Iowa State University Capstones, Theses and Retrospective Theses and Dissertations Dissertations 2003 Flow-induced vibration of elastically supported rectangular cylinders Jeffrey L. Garrett Iowa State University Follow this and additional works at: https://lib.dr.iastate.edu/rtd Part of the Civil Engineering Commons Recommended Citation Garrett, Jeffrey L., "Flow-induced vibration of elastically supported rectangular cylinders " (2003). Retrospective Theses and Dissertations. 713. https://lib.dr.iastate.edu/rtd/713 This Dissertation is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Retrospective Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. Flow-induced vibration of elastically supported rectangular cylinders by Jeffrey L. Garrett A dissertation submitted to the graduate faculty in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Major: Civil Engineering (Structural Engineering) Program of Study Committee: Lowell F. Greimann, Co-major Professor Partha P. Sarkar, Co-major Professor Fouad S. Fanous Terry J. Wipf Loren W. Zachary Iowa State University Ames, Iowa 2003 UMI Number: 3118227 INFORMATION TO USERS The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleed-through, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. UMI UMI Microform 3118227 Copyright 2004 by ProQuest Information and Learning Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. ProQuest Information and Learning Company 300 North Zeeb Road P.O. Box 1346 Ann Arbor, Ml 48106-1346 ii Graduate College Iowa State University This is to certify that the doctoral dissertation of Jeffrey L. Garrett has met the dissertation requirements of Iowa State University Signature was redacted for privacy. Committee Member Signature was redacted for privacy. Committee Member Signature was redacted for privacy. Committee M ber Signature was redacted for privacy. Co-major Professor Signature was redacted for privacy. o- ajor Professor Signature was redacted for privacy. For the Major Program iii DEDICATION I wish to dedicate the entire academic endeavor summarized in this dissertation to my Dad, Ross B., and to the memory of my Mother, Evelyn. Because the two of them understood the value of education, I spent my entire childhood knowing that I would attend college and I have spent my entire adult life, thus far, benefiting from their wisdom and foresight. Their love, support, encouragement and, sometimes forceful but necessary, insistence have made my life possible. iv TABLE OF CONTENTS LIST OF FIGURES vi LIST OF TABLES ix ACKNOWLEDGMENTS xv CHAPTER 1. INTRODUCTION 1 1.1. Background 1 1.2. Objective 5 1.3. Approach 6 1.4. Scope of Work 6 CHAPTER 2. LITERATURE REVIEW: BLUFF BODY AERODYNAMICS 9 2.1. Introduction 9 2.2. Vortex Induced Vibration 11 2.3. Circular Cylinders 20 2.4. Stationary Rectangular Cylinders 30 2.5. Elastically Supported Rectangular Cylinders 40 2.6. Summary 55 CHAPTER 3. LITERATURE REVIEW: WIND ENGINEERING 58 3.1. Introduction 58 3.2. Wind Engineering 58 3.3. Metal Fatigue 64 3.4. Dynamic Response of Linear SDOF System 67 3.5. Statistics of Linear Systems 69 3.6. Wind-Induced Fatigue 73 CHAPTER 4. EXPERIMENTAL SETUP AND PROCEDURES 80 4.1. Objectives 80 4.2. Test Models 81 4.3. Wind Tunnel 85 4.4. Force-Balance System 86 4.5. Electronic Data Acquisition 89 4.6. Experimental Procedure 91 V CHAPTER 5. RESULTS AND DISCUSSION 100 5.1. Introduction 100 5.2. Wind-Induced Vibrations 101 5.3. Modified Strouhal Numbers 110 5.4. Scruton Numbers 114 CHAPTER 6. CONCLUSION 158 6.1. Introduction 158 6.2. Vortex-Induced Vibrations 159 6.3. Modified Strouhal Number 160 6.4. Scruton Number for Rectangular Cylinders 161 6.5. Response Equation 161 6.6. Future Work 162 APPENDIX A. FAN SPEED CALIBRATION 164 APPENDIX B. SYSTEM MASS, STIFFNESS & FREQUENCY 166 APPENDIX C. SYSTEM DAMPING 176 APPENDIX D. SCRUTON NUMBER 182 APPENDIX E. WIND SPEED AND AMPLITUDE DATA 188 APPENDIX F. ELECTRONIC DATA 235 REFERENCES 280 vi LIST OF FIGURES FIGURE 1.1. Advertising sign elevation 2 FIGURE 1.2. Detail of failed connection 3 FIGURE 1.3. Detail of failed connection 4 FIGURE 2.1. Flow around a bluff body 13 FIGURE 2.2. Lock-in region 19 FIGURE 2.3. Vortex shedding regimes 21 FIGURE 2.4. Strouhal number for circular cylinder 22 FIGURE 2.5. Plot of Equation 2.14 30 FIGURE 2.6. Strouhal numbers for rectangular cylinders 37 FIGURE 2.7. Strouhal number based on body length, L 39 FIGURE 2.8. Cross-flow vibrations, L/D = 2.0 44 FIGURE 2.9. Cross-flow vibrations, L/D = 4.0 45 FIGURE 2.10. Response curves, 2 < L/D < 5 47 FIGURE 2.11. Reduced velocity at peak amplitudes 48 FIGURE 2.12. Critical reduced velocities 49 FIGURE 2.13. Cross-flow response, 1 <L/D < 8 51 FIGURE 2.14. Cross-flow response 54 FIGURE 2.15. Cross-flow response 57 FIGURE 3.1. Durst chart 59 FIGURE 3.2. von Kârmân-Harris wind spectrum 62 FIGURE 3.3. Turbulence parameters 63 vii FIGURE 3.4. Typical S-N curves for mild steel and aluminum 66 FIGURE 4.1. Cross-Section through model 84 FIGURE 4.2. Control station, Bill James Wind Tunnel 86 FIGURE 4.3. Schematic diagram of test set-up 87 FIGURE 4.4. Force-balance system with model in place 88 FIGURE 4.5. Fan speed vs. wind speed calibration 93 FIGURE 5.1. Amplitude vs. wind speed, L/D = 2.0 129 FIGURE 5.2. Amplitude vs. wind speed, L/D = 2.0 130 FIGURE 5.3. Amplitude vs. wind speed, L/D = 3.0 131 FIGURE 5.4. Amplitude vs. wind speed, L/D = 4.0 132 FIGURE 5.5. Amplitude vs. wind speed, L/D = 5.0 133 FIGURE 5.6. Amplitude vs. wind speed, L/D = 5.5 134 FIGURE 5.7. Amplitude vs. wind speed, L/D = 6.0 135 FIGURE 5.8. Amplitude vs. wind speed, L/D = 6.5 136 FIGURE 5.9. Amplitude vs. wind speed, L/D = 7.0 137 FIGURE 5.10. Reduced amplitude vs. reduced velocity, L/D = 2.0 138 FIGURE 5.11. Reduced amplitude vs. reduced velocity, L/D = 3.0 139 FIGURE 5.12. Reduced amplitude vs. reduced velocity, L/D = 4.0 140 FIGURE 5.13. Reduced amplitude vs. reduced velocity, L/D = 5.0 141 FIGURE 5.14. Reduced amplitude vs. reduced velocity, L/D = 5.5 142 FIGURE 5.15. Reduced amplitude vs. reduced velocity, L/D = 6.0 143 FIGURE 5.16. Reduced amplitude vs. reduced velocity, L/D = 6.5 144 FIGURE 5.17. Reduced amplitude vs. reduced velocity, L/D = 7.0 145 viii FIGURE 5.18. Modified Strouhal number vs. aspect ratio, L/D 146 FIGURE 5.19. Reduced velocity vs. aspect ratio, L/D 147 FIGURE 5.20. Maximumyo/D vs. L/D and St„ 148 FIGURE 5.21. Reduced amplitude vs. Scl 149 FIGURE 5.22. Reduced amplitude vs. Sc2 150 FIGURE 5.23. Reduced amplitude vs.(Scl)(L/D) 151 FIGURE 5.24. Reduced amplitude vs.(Sc2)(L/D) 152 FIGURE 5.25. Reduced amplitude vs. Sc, circular cylinders 153 FIGURE 5.26. Maximum reduced amplitude vs. x for Scl 154 FIGURE 5.27. Maximum reduced amplitude vs. x for Sc2 155 FIGURE 5.28. Reduced amplitude vs. Sc(r), rectangular cylinders 156 FIGURE 5.29. Response equation curve, rectangular cylinders 157 FIGURE A.l. Fan speed vs. wind speed calibration 165 ix LIST OF TABLES TABLE 4.1. Model dimensions 82 TABLE 4.2. Model properties, L/D = 2.0 96 TABLE 4.3. Model properties, L/D = 3.0 96 TABLE 4.4. Model properties, L/D = 4.0 97 TABLE 4.5. Model properties, L/D = 5.0 97 TABLE 4.6. Model properties, L/D = 5.5 98 TABLE 4.7. Model properties, L/D = 6.0 98 TABLE 4.8. Model properties, L/D = 6.5 99 TABLE 4.9. Model properties, L/D = 7.0 99 TABLE 5.1. Range of Reynolds numbers 101 TABLE 5.2. Range of Vr during lock-in 109 TABLE 5.3. Maximum reduced amplitudes 110 TABLE 5.4. Modified Strouhal numbers Ill TABLE 5.5. Response equation constants 121 TABLE 5.6. Rectangular Scruton number, Sc(r), L/D = 2.0 125 TABLE 5.7. Rectangular Scruton number, Sc(r), L/D = 3.0 125 TABLE 5.8. Rectangular Scruton number, Sc(r), L/D = 4.0 126 TABLE 5.9. Rectangular Scruton number, Sc(r), L/D = 5.0 126 TABLE 5.10. Rectangular Scruton number, Sc(r), L/D = 5.5 127 TABLE 5.11. Rectangular Scruton number, Sc(r), L/D = 6.0 127 TABLE 5.12. Rectangular Scruton number, Sc(r), L/D = 6.5 128 X TABLE 5.13. Rectangular Scruton number, Sc(r), L/D = 7.0 128 TABLE A.l. Fan speed vs. wind speed 165 TABLE B.l. Recorded frequencies, L/D = 2.0 168 TABLE B.2. Recorded frequencies, L/D = 3.0 168 TABLE B.3. Recorded frequencies, L/D = 4.0 169 TABLE B.4.