manufacturing, one point is making tool mold with easiness and accuracy, and the other is layup simulation on a curved surface. The system aided for making tool mold was developed by means of generating surfaces which are apart thickness from the base surface. By using a numerical cutting machine with cutting paths on the offset surfaces, it is available to obtain an accurate male mold, which is achieved smooth outer surfaces. In order to simulate of prepreg layup process on a curved surface, three deformation mechanisms of laminated materials are investigated in the point of fitability, plastic deformation, shear deformation, and apparently deformation induced to out-plane deformation. According to observations, unidir ectional fiber yarn is discrepancy from the curved surfaces without some points, and it induced that fiber wrinkles in a vacuuming process. Then a criterion of fitability is proposed by means of calculating apparently in-plane deformations. Some examples are demonstrated, and it shows that the developed system is effective in manufactur ing simulations of laminated panels. 1. (± D tb (C (Advanced Composite Materials: ACM) li, —S', S£ff"sHSfFIIi'C, If gE&ffiSfcWU SEEK Ensa ¥s5c 9 4? i n io b 262 mm# Requirements Designed Parameters Evaluated Parameters Boundary Conditions Developed Systems CAD Shape Design Laminate Design Product Design Lamina Laminated Structure X \ r...... CAE ...... : ...... CAM ...... ; Mechanical Analysis i Mold Manufacturing i Thermal Analysis Weight Estimation fiber direction ! Optimization Laminated Simulation Layup Plan Automatic Layup Fig. 2 Stratum of laminated composite structures Fig. 1 Flowchart of laminate design and process design for composite structures Fig. 2 = k K&gu, <- yff 4 yf-K ACM &3UEL, ACM %K#%rt5Ck&aRBL*:. CAD/CAE/CAM -T&R9M9 ;<-?#, m*k%Bg0m»-&k-&0m(, i/3 yeofUffl-efid 1 y9 —7z.~7s\,zMWfih% z. t £f! MLA:.i:OA:*,mc*"TH,Fig.l a:%m0^kmxH-3#BAit&. tz-r, ##*e# f iloj 0 K #-3* 11T ^ fit £ eSH-fc C*SL fco ## A: cA. aMMBetEjsuT, A!^K50#AOBK&%gf50-r, C k gL*:o TH, # h K i LTgm^kA#*^ Fig. 4 Graphical User Interface of the developed CAD systems Up Down Right Left -1 Fig. 5 Graphical User Interface of the developed Fig. 3 Definition of local coordinate, which is postprocessor system subjected on mold surface ^a^kT, %m*7KmR»# KEXOlSB^SWiT —£ k Fig. 5 ■to u^u, 3. «s^<7)EfFXEtcmtzmu&mfa u & c k K » Mi— /\9A;$o, -#K»##i±muwa-gT$»A*, ##© k A%% » V ^ k V ^ A^ #)(. ?, A#A%$6. C: kTjhf^LA. 6%@&Fig.6K#f. &6A^U*#{|g^mmK#S$t #T*#@###%A:##L, #U#©S*r©J#k#Rg -c$&gE'fki#[F0^#gAT$&y; yi/y©%#ftfz» XK-#i%R#kLT©W-ykA:m#*#U*3fL n, ^-x#A^/x#©gg#m©±KKiBi» normal vector base surface normal vector normal vector Fig. 6 Manufacturing sequence of advanced composite structures base surface 77777777777Z- tool surface *-Y 7 v-T’ipCAftiDfl • 5, h V 5 7777777777 tool surface k@#HrK:, a) female mold b) male mold #$TM3A^fg#LTtX. A61C, n-/P Fig. 7 Relations of laminates and base surface on male and female mold @@0 %fR^yXTAKB$3tt&:kLTi% FKe$ft5Ck^<, m##Kj:6#A3e &%, y;y 4.1 l&JfmoMfFt-OI'T vy*#@K:)6k»v^if0mAT, 2%K^-*ILTM6 tiiz'o, |gs$ttfc^gs-'t^'r©{4ttT*®T*^ofc y f&7kA, ##TO%^v^KEA%]>(.g,iL3o C0##T i±, kK i SSlitSeJEHk » 3 A*y"C& < , ##tk(±#»5#%#imLT c k**m$ ^-cv^ C k K# 9 - ma@T® 5= i#ak»& k k*%&3. ipmo^xf Ae#jmL-c, mt#**m**±-cmbL (6^n±O.K. Bergsma J. S. Tsai 6" ##88 k#t#k ###&?%& krR#tKgmW#m0*#^Rf#k»^T^6. Kff -3TW&. B$Tkt, mK^^AimRoee&fz^^Tv^ ^*>/AfAkL-CH, $6K, ^#mkLT/X# •So tti, Bergsma 3%B%W%L%mR#03m - m%@TO^Kkm-#® (DU^X’hi, ffiMCJ&fc^CV^k'oafit*, 2&C#@ILT ftR» < » $ ft? W &. 4. Sa'>XTAOTf±i kW6. #*Tt0i(.6^iMA)V)3gMU, m##Al0m afmtkl±#»6mS-m%tRc»c:kK:Kif-3< ck 265 Area A Lamina Surface allowance length expanded ratio Fig. 9 Schematic of area calculation of each ply Layup Plan Cut Plan j c kr, *&ma©#8*&fT»5 = k 5.2 ^mmtmmomm *f, Fig. 8 Schematic of layup simulation in the developed sHknftf, °smwr"h%z. ko^s+^fHi, a±© systems 7^T0jaKj3t)T^7^#^^nT$3 i: k^%6jl il^VMDEIflS/ 5 a u — 'y 3 jt£-?tz*> IT, k*©ti" L^L, mm $£M 5.i mm, mmt$*6mec-3i'% J.S.Tsai 6H, *m#tmBE*m7& yotXKdWT, jXT©aA©#^&K#&ZkT#@ #KT»WT#M7%.Fig.9 #$r%gmLTw%". Kmmu, c#*k#*©m*i±#rm»L»w c#*k#*0%mKey^3-f > 5T$& $6C, #@#*39 o^otf >^ad > ©%aT&6##©B@*A:K3 7©#a^-#i(.6^TV^ 0##K^AE^B#E@# LT % $©r, 266 181 BTfbk&50 Fig. 10 KSrT<£ -5 c, 6@±©iE*kjg*© P(m+l,n+l) SS.^TS) 5 S P(m, n), P(m + 1, «), P(m, n + 1) A%t &k, *#f5AR±©RIKa#t/*|g»L»t)©T, #*)KAP(M+l, w+l)A%&&i:kK:»3. o*9, @ warp hT< ttfOKikk^&Cka^Teto —#*iK:, %*k#*©%g©ti:* (#9©#B) -^, Fig. 10 Warp and weft yarn paths on a curved surface #*»#*&f&Xt'9>F©*3K:.):0, AW^© »9*f"Xh9 >F©±gKJ:9, k »»T i: k a:mn&5. 5.3.3 #©*©## U#»3s j: tf^A,*r^B©#%#*i/J\$ v^K 6 Mk (,f, F*HKiti%kkasrS5o EtiBAUttcth^T, Bfl-U Fig. 11 l/^k k*SHJ?.^C&ofco #WTt^9, L.kA3A&»k©m^t-^BKj:6t0k» c: k %%#©#e, ea so ma-©EK«* &^|q]K:iK)3%©»a^^©#3Ba:AC6 ^ kai^gT*, So 5.4 —Jifatt<7)m§ IZ-Ol'Z K*k@*^#5A:»K:#f^iqiK:#MTLTw^#W a) Front view a, — —;5rWE HI'#- 5 ftB-\©;|XJI &M&i~ 5 ^ ka%Bk»&a*, —^lAl#K:Mi-3K9^©WSl± k A/ If (, =h,%i,)«, ec:T#:#TK, — f 5fcib©^ifS-fT»o/2o — &©^©±&3estm#:eBK: a amm©**)#©##; kS»A:. (,, ##**—f©f@&*Rg'fk©#g^o»^'rv) %#&?&%©?, m=#T#A,BrU'f*d:, *##K: ^rA,»rU'f^K:Z&^B6imm ^c#e##Ta&&as, m%#kmB©#^ia#»9, tf L 5K©K#K)ai^ k C k a%)R% o 5.5 ^y'fT'jTtm^mcomm b) Side view *#Ti±, —^|6lti"©ffi@^x©E)ltSBFS©<»a:>tl'©# !Sai±»3gaTt3kL, ^*-f7^TVTkLTmv^ Fig. 11 Discrepancy of paper and sphere surface ©tan- • ims^xtaob^ 267 Fiber Direction ply area base line 3<-y ,-' Fig. 12 Unidirectional yarn paths on a curved surface T, 3##K—#©*#rMfL3a'M:h,&W&©#| Fig. 13 Schematic of curved surface which is a part of sphere —f 11 -Sallow I j^b I | u | t t ' 1 Sallow I | CCT, Li4, Fig. 12Ki3Vf iLfaEE^I=l®ffl©5 %, *3* p S-a3aR®*5, L„ 14 mmK:mc-cs#gfLA:*#^i=i©giiT, *#^Q%m3 zFIB'C 14:5:21 $■<$• ;t» ti" © #Slit (Expanded Ratio) fcHf (f, r, r"C3&bi-. r, K14, ##ka A^iujKMLT, 3Bl5lK^U4:»A^4©# Fig. 14 Initial layup plan of the curved surface %atmT#%7C'fk L A: 6 © T * 3 . C©^7^ f V -tT©^PTimaf 3 #e, c©@#i:-a-r%3c:kAiw@ek#3|mf3.-tk TR@m^^3^kK*3. ##^iuijsj:mRmkmA^ie]tEa!]L, M#©@mm 3 3 kT— **44©##:5l5©#&&msf 3#a-,R K, 3 ##©## js 4 L%ga©###% k ##©B1B K 3^»T*9, -fb^*#*»%©Ft/-y&"K:#l:7k^& 0.4 - tmtiT, »^14©%#gA)(,*m^3 3 k a.Tt,)3„ 0.2 - 6. -}fzo #l'>5al^-^a>Ciht, #M©—g|3K## Normalized Width B/B f3#e, ##rm^7k^E%^143%*^K:#3@-f3# ^©--3®##|&a 6.1 I#@©$^ll #g/Ak, f©#*T±f3»A'#©#5Klt©#;t# #S®-g|i £-@ 9 iti L 4:6B® WJ K o v > T, ilfflLfc rm»©M#&Fig.l5K:#i-. 4@&3%&-Cfr< kt#### Fig. 13 Ctf. Fig. 14 f 4i)K:@#&3^#gL, ±mK*af3#^A3. /h$ < # o, wornm# o.8 ©#E, o.8%&Tim 9, C©@$T—KT*@f3CkA%3K3 3k}»i%6A) cF*®@#©$g^|q]©#$ B $^11 Bo ril^TC-fb L tz 268 Bo a) Schematic of layup region ------Odirection ------90direction Fig. 16 Schematic of curved surface tube (half model) 0.4 0.45 0.5 0.55 0.6 0.65 Normalized Width B/Bq b) Relations of rmax and B/B0 Fig. 17 Additional patch on the curved surface tube Fig. 18 Relations of maximum expanded ratio and normalized width ¥S 200mm©3$@ 6.2 fi,^©@(#K:, $S/XTAt3ML-A:o Fig. 16Ktf;v© ^ Fig. i? j: ^ < t; if C Fig. 18 a) j: ^ k, f© ##^©#5Rlt©#*#rm^, r^©M#^Fig. 18b)K Fig. 19 Final layup plan of the additional patch C©##T(±, ##^|q]©#gl±id:@^^:# < LT y X f A mA0 & Fig. 19Kar)-. C©j=^KL, E30©##Ka#L%V)k%%^ ka*T##w. ^xm©fR#m©3@#%^:*f6i/XTAi±, ^.gp© CAM 7 7 h 71 y h LAB©##*- IGES 7 y-f/i/kLT#fi:k&B#kL-Ct:'5. t:©A*), ^X TA©S@tij*tt, Fig. 20 1 -5 %##%»6©Ck 269 if»T$5. TmA:*#@T, f ©±Kl#&MeK:#WBL rv^o ±M^Sy Bnn©ESfl-cffiS'f-5©T% i©BKi& S # 3: E A: V - ;wf x T NC ? y y » ifr^B#&g^ i) AM m ^ m, ape*, TiUTT vy ^#%A##Kj:6-7Vyxhyyf y©Mf-'K 7. m m #3:gyxf A©M% #1#, iSemsy b©R # - KfF - 9M), 174 (1993), a#m©KfR^Rk* p. 815 |#y$a.y-yay©0:M^AA. ##y$jLV z) amm, AM #, mmmep, ^wmA##K ^ & —-y 3 yK-OV^Ttt, — ^iRj^nlJgBT&ViffiijKfXJi -?!) yx t-yyf f©R#f-'#f%gyxTA©M # (#2#, aW###fGCAD/CAEy%f A©R f3R©geBk:oV)-c##^e»v\ #f-- M%), B^)@l6#Am3:*, 177 (1995), p.277 I7©#®»SeE^SB"C$i 5 b L, 16il€> MtSiL^Vi^© nj 3) *F@#, AM #, mmmep, ^m*A M#KML-C, yyTfV7%*MLA. ##K Z3-?'; >x h9y^^©mf--MfR#y %f A©m% (#3#, %LA:yxfAKiB»aA,^. C©yXTA$rm^T, % MM**©mm), B^)BI6#AgA3:M, 178 (1995), p. 593 0©##KOWT#l#ySjLl/-ya>'&;SmL, 4) AM m,Rae©FRPK##m, ©#%©#f#M^#^.fUf, -tk-r%6CkAiTg&m# 755 (1992), p. 39 &3E&5Z: ):##*& f ©#%&$-#%?# 5) 0. K. Bergsma, J. Huisman, Deep Drawing of 7i= Fabric Reinforced Thermoplastics, Computer A#»^K:©», @#-*1* Aided Design in Composite Material Technology, Computational Mechanics Publications Springer- mm©-? v yx h ? Verlag, 1988 Xf-ySfcfeKtt, S8f, W#r^6EfE*"C$— 6) J. S. Tsai, S. J. Li, L. J. Lee, Preforming Analysis K#f--##-&! and Mechanical Properties of Composite Parts %LT^Si-3 Z A© Made from Textile Preform RTM, 41 st. Int. #%A^^LACktc»6. A#«, #v^-rw"fy?- SAMPE symposium, 1996 7) mm%, me o ABc i &m%»fkmwm#y7 y^-%©am, i Xf yf#©BB##, M24EFRPyydfs;?A m*#^©^, Al»if JM L y 271 3-1 IEm * IEm ^ B 5 A Consideration on the Elastic Response and Design of Deepwater Riser by Hideyuki Suzuki, Member Koichiro Yoshida, Member Tomonari Ishizaka, Student Member Summary Research and development of deepwater risers for scientific drilling and offshore oil development are now under way in Japan. Depending on the purpose of riser, target water depth varies from 2000 m of offshore oil development to 4000 m of scientific drilling. Water depth of 4000 m is far deeper than the world record of deepwater drilling with riser, and the technology to be developed in the research and development will be one of the most advanced one. This technology will be also applicable for other fields such as sequestration system of carbon dioxide into deepwater and so on. This paper discusses overview of dynamic elastic response of a deepwater riser and design of the response. It becomes clear that a lighter and more rigid riser is generally desirable for deepwater from a viewpoint of elastic response. It also becomes clear that the distribution of buoyancy material must be designed so that the initial tension distribution is optimized and compressive axial force becomes hard to excite under dynamic tension fluctuation in hung-off condition. Two types of coupled response of riser, riser-mud coupled response and longitudinal-lateral coupled response of riser, which might have significant effects on the design and operation of a deepwater riser are chosen and examined. From a series of calculation, it is understood that dynamic response of mud has significant effects on the dynamic tension induced in the riser. Natural frequency of mud column is around 12 seconds for 4000 m riser case and a sharp peak is observed in the frequency response of riser tension. The peak height is still significant even when highly viscous mud is used. In a hung-off condition LMRP will need to be opened under severe weather condition. It is shown that the lateral response, so called parametric oscillation induced by tension fluctuation under longitudinal vibration, will not be a serious problems for real 4000 m riser case. Deepwater risers are designed so that the compressive axial force will not be induced even in hung-off condition. Under this condition, some amount of lateral drag force which is usually expected for normal configuration of riser will suppress the lateral response. But it is also shown that if a large longitudinal response is applied or lateral drag is very small, lateral large response can be induced. 2000m*? i. « n » iz 4000 m &7-Y 0, ICfilSS ¥Jt 9 ¥ 18 B 9 ¥ 5 JJ 15 B 272 #181# 4 if— \tSdcCh Z>tzzt>:£:!? 69 Clltt * 5f&TL Hex/ball a -Y > h 3GT0 S »2ffE 7-fif-T%»%D#L, emW'OB 97## Fig. 1TK, Tsk*. >±*ESlaK 9 #'BSKc^viTBT*?> k|51WJlz6E4s{5T #K#Ki#K:ov)-ci±T%©5g±,a%t@;<»s. z:©T LTiSx^x h;v©JligEfiHcSS1"5i£6, MMW) 2. *7X;$7 Operation Hung-off #*#K7S;:ka%#k#^0fLS. 7-fif-@#© ^m6#»P9@k7s^B#a%©m^ s. 7/fif-&eba#ai7^if-@:&R&2mKf imk»S.4000m@7/f ir-Ta^0@a*3#ti@^5c Relative Positive Motion ^©7^if-#KK7a-7-*;i/7^7, 7-x7- Tension between riser 7 -f >» 2f#*#a%##mk L-ctmks©r, mim# and mud l±g&K:#<»9, &x-:Xh;F#HK:At)*@a#ak »sw#&a;^cs. 7dif-©K#mccv)-ca#*as #KK/|\$WA:A, LMRP @a4&mK:*# < »9##KE*AA%C"CL*^©r, "S BOP c^±?, $ 6K^m,3U7*-*^3-*smt-a)mBT&s. Fig. 1 Schematic diagram of deepwater risdr in opera tion and hung-off mode. 6 a^c L, z.ti%±®z ±5e 273 ka^g-c&e. *Em#©A# >h#@H8 &BC%*K:-MkLT 7^-f-T%0 %7^?-0:Sa%mg:%&A# <%fl30T-#K#U @#as#±4° Kmf6k##»f±L, 6° &i@2.&k T$ &a^, —^TA*#7 < f-#&» D om#% k » 0, %9 *L 7otX&5<:kaiTT:biT-C:B9 , AbA# oa^c^K&a. 0TW#«©A&%aia>»9 A# < #@kLTW:#*FEM, 9 d1f-g)#»K:iBl:a:t- FEK i. #&» k* —jEto&tofnStKte, 5. La^L, 4000m© fK#Sr^R*)K#n:g^aOTiem#$M*6^ kA^g* 9^f-Kov^Te{-#La:g!l&Fig.3E#i-. HOE#/' L <, a c k K z o m83&% yx> 7^ErSi$©±i$-C*¥^|6j KSIS 10 m, mm® ^#&K#f6C:ka%#k»5. Fig.2 0#^:B[K:a No compression -i- Initial Tension > Dynamic tension Initial tension (effective tension) Dynamic tension Fig. 3 Deflection of hung-off riser oshillated at top Fig. 2 Design of initial tension and dynamic tension of (length = 4000m, amp. = 10m, angular fre deepwater riser. quency = 0.2rad/sec, plotinterval = ?r/2 sec). 274 #181# mom# k 9 ^ 774 7K#i%i fEAr 0 Us T VtQ = 0 (5) LT7-Y if-T%» BOPg± (:##$-&a:> p V-»fr L o EAmJ L Us J **#K:*) 7THT%^ J:%fJJ@©m*&-^©#BK:M^a d kC »f 0 ~Ud C1 + C2 ~Cz Ud Q)2 + ia> j=0»*$$-±Wack*iW#Bk»a. 77f^7mi#K: F -Vd„ . —Cz Cz . -Vd, i 0 9-f-f-of5@wmL3og*o@m$-#;mf 6^ f£Ar 0 1 ’u'd =0 (6) kKj:D, 5 _Vd. NOR&R:i5C:©(6)^©#t*©j:^KiS^i-5. Ud 3. 7'flf-kV-y H<7)368®^ (7) -Vd(x)_ .Ud. :t*%s7^-f-®#@mcmLT%a#@m@k u% LT#^fL5. l±, /\>7^"7#KM#g»6if7 — Fig.iK^-ri — icuci - (o2ma + imc2 - EAmA2 9 c-RfT^© LMRP £HBi;-C7-f if-ftfc&jf L ft#; =0 (8 ) #k»a. C©#^, 7-fif-©^e^^%%*kLT 7-4f-T#©#f*mkL-C%D#t'^5 k, -®sti@wfa, p;p, * 1, -7yP@^0K%fG:#^#!#:73^g^6. 7^if T© i 5 lu#£iia0 -em©7 y p ©awmima#*#*^ 7 p * 7 A©#* Wd(z) Udl UdZ d\ e"*+4: »2@«faRMk»a. 77P©####3kEACj: -^dW. . Udl. . UdZ. D7^if-#*i#^K:#ig7a%#WaL-CB#f 3 UdZ M k% 2000 m ©7-f if-T 6 sec, 4000 m 7 'f if-T 12 sec . UdZ. . UdA. @gk%&. C©MK#K##^#»m7CkT#*l#g,fl5. T%© f©#i#ktlO%#gT&a<, C©B#^g8K&%-: LMRP *iBU-C^5#a-©%#$#Kog© j: ^ K»a. 7 PiPKBK^^aft*, /\y/^7#©7y p#### (1) 7 -i v-iMtommwmm t * a „ »-»0^:g<»5^k*if^gfL5©T, (2) 77 P±%TEAifo ^.5A5*l&5. *IBKK7^if-k77p(im^Lft# (3) T#7^f if-0#:&k7 7 P©^a*i9Lvi m&^f©?, ^ypa^x (4) T#«@ATtD7'f if-T*m^k77 PT*M&& f mBR©K%ie# 0R*iifnT*)5 ammm#&^7©r#B©#mmk L-cmmm Figs. 4-7 i±7^if-k77 P©^»#v^-C#&fLft7 ^@^K:#A7a k)k© J: ^ K»5. ^-7-Wa©)#&8WB#M%r, 77p©K#&ifo^6 — mrii~c\u ~cz{u — i>) + EAru"—^rff=0 (1) 120 cp ©a##m $ fb5#BTmHk3 -e A#a-©m#R ~maV — c2( v — u) + EA„v"—ptn,g=0 (2) (B#t^Lftt©r*,a. #t#K#jmWk7-f if-« ;;c, u = 7 4 +h*-©l673|6l$e, i/ = 7-y p©#^|6l$ Table 1 j: 3 t ©n*#»#Kmf {st, mT=y'( if—©W55SMS, ci=W*k 7^ if—© ^fT7 7k±r^&EMiti&ffyfZ i>0Ti> #*#», cz= 7 -f if- k 7 y P ©3mm, EA, = 7 ^ if 5„ 7^if-###©#e©@WI@m©tf-7*i6sec^ -©toHOtt, !+r= 7 -Y ■y-oWS £39 ©**S», T 0 ' "C1 + C2 " U~ Wlr ~ U — c p©K#©#Bri±tf-7a#<»a»v^ 77P©@w + 0 W-m_ . V. . —Cz Cz . . V. )@%©tf-^i±&7.^^P/l/#BC^$f|,-Cj30, c©^ 'EAr 0 ' u"' >7-5* kKLMRP$rMCT7-fif-^^K:7 7 + =0 0 EAm, .v" _ .{J-mQ. ]|BT/\yy^7L7k#e, 7 7P&Ztf7-fif-K:#'»D 7-fif-&K^I=IK:)gK&(uTlm@Lft#-g-K:3^T, (5 *@»#;%a!±Uaam#&aTLTwa«, %R©&*TK: j= ^ c 'u "zfdW mmf&ckai^gTto, 77F&m#L%ms/\:/y + . V. _yd(%)_ ^-7fac:kamL< LMRP Ck*ii2'Bk»ak 275 no relative friction viscosity=120cp 1.46+07 depth at 3600m — depth at 3600m — 3e+07 2e+07 4e+06 le+07 2e+06 0 1------'— ' ------1 1 1 15 0 5 10 15 20 25 30 period(sec) period(sec) Fig. 4 Frequency response of tension of riner induced Fig. 7 Frequency response of tension of riser induced by riser-mud coupled response (mud: no fric tion) . by riser-mud coupled response (mud: 120 cp) . Table 1 Priincipal properties of a riser used in the mud viscosity=20cp 2.5e+07 numerical calculation. depth at 3600m — Upper Half Lower Half O.D. (m) 0.4064 0.4064 I.D. (m) 0.3556 0.3734 Weight of pipe (kg/m) 239.0. 158.9 Auxiliary pipe (kg/m) 107.2 107.2 Buoyancy (kg/m) 120 (density 0.45) 120 (denslty0.63) Weightofriser Wm) 466.1 409.4 Weight of mud (kg/m) 143.0 157.7 Weight of riser in water (kg/m) 179.9 198.2 15 4. mmm-tzt> period(sec) Fig. 5 Frequency response of tension of riser induced by riser-mud coupled response (mud : 20 cp) . 4.1 depth at 3600m — 1.8e+07 (mp + mm-\-rnu}u —cdu +EAu" +-^~EA(w'2)' + y7<7=0 (10) 1e+07 (nip + m, + mw) w — EIw""+EA{ u' w')' —IzpCdD — (w — v)=0 6e+06 (11) , mP= y 4SBSEfrS VYlu 2e+06 SKlalfiftEite:, ma,=@S‘|tofTSD*e, % = £A=7-ff-»iI 15 w=?4^- k, c: k**T#, 0 *KSK«HA:k»fE#kBLa:K:#< CkA4T#6c#(±# 500 u=£^-x (l—+ Cix + C2 (12) 1000 #Tt 9 %© Z ^ K##fb Jo K=e^g*" 1500 'e «> \ ^ 2000 ■J co2+d2) I 2500 d=____ Si____ cz=----- EA___ (14) mp + mm + mu' mp + mm + mu 3000 LAAicT, u = [eMcos(y?x + cot) e“sin(@x + cot) e~axcos( — 0x Ci 3500 02 + wt) e “sin( — ffx + a)t)\ (15) Os 4000 .<2:4- -1 . -0.5 0 0.5 1 deflection(m) £ ti% (11) & Ctt\-f JiiCiOftfc Fig. 8 Lateral parametric oscillation induced by longi S* 5f#5>#i5io tudinal oscillation (longitudinal oshillation : 4.2 h U -y amp. = 8m, angular frequency=0.6rad/sec ; lat K@*©#u t Tkk) »©)g#^@^;(11)3%KRA LT eral response : angular frequency=0.3rad/sec ; plot interval = 2sec). W*#iB3Wkk-r& #&9. 7tk»(6#®m6^KgK:mgg^TW5,'.'% w = m#fk G>2Hk»6. LTk^-^T. %^^9Ao. kEj: 9f5gt3^Ef &±5»/ > tension limit — F+G > 2H divergence when c=1000or ♦ ♦ divergence when c=300o» 4- divergence when c=100tv ■ Stable Unstable Stable Unstable Stable, Unstable 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Unstable vertical oscillation frequency w (rad/sec) Fig. 10 Calculated stability of lateral parametric responses due to longitudinal oscillation (lat eral drag c=1000to, 300to, lOOcu). Unstable 1 c©#e, Unstable AL»w$)g&fHic>250kg/(msec)k#&. C©#lf ^m©»gk aim c#k »&©-?, 5^ Fig. 9 Stability judgment of parametric oscillation of deepwater riser. ka%M3. 26K:, », f6#a#K±©%#b:KS&-f 9 $ y f:lkk»%. 3#^e^(lG)Km^-C8/9-Xgf-#*- (20) e^^n@*&Fig. locarf. C^j;9±T«9'f'f-K:EmilA!±l:-C^6 ckL-cw6. tifcJiftliDffitl c=1000to SfSL'fcS'B'KoV'T, ±T 13 IrJ ©MIlStM SliLTvxo tzMi-& E fc t> frfc&imWc? V^iirn So "T b F©SMS* 5#! ;k SSnffiSfiSrTjxLTdo 9 , tz k %.i£, cu=l rad/sec ©So", ©#a-KA c i±##mm© 2#Kitg!iL^RA»ie#fkL %%&a&&wE##T5#k»^Tir>6,, dOBEfft if, omrat$ft.&a%©Ax*9/|\g» c^iooto ©#-e, C ^ 2k7 > (21) a&w;e±L&< -c&/<9/ b 9 y9##E f 9 2a>o ^ 4(F+G) 1SJ1 zSErtinS$ n sS-n f tivjx$ h;F©#@TK/< kLTF'#f 6. k if-0%^l=I 9 / b 9 y?m#B&U»WS, (5E@%E**ai/j\^» oambtmak7'ff'-*4'%TwmgojtK»5. #^-E » Z k ^ S. 0.5 rad/sec WTT K: 9 -f & k f & k C j: -) KK ZfWf, )@&%E*#L (22) /k%BMSa*#@E/J\g<»5CkEj:6t©TtS. Z Z.Z.T, —$Jk LX m = W}aWMb^^tz^-^i ’Smim ©a&E#%K"3V^-C*##R9lt#aLT(10), (11)5% kg/m, « = $6^|n]jra$EiE5m, to = 6to|R]MIM$lB 1 rad/sec, /ug=9d" If—©SSSTSlKI® 5 m/sec2©/®^ m@@©9 t y blf^f 9;t/»^Tk 278 B #§###%&%* #181# 5.i# m Fig. 10 Kjmg#@$#LTt^A##K, k(Dhtz D fr Flg.llI4c = 1000(U tension Iimit — osci 1iation at w ♦ osci i Iat ion at w/2 + 3) ESS) b tz ;b friggKDMl$ tc ov > r tt, SH±ttEiig -f k©*#©TTC ©JSS^HJliPrSM k % G & © £ b Ltzo # # £ m 1) M. Ozaki, Y. Fujioka, K. Takeuchi, K. Sonoda and O. Tsukamoto, “Length of Vertical Pipes for Deep-Ocean Sequestration of CO 2 in Rough Seas”, International J. of Energy, Vol. 22, No. 2/3, 0.2 0.4 0.6 0. 1.2 1.4 1.6 1. pp. 229-237, 1997. vertical oscillation frequency oi (rad/sec) 2) C-T. Kwan, T. L. Marion and T. N. Gardner, “Storm Disconnect of Deepwater Drilling Risers”, Fig. 11 Frequency of lateral oscillation due to longitu OTC 3586, 1979. dinal oscillation co (lateral drag c = 1000tv). 3) “Recommended Practice for Design, Selection, Operation and Maintenance of .Marine Drilling Riser Systems ”, API. Recommended Practice 16 Q (RP 16 Q), First Edition, November 1, 1993 (Fo rmerly RP 2 Q and RP 2 K) 4) C. P. Sparks, “The Influence of Tension, Pressure and Weight on Pipe and Riser Deformations and Stresses”, J. of Energy Resources Technology, ~ 1.2 Vol. 106, pp. 46-54, 1984. 5) ±##, o 0.8 voi. 167, mo, pp. 137-145. 6) #*3% WEES-S : “zk ip © IB### mkf©mmEowT', voi. 168, 1990, pp.381-389. 7) &M3E2:, WBB&-GF, mm, ##&m ±, : “T 7 t 4 7*®J#PC -f 0.2 0.4 0.6 0.8 . 1.2.... 1.4...... 1.6 1.8 horizontal oscillation frequency(rad/sec) UlScS, Vol. 174, 1993, pp.865-874. Fig. 12 Natural frequencies of lateral response of dee s) smeE#: pwater riser (riser length = 4000m, at mid point eufiie h 5 **i$ 7 -i v-*-©#SBttiRi± citsi of riser). ^B", voi. 175,1994, pp.223- 279 232. Long Cylindrical Marine Structures under 9) J. E. Miller and R. D. Young, "Influence of Mud Different Excitation ”, ISOPE’94, pp. 231-237, Column Dynamics on Top Tension of Suspended 1994. Deepwater Drilling Riser’’, OTC5015, 1985. 11) ms#, 86,1982. 10) H. 1. Park, “The Response Characteristics of 1^1 ^ lj' 3-2 - -ft* IE# e m s-sip lEfi S£ * n z* Structural Analyses of Very Large Semi-submersibles in Waves by Kazuhiro Iijima, Student Member Koichiro Yoshida, Member Hideyuki Suzuki, Member Summary Very large floating structures have been proposed for various applications, e. g. floating airports, cities and plants. Among them are semi-submersible type structures. This paper presents a computational method for analyzing responses of very large semi-submersibles in waves. When designing usual semi-submersibles, we need to model and analyze them as three-dimensional frame structure. The output data from this analysis is used as input at the next stage. This will be also true even in very large semi-submersible case. Because of their enormous size, some techniques are needed for such frame analyses. We have extended the formerly developed method by the authors applying sub-structure method. This is rational because the structure is expected to be composed of repetitions of simular structures. We newly introduce the concept of group body by which several columns are treated as one body in terms of hydrodynamics. The unknowns concerning both hydrodynamic and structural equations can be reduced greatly in number. In this process, both hydro-elasticity and hydrodynamic interactions among floating bodies are considered. The results obtained by the present method are compared with the results of the formerly developed method for validity check. We show the 3,000(m) structure case. The results are shown to be applicable to zoom-up FEM analyses of local structure as input data. 1. ft 16 i tmAemwaf & ###& act & -c ^a. a#, u-ctf/h-fbu-cmifi-a to — to# ???%##& zf&SM-ra&AT&a,, b k 3 fia £ kAiiLBSiiao L&L, A#&S#7C# tazkO::A##tfG;h,a:%a% Hji^OCkA^, HESS 9 ¥ 1 E 10 B ## 6 k t & ¥|&9¥5H15B 282 #181# Goo's Method Present Method c cr, A b v zx», Response Analysis in Waves Response Analysis in Waves ## a k %R.(D d "5 btl%> o ([A^]-[&.][Au]-'[Au]){%} STRUCTURE FLOATING BODIES STRUCTURE GROUP BODIES = {Fb}-[Z21][2„]-1{F/„} (2) PANELS SUB-STRUCTURES FLOATING BODIES {W=[Aii]-'{FU-[A.i]-'[&,](%) (3) (SOURCE DISTRIBUTION METHOD) C C T, ^ (2) k ###—U a H -CKD Fig. 1 Philosophy of the present method ([A22] - [FaiKA,,]-‘[-K,,]) = [Kb ] ( 4 ) -CSSn-BlItt^it-o —o@ESk»»LT C #mA# ma^-caFEMta^aki^torta. ^(3)tC%?T#mftAi-$CkT#f,fi3. o#0^»rm##^.6Cktcj:-3r, a e t m u#*#am faf&Tta#, rga. Mil M12 [Vm\ . Cn C12 \ 1(0 \ Vb >f _M%i M22. .C21 C22. ID Ksu Ksi C0#&KZO, Kr 11 Kr 12 COH-COT^ROR, f»k-&%iA0&^#f3Ck# Kr2\ Kr2z\ VK.w Ks22 ID r#a. &oa'®##&O'k-30##k»»f, (5) group body OSt^SSffc KSA# a. -^00#, fiffCi fa^A&^fack^rga. ji(±0-30#f-%±0 M, C, Ar, A. H#icg*7 b V ? X, b V XX, B*EE d aEjcb^grr-x b V XX, liJtt-7 b T#a. C0Ckt±#^*7KFig.lK^$il,a. #mE#b# V XX £il To 0 , S©##* b 0 radia tion 0#*#a_a k5#, -o* c0##A^ag##$m#r#, com### LA:Ck^.ak, BPa-#m@K:i@^B0'7bVZZ,K $Mm#0A#k»aCkf. ama'#B&KUd#-^*%v^d^K:mk,m.a. L#L, % 2. an mm rma# a d ^ K^-#ac0^#m$-3t*-#-ag#03E 2.i mmm mztkfflTZtl (ftiMl43dt/il$zSS) km#KMf a^#&yf^r#$fiack#^$fi.a. f#o%a^k A<0@m#Kkv^Ck«#L ^.Akfak, c®k#&a0-7b';zxi±a^-#gA# 5*fLT, CT#o##timuB#-Bam#&kr, $c*: % k, sB##m®m8 G®a&a k » a r A^&mmrmv^^aiRe^K^a. t a. C k ^0 j; ^ K » a . #m# - #m#-c, mwo'mmmm&x’, Kn Kiz {?ii7i\_rFf.'i !RK:jE#^Tv^akfa. *wa —)ST, #*@a#kA (1) .K21 K22. ~Qe I *- Fb I kf a. A#0#*K:A*K#A 283 #L, il3„ 3® diffraction d\f f ;!/&, diffraction b g* i C±5 diffraction i&T's 'y ^ A/©*®#TgLAk #®#»tmif kf 3? b !) ?X& *®j:3K:g3fL3. [BiY X^to [Si]T Kg* z ® diffraction ##& 7 ii>?=ffs OiGidS ( 6 ) bVXXkk^3k di*T# 3. 3 3TK [g,]^ 3 K {R‘J t$»3EKt^@ 3 3 T KiFfitilliTjgljf" 3 E® radiation df T > '> -y ;VK&® <1 £"C0rA C group body ©#±Ai"3 o 3 ©@# j=^K*i"3kdit-r#3. K j: 3f#*rm®#4 > b Kdieraction#%%#f fz^l 4>1i={Ru¥ {?} (8) [g] tmv^3 3k?t3.3©3kEj:cT,Dko©g* 33T {/?«} 0i*Kg* z A5^SC#SLT, / TjIiWS #@±©## < ®/f^-;P±® source KfSSfc^X b ;V {A} 3 K® radiation bbtAo %o^®g*tlb k * k * !) k LA# @® diffractionj: D & < ®/, f ©df-f ;f/K f®m*®#f3me#m®##m^? ^$ft3, kW^-o®(RS%T3. C®k@(12)^4;® 4>j= 4>o + 2{A,} r{ 4*f} 9« »^a-kf3g*®$&-(X b;i/(9}K^®j:i5K# +gg(-«W«W(^) {z?}=[L,-]{>?b} (13) =({a,}" + Z{A,nT^] beam SS k hull WM (Fig. 2) K X -o XX r zP{b1“ 3o + 22(- imii{Ru)T[Tij\)\{(p?i (10) node H£E«£ beam $*KfiAf fctEtt* ffltt i*j . »#M^3. hullS%Km**^@K3gA, T^gft3.AAL, A##dff ;F *, K T radiation node KHlfkSo'S iLTVi^0 § iS$tVTV>3„ Vli Kg* i ® / S|n]'\®$ti®E*$ll 3 3T, ^(10) K, A#&^Xb^l3#»^^b EK^f&%®#mTfF@-f3®**j:DlELV)kmk,di, 3 ;F^^KAi-)»B^K:»^TV)3 3kAt6A^3. A*% 3 3kKLA:. b^®^^t—d©A*dff ;f/kT3 k #©g iESdff #BfbLA */ ® diffraction d ^(14)&^(5)CRAL, REFERENCE POINT FOR DISPLACEMENT / AND BENDING STRAIN K, ^1(12) k@l%$-e-%::5@5S< k kT*##A©^ REFERENCE COLUMN @k, " FOR WAVE LOADS 3. & m t # m Incident Wave 3.1 fME 4'EI#AL'Agroup body k 5 A t SUBSTRUCTURE beam element""' l sub-structure iSOtSfi^iSSTS -E> ip k V* -5 A k $ Fig. |/EI=1.05E12(k|fm2) X p =73.5E2 (kgf sec/m4) I A^.=l.0(m2) floating body * 8 boundary nodes (Diameter. 20 (m) Height: 25 (m) i^Draft: 20 (in) Consisting one group body Fig. 3 Schematic sketch of the model on 16 columns hull element S 35 ■PRESENT CALI Sr 30 beam element g 10 0.2 0.-1 0.6 0.8 1 1.2 1.4 WAVE CIRCULAR FREQUENCY (RAD/SEC) Fig. 2 Subdivision of models by hull elements and beam elements Fig. 4 Surge forces on one column 285 *1, S:te»groupbody0#&, #%#»U)/s»ElfR ig'f L 6 C ©##*%IK@&Rm-E ±#^^6 group &-p T ti S fo it'Cii^tVio n 5 A 4 oS-oC group body body If #@##±^#1 E»5#e6$6k#^.6iL^.k L?&i)©?, 25OfB0g#M©fgSf#0RmK»5. § 6 E, radiation f^MT, —o© group body %MM$k L flUenE^ff Fig. 6 tf1 E S § it. $ f ■) % sub-structure ~C ^ 2X2 f 3X3 @a@ group body * 25@EA4H$fLTV)5. #**»%##%©$%&©»lf A:^L, 250 X 9=2,250?, [5U<#mm#(###jS)©#a#© group body ©A#S if AtM©$?fi 10f8*Kl%A# § Eli 260X6 = 1,560 T*^-H-3,810®E»oTV^ o ffiE »©?, 37A#A^A<39ARRt/|'g»##^*k group body J5 j: Xf sub-structure E|% ibfcS ’nidC 6 if 3x3~4X4 © group body b RTtbTt> 5 5o 34,000 #?*%Klf 1/9 E6c?w3. -7 > 'J ? X®^7C© 3 $E.fcfc$]t" 6 k ttlii, 4"@©SS 4-0©%#^-#&%4x9©3 9AE ?lf#mfSA%if#&B?&& : k WJ#L? #©M%L^3-Fkem If 1/100 ©^-/-E»^?U)%k#^^iL, <—E&T&i:kt#RL^,4x9©37AT^:Rrg^ ^±@E±A%??v^b©k#^&iL». »33, %g#lf, 16#©37AT3^#$j%5g#k%©eBTfTi) b |6]V>Effltigi©tf-S£ Lfco @^##kC#E@mfL?3S/uff. #&E l,000m©g##E#<%%M*EoV^?m?^ 3.2 @ae-;s»©ssji5W -----PRESENT CAL O 100 • o ffTHOUT INTERACTION column center “ 20 1,p00 (m) .495.(13), 0-2 0.4 0.6 0.8 1 1.2 1.4 WAVE CIRCULAR FREQUENCY (RAD/SEC) node255 node135 node5 Fig. 5 Bending strains at a reference point Fig. 7 Reference points in V. L. F. S. model V.L.F.S. 2nd 1st substructure 3,000 (m) 300 (m) beam element f f'EI=1.05E12 (kgfm 2) tot) / j p =73.5E2 (kgf sec/m4) -^yvY lsAsec=1.0(m2) B 100 -----col485 —col495 ...... col505 — single body group body Substructure Diameter: 20 (m) Height: 25 (m) Draft: 20 (m) '•boundary node 0.2 0.4 0. 6 0.8 1 1.2 1.4 WAVE CIRCULAR FREQUENCY (RAD/SEC) Fig. 6 Schematic sketch of V. L. F. S. model Fig. 8 Surge forces on one column in V. L. F. S. case 286 a mm# Newman101 trapping k IrIS® S,S* si3 M&©/N# #K&oTU &c:kr&&. iT©##?*) suige*l%©^@BRUK»3Bffg^6, C^LB#)S© ©37A©B#©2#K»oT^3. C©jggia heave ^[=|©^6B E, < f < 1"5^|6lK® < fllnJSr^fiSJl TB/JnS Vi, (2)-"=0.67(rad!sec)fifiS© t° — y 7 tt heave ©g| 3.3 &o fy*@3©0Bg^fG:# (Fig. 12) Fig. 10 k Fig. 11 KB Fig. 7 K#$#,&3&&0 surge ft (Fig. 13) 4-Svt'o © aft * fc*B Fig. 7 TEEUfigl^ |6] ©$(5 jo J: If heave ^[6]ffl$fiIAs7S surge ^l%©g!AT3(A;# < © B, ##©M%©^&©^: # $ k kttWS"CBIi:©6i, ©f futMW)©!# k#^_ 6iL5o #itB, a)=0.67(rad/sec) it Ji, a©i^Kheave©@Wm%Tt5U, ---- C01475 o 6 -----co!485 TM6fL&e-?BBk,Lk*s#ig©@#m(Brt5% —.col495 ...... co!505 ##3*±©%©#e, heave © — single body @##88 jzD^#^kC5K:^l:%ku^i:k B###© —SISK B-sTfS StvtTt^^)11^ $7i, a>=0.8(rad/sec) B# C k A*T # S. C ©@K&T3 standing wave K: j: 0.2 0.4 0.6 0.8 1 1. 2 1.4 0 spHt%##;&a%Ua;:kA%5w2:KTV)5"«, WAVE CIRCULAR FREQUENCY (RAD/SEC) Fig. 12^ 6 B, fy4f©k©*i0-T±#»^*$±U% Fig. 9 Heave forces on one column in V. L. F. S. case 0.16 0.14 0.12 0.10 0.08 0.06 0.04 0.02 0.00 0.2 0.4 0.6 0.8 1 1.2 1.4 0.2 0.4 0.6 0.8 1 1.2 1.4 WAVE CIRCULAR FRREQUENCY (RAD/SEC) WAVE CIRCULAR FREQUENCY (RAD/SEC) Fig. 10 Displacements in surge direction Fig. 12 R. A. O. of vertical bending strains de5 — node255 | j! As '"MU' m%A_ 0.2 0.4 0.6 0.8 1 1.2 1.4 0.2 0.4 0.6 0.8 1 1.2 1.4 WAVE CIRCULAR FREQUENCY (RAD/SEC) WAVE CIRCULAR FREQUENCY (RAD/SEC) Fig. 11 Vertical deflections Fig. 13 R. A. O. of axial strains 287 Table 1 Forces and moments at each point upper: T=10.0(sec) w =0.63 (rad/sec) lower: T=21.0(sec) w =0.30 (rad/sec) 6th Substructure Fx Fv Fz My tonf rad tonf rad tonf rad tonfm rad 1 502 -0.30 85 1.48 133 -0.81 1312 -2.44 2 88 1.52 79 2.10 65 2.66 392 1.66 3 88 -0.63 75 -0.58 60 -0.33 747 2.00 4 600 -2.46 258 -1.07 150 2.44 10400 1.85 Fig. 14 Zoom-up sketch of the structure 5 500 1.75 192 2.51 27 -0.52 823 1.77 a^KC5Ck(±r@»^c L&L, < »a ^ ka^kA^c *7:, Fig. Fx Fy Fz My 13 j: f tonf rad tonf rad tonf rad tonfm rad /J\$<»7TV^5Cka%a^5c 1 171 1.39 13.3 2.34 26.4 -0.46 5170 -2.41 6%k»c-Cv^5CkkM#ai*,5k#t6ki, 2 3.6 2.74 11.6 0.24 2.9 3.10 54 2.76 ka^o < z k fuf " ©#* t 3 29 -0.83 8.8 -2.84 8.3 -2.10 309 2.19 4 247 -1.57 17.0 -0.60 43.4 -2.76 5580 1.13 %vi% $-o y 72^t;v ti^tfS^&TIsz 9 $ -5 ^ k a*T#5» 5 109 2.00 7.7 -3.12 23.2 0.08 894 2.03 (Table. 1T#S!) rt©@aM'$<»5©B, ml #K36J##K# < w7k»K@l #K#<#*$5wB-&A,#r*KBA#»K#^_»w T(±yv —xo j: ^»#3@@5#KAoTi)»v^#*»60 72*T&5c »©T, #lkLT37A#om:)%*bOK« for Huge Semisubmersible Responses in Waves, SNAME Transactions, 1990, vol. 98 6) Kagemoto, H and Dick K, P. Yue: Interactions *o among multiple three-dimensional bodies in water waves, J. Fluid Mech., 1986, vol. 166, pp. 189-209 7) #a.K amam#: 6%, p. 62-p. 70 8) Yoshida, K. and Ozaki, M: A Dynamic Response Analysis Method of Tension Leg Platforms Sub # # 3t E jected to Waves, 1984, Journal of the Faculty of 1) #BA%: Eng., the University of Tokyo, Vol. XXXVII, No. 4 #,#1785,1995 2) ##asm#: ?#am (e®2), #1755, KOV)T, #178 5, 1995 1994 3) %##%, 10) J. N. Newman, et. al: Analysis of Wave Effects fS^Kev^T, B#:imim#^*3t#, #180 5, 1996 for Very Large Floating Structures, Proc. of V. L. 4) ##%#gaa#me: F. S.' 96, 1996 #m#wa( 4), 6?? 5, eo 11) M a##, # 5) Goo, J. S. and Yoshida, K: A Numerical Method 178 5, 1995 289 3-3 1EM M E 1S K* An Investigation on the Dynamic Response and Strength of Very Long Floating Structures by Beam Modeling on an Elastic Foundation by Takashi Tsubogo, Member Hiroo Okada, Member Summary A number of studies on the dynamic structural analysis of large scale floating structures with length or breadth to the order of several thousands of meters have been done by several authors, as reviewed by MIYAJIMA et a!.*)^). Most of the studies deal with the basic characteristics of the vertical vibrations of the structure modeled as a beam or plate on an elastic foundation^) 4) 5) G) 7) 8) Especially SUZUKI and YOSHIDA®) have given relatively precise prediction for the deflection and stress of the structure at the lower frequency zone by deriving the analytical solution of such models. This paper firstly deals with the dynamic response and strength of a very large floating struc- ture(about 4560m X 1000m) using the simple beam modeling by the analytical method. Effects of boundary conditions and structural parameters on characteristics of dynamic behavior of the struc ture are discussed including the characteristic wave number derived by SUZUKI and YOSHIDA. Finally, the dynamic behavior for the same structure replaced with a plane framework is also investigated by applying FEM. The modes and natural circular frequencies obtained are compared with those for the structure modeled as a beam on an elastic foundation. It is also pointed out that not only vertical bending vibrations but horizontal bending vibrations and longitudinal vibrations should be considered at the lower frequency zone. 1 * m isoii, cc-cas fTkil-TWa. C4:(DOLTS' ^ j;0Ka, 6 ‘-*1 t#* 6*15. '-k K 4560m X 1000m Vciwixoi'flfsns 3)4)5)6)7)8 ). ffTfe, * *s 6)icj:s, lt«, me^r6i©s«)©»»6T, £ £6)KjEB UT1A-5. *E9ETtt, stem urn*. 2 BWlESiSt^# m, $-r#14SB$-h%©S j:yssnfc MUSS 9 ¥ 1 B 10 B Ko 5. Fig.IK T^9¥5H15B 290 BzRmm##### mm# W-n-toSEASiUt:#:©^ lc£t£. aa##@cat& d, v^vj5W*#(-*viTt>@*s$i pA^-^-+ EI^-^-+ kcw = Fcos(kx - wt) (1) Sctt^©(i =fc o a# < as. at4 ox* ZCiZ, w: m.fr,pA : EE : ______L ,kc : ff A# 14, F cos (for - art) : WLtl,F = fcc|C|, |C| : A B §E&s«jne(ctt#«# v/jv^eo, *©x* Long Beam . w = H 6 EtiSSb-r e. x=0m x-4560m Fig.l Elastic beam on elastic foundation Mg-rgs 6). tarn2s^iET^ssicESt"stm ****&, 3 sr, s(i) !)4aSj5V^tlTH-6. 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ZoTfcpl4??^^*g|51C43l4S|BlW!S &?&%. £ttl4S5i*6©$Sm#S6)Z1t>£$S(T£3. too Z toupper mm%#et)fG©m#i4t= tp?ima®#&z%z# fcp < fci x6tl(31)3$ZD. ra*u>. s gm*?©&A#*©iB#e* |f Irani _ kc______1______, . (kl/KI = i/o,«> i)*m&saaz. a(40) ZD. 1(1 2&2Z / cop y ^ ) , ^ kiOVJer X V2too / kP < / — ^J=r- =- (41) yof 2 + Va4 4- c* 2 — 1 t.l3.Z>Z.£.tfit>ftmZ Dtop « too?14, to 0(ab-5H 14PA) #4»**ti53 © S® ©ffilft l:l4&Z/uZW# ST, kltptT §$© -a-T. feto 0©14B (&»*«©ZIB) tfinx> Biltt E/£’£xa S ZlStea. it(34) ZD MOteS:** < U afcit?%t©ut0©«-& zstsfii] etc 14a. zfcwp «u% kp £ ns m & dm ic -r e. -r z g tu ssi m e is m ic w m ? * a. ?i4 (si) (&too?&Tczic) zDm&mmm?© 6 ill SHettH-ito ©®M 1C ? V>T 14, m#miTll(36) rU ®j m &*,1 in i4, ik d 74 < if- w m © t) © tc ia r <. j D teto 14 fcp(E/) l-Z^-r, W MT14 (39) EtZ D kprfX 37c7ZU Itrlmux/ICI ©*H4**©*iiS#© l/2FfZ74o S< (E/at/J\S<)&aZHHfll4;Ac£<&a. rvia. 295 — dynamic cal. ------dynamic cal. --- static cal...... static cal. at 160m from near supported end supported end - co=0.40/s co =1.00/s 500 co =1.50/S 1000 Angular Frequency [rad/sec] o> Horizontal Distance [m] Fig.6 Frequency response of deflection am Fig.9 Bending moment amplitude distribu plitude at 160m from supported tion near supported end(long beam) end(long beam) ------dynamic cal. — dynamic cal...... static cal. -- static cal. at 70m from at center supported end 2 2.0 Angular Frequency [rad/sec] co Angular Frequency [rad/sec] to Fig.7 Frequency response of bending mo Fig. 10 Frequency response of deflection am ment amplitude at 70m from sup plitude at 1000m from free end(long ported end(long beam) beam) ------dynamic cal. — dynamic cal. ------static cal. --- static cal. near supported end at center £ 2.0 j 0.05- 500 co =1.50/s 1000 U4 Horizontal Distance [m] Angular Frequency [rad/sec] co Fig.8 Deflection amplitude distribution Fig. 11 Frequency response of bending mo near supported end(long beam) ment amplitude at 1000m from free end (long beam) 296 $ii o ^ t tt® M & ® -£r t£H8( 98 ® Mv2 = ak CV = wt# 4wg/ W4=0.4465/s |wj K1 t&. ST, w0mfCicpSff,t;i^x5i, %m *% C t CA&. l£(32) L kp&mmmicT 8 C C £TS&E* In] Table 2 Numerical data and results for the horizontal vibration EIh 1.088xl0 1KNm2 Eh 2.901 xl09 N/m2 &Hp 0/m WHO 0/s WH 0.2570/s VH1 0.443(0.5826)/s “H2 0.922(1.606) /s ( ): When only bending rigidity is considered Table 3 Numerical data and results for the longitudinal vibration EA 1.108X 1013N Ei. 2.462xl09 N/m2 WL0 0/s w* (= wLi) 1.190/s (Miss A) Table 21:^1-. (mm g Eb) ©@Wi81lSC& Table 3CST. Tfritvtcmk (iaag 6) i:ovvrFEM##&fTt\ b'ictet^T, Fig.i2ic^f J:t>fi£*ymroESb t— w < w0roWitiilC43HTtt, $1'fc)9»Sci Table 2,31: Fig. 12 Eigen vibration modes for the floating structure on an elastic foundation >Tt-f * f• ifii(Xitii®jro IM Aj Si ®j Sc t: ft: fi -T 3 & 2SS rt* * &. 297 9 #Ss 3) Toki, N. : A Study on the Behavior of Huge Float ing Structure in Regular Waves, Journal of Soci @*s#*siet4$E±ro$tce€ ety of Naval Architects of Japan, Vol. 146(1979), mx.zztiz£v, mmf# pp. 185-194. *6©fl,v^tii75: VfcS*^S#: SSEiSWA 178 # (1995), pp.399-403. 6) WBS-6R : j@:*S!#*<0#m$m43«k Mfcftf), mR*3ER##kmiBfK*6A5. 178 # (1995), pp.473 —483. 3. 3#=#m©%#!:T5*&»*m2:LT. &R^E* 7) Wffl$-ei5 : E*SU#«:C0®S^1,43 j; «T(oss#tt*ia^±tf5c^ttssTss. f ©2 : E**TH**0#aKK^E/'(7/-^6AQ. «4r @LA«7c#&cx#mis#©mf— , AW14«;!6tt14j£SSc3:ffl ViTSStl-S. 163CS, * 179 # (1996), pp. 339 —348. s) m&mm, xmwK : -^tewes*^ 4. &K3EK«* S4PI=J;eE±@##:©m&6#mi6###r, B* m 179 # (me), pp. 349 -358 . fFttiEtoa-T, **SR©S##14 (#m) a##AfN=j: 9 ) «sm, #«sb, WBistt: 6T££oTV^. Proc. 5. &%3ER@(*T Techno-Ocean ’96 International Symposium, Vol. II (1996), pp.651 - 656. o la it tt m n a w- n « a e, & v >. Appendix 6. $eSiBTHS6i8©:b©^*feEL< 86 sse@intcoviT$ij#q^*-9-A. as (41) $#^A. A.l pAut 2 < kc(0 7. tttfJEASEC-oviTtt, *«6l^©6C6T#-m AS (31) £«OA. Xc = Ci cos -^=27 cosh -7=27 + C% cos —px sinh -px 5E©Eft©B#CSA®i|>atttf-i7e$i:D, t©l8©J6 i /-< • ky ky . ky . ky Am#A$&*©i#i2#© 1/2#T$5 (S (42)(43)#E). +C3 sin —=x cosh —=27 + Ci sin —-rsinh —=27 8. #A£#14Sii£A#x5ASB»;WS»i©BWiBl» ■s/2 s/2 V2 V2 F cos kx i^T*5pffl8JSft©0t (44) EIki + (&-)4 m## A L%a< L AT^TA-mM* V C ky ky ky . ky As = Si cos —=27 cosh —=27 + 02 cos —=27 smh —px \/2 \/2 \/2 tt>J £ b T5R U & H fe'£43 5 £ # m * m 9 2*c r, —x2 r/n' i ^u> — =(ky) {C4COS^CO«h^ 1) sst§, *$: StCOOT — #i5©ef5E®Jt6l — , |g 13 @ ##% —, ky , ky . ky fcy f'»4 lgi = (AJ2{S4COS^CO.h^ d2Xc : (A+ )2{Ei cosh k*x + C2 sinh A4x dx2 — C% cosAp - Ci sinAp} - ~ ^ co&kx ^52j , n ^U) • , t-i . kw , k^j +i>3 cos —pix sinh ——x — S2 sin —=x cosh -r=x s/2 s/2 V2 V2 ei k* - (ki)4 d2Xs „ . ku . kw F k2 sin fca; =■ (A+)2{Si coshAp + S2 sinh A+x — Si sin -=xsinh —7=®} — (48) V2 V2 El fe4 + (fcp dx2 „ 7+ C - 7+ 1 E k2 sin kx . cA = cosh -p, sA = sinh ^=Z - S3 cos k+x-S4 sin * J®} - ^fc+ 4 (53) s/2 s/2 cA = cosh A4 Z, sA = sinh fej Z _ kijj , _ . ku C — COS —=1, S =r sin —7=i V2 V2 c = cos Ap s = sin A4 Z (iiSiS6ftro»-er) C4 - I p El k4 + (k~)4 Ei = {s2 + sA2 — 2(ssA) cos kl Ei = {ccA + ssA — 1 + (c — cA) cos kl sA2 — s2 2(ccA — 1) +V2 ^"p ) (c«A — scA) sin AZ} + ( ^jT ) (s ~ sh) sin kl} Ci 2 {—(cs + cAsA) 4- (csA 4- scA) cos AZ C13 E = E2 = {—(csh + sch) 4- ($ 4- sh) cos kl sh2 — s2 2(ccA — 1) +V2 j ^ ) (ssA) sin AZ}, C3 = C2 - ( -j-qr ] (c - ch) sin kl} Eli! Si = - -- {(cs — chsh 4- (csA — scA) cos kl) E3 = {—ccA 4- ssh 4- 1 + (c — ch) cos kl 2(ccA — 1) X ( —^ ) + V2(ssA) sin AZ} 4- I — I (s — sh) sin kl}, Ci = C2 S2 = , \ { (sA2 + (ssA) cos AZ) ^ — E13 Si {(—csA 4- sch 4- (— s sA2 — s2 2(ccA — 1) csA + scA . ------smAZ} 4-sA) cos AZ) 1 4- (c — cA) sin kl} 5,3 = 3^"{($2+(ssh)c°ski) fp E13 S2 = {(ccA — ssA — 1 4- (c 2(cch — 1) csA + scA sinAZ}, S4 = 0 -cA) cos kl) ( — J 4- (s 4- sA) sinAZ}, S3 — Si VT” At2 pAcu 2 > AC %c = Ei cosh Ap 4- C2 sinh Ap 4- C’3 cos A+ a -ch) cos kl) ( ) 4- (s 4- sA) sin kl} + C4sinfc+*+ —fc4_(fcJ)4 (49) Xs = Si cosh Ap 4- S2 sinh A4 x + S3 cos A+ x F sin kx + S4 sin k + x + (50) El k4 - (&+)" fc+ = f ~ ^ (51) " - \ El 299 3-4 b ie* jf s TEm m m m tm* A Basic Investigation on Deflection Wave Propagation and Strength of Very Large Floating Structures by Takashi Tsubogo, Member Hiroo Okada, Member Summary Recently many studies on the elastic response behavior of very large floating structures have been done. Such a very large structure is relatively flexible compared with other existing floating structures like large ships. For estimating the dynamic response behavior of structure, it is important to consider the deflection wave propagation based on fluid-structure interaction analysis. This paper deals with the dynamic response and strength of VLFS except peripheral part considering deflection wave propagation for the simple beam or plate model in regular waves. From analytical results considering fluid-structure interaction, effects of wave length and direction of incident waves on the response and strength are examined. Moreover, the dispersion relation of the deflection wave is also calculated. i m m T©Stfi, 6©E#ic=kO