applied sciences Article Control Performances of Friction Pendulum and Sloped Rolling-Type Bearings Designed with Single Parameters Shiang-Jung Wang 1,* , Yi-Lin Sung 1, Cho-Yen Yang 2, Wang-Chuen Lin 2 and Chung-Han Yu 2 1 Department of Civil and Construction Engineering, National Taiwan University of Science and Technology, Taipei 106335, Taiwan; [email protected] 2 National Center for Research on Earthquake Engineering, Taipei 106219, Taiwan; [email protected] (C.-Y.Y.); [email protected] (W.-C.L.); [email protected] (C.-H.Y.) * Correspondence: [email protected]; Tel.: +886-2-27303650 Received: 9 September 2020; Accepted: 13 October 2020; Published: 15 October 2020 Abstract: Owing to quite different features and hysteretic behavior of friction pendulum bearings (FPBs) and sloped rolling-type bearings (SRBs), their control performances might not be readily compared without some rules. In this study, first, on the premise of retaining the same horizontal acceleration control performance, the effects arising from different sloping angles and damping forces on the horizontal maximum and residual displacement responses of SRBs are numerically examined. For objective comparison of passive control performances of FPBs and SRBs, then, some criteria are considered to design FPBs with the same horizontal acceleration control performance by referring to the designed damping force and the maximum horizontal displacement response of SRBs under a given seismic demand. Based on the considered criteria, the passive control performances of FPBs and SRBs under a large number of far-field and pulse-like near-fault ground motions are quantitatively compared. The numerical comparison results indicate that the FPB models might potentially have better horizontal acceleration and isolation displacement control performances than the SRB models regardless of whether they are subjected to far-field or near-fault ground motions, while the opposite tendency is observed for their self-centering performances, especially when the SRB model designed with a larger sloping angle or a smaller damping force. Keywords: friction pendulum bearing; sloped rolling-type bearing; numerical comparison; control performance; self-centering 1. Introduction 1.1. Literature Review On a theoretical basis, the satisfactory seismic performances of friction pendulum bearings (FPBs) and sloped rolling-type bearings (SRBs) have been demonstrated separately in many past numerical and experimental studies [1,2]. Well-developed analytical models, including simplified and sophisticated ones, have also been proposed and verified to be capable of predicting the dynamic behavior of FPBs and SRBs, accordingly. Currently, FPBs and SRBs, the former in particular, have been widely applied in engineering practice for seismically protecting critical structures, facilities, and equipment to guarantee their desired functionality during and after earthquakes. FPBs designed with a single curvature radius and friction coefficient [3–6], as illustrated in Figure1a, undoubtedly, possess a very simple and reliable mechanism together with idealized bilinear hysteretic behavior, as shown in Figure2. The details about the unique features of FPBs and the notations presented in the figures will be further explained in Section 1.2. In the past few decades, Appl. Sci. 2020, 10, 7200; doi:10.3390/app10207200 www.mdpi.com/journal/applsci Appl. Sci. 2020, 10, x FOR PEER REVIEW 2 of 20 the notations presented in the figures will be further explained in Section 1.2. In the past few decades, in addition to adjusting the design parameters of FPBs for better estimating and enhancing their controlAppl. performances Sci. 2020, 10, x FOR [7],PEER there REVIEW have also been many studies on mechanically modifying2 of 20 and upgradingAppl. Sci. FPBs2020, 10 ,to 7200 offer designers greater flexibility to optimize their performance as 2much of 21 as possiblethe notationsat different presented design in thestages. figure Thes will FPBs, be further which explained can individually in Section 1.2. or In simultaneously the past few decades, present in addition to adjusting the design parameters of FPBs for better estimating and enhancing their variablein addition energy to dissipation adjusting the and design different parameters stiffness of FPBs (or forrestoring better estimating force) capabilities and enhancing by correspondingly their control control performances [7], there have also been many studies on mechanically modifying and designingperformances different [7], friction there have coefficients also been manyand varyin studiesg on curvature mechanically radii, modifying such as and the upgrading so-called FPBs double, upgrading FPBs to offer designers greater flexibility to optimize their performance as much as triple,to oandffer designerseven quintuple greater flexibilityFPBs, were to optimize analytic theirally performance and experimentally as much as possiblestudied atby di ffFenzerent and possible at different design stages. The FPBs, which can individually or simultaneously present Constantinoudesign stages. [8,9], The Kim FPBs, YS which and Yu can CB individually [10], Calvi or et simultaneously al. [11], Panchal present and variable Jangid energy[12], Bao dissipation and Becker variable energy dissipation and different stiffness (or restoring force) capabilities by correspondingly and different stiffness (or restoring force) capabilities by correspondingly designing different friction [13], anddesigning Lee and different Constantinou friction coefficients [14]. Besides and concave varying slidingcurvature surface radii, suchdesigns, as the Lu so-called et al. [15] double, and Saha coefficients and varying curvature radii, such as the so-called double, triple, and even quintuple FPBs, et al. triple,[16] analytically and even quintupleand experimentally FPBs, were studied analytic someally andcomplicated experimentally polynomial studied functions by Fenz designed and were analytically and experimentally studied by Fenz and Constantinou [8,9], Kim YS and Yu CB [10], for theConstantinou sliding surfaces [8,9], Kimof FPBs YS and so as Yu to CB present [10], Calvi variable et al. stiffness[11], Panchal properties and Jangid and [12], thus Bao achieve and Becker multiple Calvi et al. [11], Panchal and Jangid [12], Bao and Becker [13], and Lee and Constantinou [14]. Besides design[13], objectives. and Lee and Furthermore, Constantinou in [14]. addition Besides to concave studyi slidingng the surfaceunilateral designs, behavior Lu et al.of [15]double and Sahaor triple concave sliding surface designs, Lu et al. [15] and Saha et al. [16] analytically and experimentally studied FPBs,et their al. [16] multi-axial analytically behavior and experimentally was thoroughly studied stud someied complicatedby Panchal etpolynomial al. [17], Becker functions and designed Mahin [18], some complicated polynomial functions designed for the sliding surfaces of FPBs so as to present Sah andfor the Soni sliding [19], surfaces and Furinghetti of FPBs so etas toal. present [20]. Some variable research stiffness results properties indicated and thus that achieve the effect multiple arising variable stiffness properties and thus achieve multiple design objectives. Furthermore, in addition to design objectives. Furthermore, in addition to studying the unilateral behavior of double or triple fromstudying vertical theexcitations unilateral on behavior the horizontal of double seismic or triple performance FPBs, their multi-axial of double behavior or triple wasFPBs thoroughly might not be FPBs, their multi-axial behavior was thoroughly studied by Panchal et al. [17], Becker and Mahin [18], negligiblestudied for by obtaining Panchal et more al. [17 accurate], Becker and and conservative Mahin [18], Sah design and Soniresults [19 ],[21,22]. and Furinghetti Recently, et not al. only [20]. far- Sah and Soni [19], and Furinghetti et al. [20]. Some research results indicated that the effect arising field Someground research motions results but indicated the so-called that the pulse-like effect arising near-fault from vertical ones were excitations also onconsidered the horizontal in many from vertical excitations on the horizontal seismic performance of double or triple FPBs might not be relevantseismic studies performance to propose of doublethe corresponding or triple FPBs design might strategies not be negligible for FPBs for [12,23]. obtaining The more post-earthquake accurate negligible for obtaining more accurate and conservative design results [21,22]. Recently, not only far- and conservative design results [21,22]. Recently, not only far-field ground motions but the so-called self-centeringfield ground capability motions of but double the so-called or triple pulse-like FPBs, which near-fault is another ones importantwere also consideredperformance in manyindex for pulse-like near-fault ones were also considered in many relevant studies to propose the corresponding seismicrelevant isolation studies andto propose will thesignificantly corresponding affect design serviceability strategies for FPBs and [12,23]. functionality The post-earthquake of isolated design strategies for FPBs [12,23]. The post-earthquake self-centering capability of double or triple superstructuresself-centering andcapability nonstructural of double orcomponents triple FPBs, which (or issystems) another importantcrossing performance isolation indexlayers for after FPBs, which is another important performance index for seismic isolation and will significantly