Dynamics of Civil Structures, Volume 2

River Rapids Conference Proceedings of the Society for Experimental Mechanics Series Dynamics of Civil Structures, Volume 2 Juan Caicedo Shamim Pakzad Proceedings of the 35th IMAC, A Conference and Exposition on Structural Dynamics 2017 River Publishers

Conference Proceedings of the Society for Experimental Mechanics Series Series Editor Kristin B. Zimmerman, Ph.D. Society for Experimental Mechanics, Inc., Bethel, CT, USA

River Publishers Juan Caicedo • Shamim Pakzad Editors Dynamics of Civil Structures, Volume 2 Proceedings of the 35th IMAC, A Conference and Exposition on Structural Dynamics 2017

Published, sold and distributed by: River Publishers Broagervej 10 9260 Gistrup Denmark www.riverpublishers.com ISBN 978-87-7004-947-4 (eBook) Conference Proceedings of the Society for Experimental Mechanics An imprint of River Publishers © The Society for Experimental Mechanics, Inc. 2017 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, or reproduction in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Preface Dynamics of Civil Structures represents one of ten volumes of technical papers presented at the 35th IMAC, A Conference and Exposition on Structural Dynamics, organized by the Society for Experimental Mechanics, and held in Garden Grove, California, January 30–February 2, 2017. The full proceedings also include volumes on Nonlinear Dynamics; Model Validation and Uncertainty Quantification; Dynamics of Coupled Structures; Sensors and Instrumentation; Special Topics in Structural Dynamics; Structural Health Monitoring and Damage Detection; Rotating Machinery, Hybrid Test Methods, Vibro-Acoustics & Laser Vibrometry; Shock & Vibration, Aircraft/Aerospace and Energy Harvesting; and Topics in Modal Analysis & Testing. Each collection presents early findings from analytical, experimental, and computational investigations on an important area within structural dynamics. Dynamics of Civil Structures is one of these areas which cover topics of interest of several disciplines in engineering and science. The Dynamics of Civil Structures Technical Division serves as a primary focal point within the SEM umbrella for technical activities devoted to civil structure analysis, testing, monitoring, and assessment. This volume covers a variety of topics including damage identification, human-structure interaction, hybrid testing, vibration control, model updating, modal analysis of in-service structures, sensing and measurements of structural systems, and bridge dynamics. Papers cover testing and analysis of all kinds of civil engineering structures such as buildings, bridges, stadiums, dams, and others. The organizers would like to thank the authors, presenters, session organizers, and session chairs for their participation in this track. Columbia, SC, USA Juan Caicedo Bethlehem, PA, USA Shamim Pakzad v

Contents 1 Semi-Active Base Isolation of Civil Engineering Structures Based on Optimal Viscous Damping and Zero Dynamic Stiffness ............................................................................................ 1 Felix Weber, Hans Distl, and Christian Braun 2 Long-Term Performance of Specialized Fluid Dampers Under Continuous Vibration on a Pedestrian Bridge..................................................................................................................... 11 Alan R. Klembczyk 3 Analysis of Variation Rate of Displacement to Temperature of Service Stage Cable-Stayed Bridge Using Temperatures and Displacement Data......................................................................... 21 Hyun-Joong Kim 4 Triple Friction Pendulum: Does It Improve the Isolation Performance? ......................................... 27 Felix Weber, Peter Huber, Hans Distl, and Christian Braun 5 Experimental Investigation of the Dynamic Characteristics of a Glass-FRP Suspension Footbridge ......... 37 Xiaojun Wei, Justin Russell, Stana Živanovic´, and J. Toby Mottram 6 Vibration-Based Occupant Detection Using a Multiple-Model Approach........................................ 49 Yves Reuland, Sai G. S. Pai, Slah Drira, and Ian F. C. Smith 7 Vibration Assessment and Control in Technical Facilities Using an Integrated Multidisciplinary Approach.................................................................... 57 Nicholas Christie, James Hargreaves, Rob Harrison, and Francois Lancelot 8 Iterative Pole-Zero Model Updating Using Multiple Frequency Response Functions........................... 65 M. Dorosti, R.H.B. Fey, M.F. Heertjes, M.M.J. van de Wal, and H. Nijmeijer 9 Vision-Based Concrete Crack Detection Using a Convolutional Neural Network ............................... 71 Young-Jin Cha and Wooram Choi 10 Analytical and Experimental Analysis of Rocking Columns Subject to Seismic Excitation .................... 75 Ryan Kent Giles and Thomas John Kennedy 11 Extending the Fixed-Points Technique for Optimum Design of Rotational Inertial Tuned Mass Dampers... 83 Abdollah Javidialesaadi and Nicholas Wierschem 12 Temperature Effects on the Modal Properties of a Suspension Bridge............................................ 87 Etienne Cheynet, Jonas Snæbjörnsson, and Jasna Bogunovic´ Jakobsen 13 Mass Scaling of Mode Shapes Based on the Effect of Traffic on Bridges: A Numerical Study ................. 95 M. Sheibani, A.H. Hadjian-Shahri, and A.K. Ghorbani-Tanha 14 Covariance-Driven Stochastic Subspace Identification of an End-Supported Pontoon Bridge Under Varying Environmental Conditions.................................................................................... 107 Knut Andreas Kvåle, Ole Øiseth, and Anders Rönnquist vii

viii Contents 15 Probabilistic Analysis of Human-Structure Interaction in the Vertical Direction for Pedestrian Bridges .... 117 Federica Tubino 16 Effects of Seismic Retrofit on the Dynamic Properties of a 4-Storey Parking Garage........................... 121 Ilaria Capraro and Carlos E. Ventura 17 Analytical and Experimental Study of Eddy Current Damper for Vibration Suppression in a Footbridge Structure.................................................................................................... 131 Wai Kei Ao and Paul Reynolds 18 Nonlinear Damping in Floor Vibrations Serviceability: Verification on a Laboratory Structure.............. 139 OnurAvci 19 Addressing Parking Garage Vibrations for the Design of Research and Healthcare Facilities................. 147 Brad Pridham, Nick Walters, Luke Nelson, and Brian Roeder 20 Modeling and Measurement of a Pedestrian’s Center-of-Mass Trajectory ....................................... 159 Albert R. Ortiz, Bartlomiej Blachowski, Pawel Holobut, Jean M. Franco, Johannio Marulanda, and Peter Thomson 21 Evaluation of Mass-Spring-Damper Models for Dynamic Interaction Between Walking Humans and Civil Structures ..................................................................................................... 169 Ahmed S. Mohammed and Aleksandar Pavic 22 Numerical Model for Human Induced Vibrations ................................................................... 179 Marcello Vanali, Marta Berardengo, and Stefano Manzoni 23 Dynamic Testing on the New Ticino Bridge of the A4 Highway.................................................... 187 Elena Mola, Franco Mola, Alfredo Cigada, and Giorgio Busca 24 Predicting Footbridge Vibrations Using a Probability-Based Approach.......................................... 197 Lars Pedersen and Christian Frier 25 Flooring-Systems and Their Interaction with Usage of the Floor.................................................. 205 Lars Pedersen, Christian Frier, and Lars Andersen 26 Benchmark Problem for Assessing Effects of Human-Structure Interaction in Footbridges................... 213 S. Gómez, J. Marulanda, P. Thomson, J. J. García, D. Gómez, Albert R. Ortiz, S. J. Dyke, J. Caicedo, and S. Rietdyk 27 A Discrete-Time Feedforward-Feedback Compensator for Real-Time Hybrid Simulation..................... 223 Saeid Hayati and Wei Song 28 Sensing and Rating of Vehicle–Railroad Bridge Collision .......................................................... 227 Shreya Vemuganti, Ali Ozdagli, Bideng Liu, Anela Bajric, Fernando Moreu, Matthew R. W. Brake, and Kevin Troyer 29 High-Frequency Impedance Measurements for Microsecond State Detection ................................... 235 Ryan A. Kettle, Jacob C. Dodson, and Steven R. Anton 30 Structural Stiffness Identification of Skewed Slab Bridges with Limited Information for Load Rating Purpose................................................................................................ 243 Abdollah Bagheri, Mohamad Alipour, Salman Usmani, Osman E. Ozbulut, and Devin K. Harris 31 Online Systems Parameters Identification for Structural Monitoring Using Algebraic Techniques........... 251 L.G. Trujillo-Franco, G. Silva-Navarro, and F. Beltrán-Carbajal 32 Structural Vibration Control Using High Strength and Damping Capacity Shape Memory Alloys........... 259 Soheil Saedi, Farzad S. Dizaji, Osman E. Ozbulut, and Haluk E. Karaca 33 Comparative Study on Modal Identification of a 10 Story RC Structure Using Free, Ambient and Forced Vibration Data ............................................................................................. 267 Seyedsina Yousefianmoghadam, Andreas Stavridis, and Babak Moaveni

Contents ix 34 Kronecker Product Formulation for System Identification of Discrete Convolution Filters.................... 277 Lee Mazurek, Michael Harris, and Richard Christenson 35 Calibration-Free Footstep Frequency Estimation Using Structural Vibration................................... 287 Mostafa Mirshekari, Pei Zhang, and Hae Young Noh 36 Optimal Bridge Displacement Controlled by Train Speed on Real-Time......................................... 291 Piyush Garg, Ali Ozdagli, and Fernando Moreu 37 System Identification and Structural Modelling of Italian School Buildings ..................................... 301 Gerard O’Reilly, Ricardo Monteiro, Daniele Perrone, Igor Lanese, Matthew Fox, Alberto Pavese, and Andre Filiatrault 38 Investigation of Transmission of Pedestrian-Induced Vibration into a Vibration-Sensitive Experimental Facility ................................................................................................... 305 Donald Nyawako, Paul Reynolds, Emma J. Hudson 39 An Ambient Vibration Test of an R/C Wall of an 18-Story Wood Building at the UBC Campus .............. 315 Yavuz Kaya, Carlos E. Ventura, and Alireza Taale 40 The Day the Earth Shook: Controlling Construction-Induced Vibrations in Sensitive Occupancies.......... 321 Michael J. Wesolowsky, Melissa W.Y. Wong, Todd A. Busch, and John C. Swallow 41 An Exploratory Study on Removing Environmental and Operational Effects Using a Regime-Switching Cointegration Method ............................................................................ 329 Haichen Shi, Keith Worden, and Elizabeth J. Cross 42 Evaluation of Contemporary Guidelines for Floor Vibration Serviceability Assessment ....................... 339 Zandy O. Muhammad, Paul Reynolds, and Emma J. Hudson 43 Excitation Energy Distribution of Measured Walking Forces...................................................... 347 Atheer F. Hameed and Aleksandar Pavic 44 Identification of Human-Induced Loading Using a Joint Input-State Estimation Algorithm.................. 353 Katrien Van Nimmen, Kristof Maes, Peter Van den Broeck, and Geert Lombaert

Chapter 1 Semi-Active Base Isolation of Civil Engineering Structures Based on Optimal Viscous Damping and Zero Dynamic Stiffness Felix Weber, Hans Distl, and Christian Braun Abstract Spherical friction pendulums (FP) represent the common approach to isolate civil engineering structures against earthquake excitation. As these devices are passive and friction damping is nonlinear the optimal friction coefficient for minimum absolute acceleration of the building depends on the peak ground acceleration (PGA). Therefore, the common procedure is to optimize the friction coefficient for the PGA of the design basis earthquake (DBE) and to verify by simulations that the absolute structural acceleration for the maximum considered earthquake (MCE) is within a tolerable limit which is far from optimal. In order to overcome this drawback of passive FPs, a semi-active FP based on real-time controlled oil damper with the use of the collocated bearing displacement only is described in this paper. Four different semi-active control laws are presented that target to produce controlled dynamic stiffness depending on the actual bearing displacement amplitude in order to control the isolation period in real-time. The desired damping is formulated based on optimal viscous damping taking into account the passive lubricated friction of the spherical surface. The four control laws are compared in terms of absolute structural acceleration, bearing force, bearing displacement and residual bearing displacement. The results point out that the approach of zero dynamic stiffness at center position of the slider and nominal stiffness at design displacement of the FP improves the isolation of the structure within the entire PGA range significantly and at the same time minimize maximum bearing force, maximum bearing displacement and maximum residual bearing displacement. Keywords Control • Damping • Seismic • Semi-active • Negative stiffness 1.1 Introduction Spherical friction pendulums (FP) are widely used to significantly reduce the absolute structural acceleration due to ground excitation by their effective radius that shifts the fundamental time period of the isolated structure into the region of attenuation and their friction damping that augments the damping of the structure [1]. The inherent drawback of FPs is that friction damping is nonlinear whereby the optimal friction coefficient depends on the displacement amplitude of the FP and consequently peak ground acceleration (PGA) [2]. The common approach is therefore to optimize the friction coefficient for the PGA of the design basis earthquake (DBE) and, subsequently, to check if the absolute structural acceleration due to the maximum credible earthquake (MCE) is acceptable. In addition, it must be checked if the isolation of the structure at very small PGAs is acceptable from the comfort point of view since the constant friction coefficient being optimal for the PGA of the DBE may lead to clamping effects in the FP whereby the relative motion stops in the FP and consequently the structural absolute acceleration is equal to the ground acceleration. In order to overcome these drawbacks of FPs several types of adaptive FPs have been developed: FPs with several sliding surfaces with different friction coefficients and effective radii [3] and pendulums that are extended by an external active or semi-active actuator such as hydraulic cylinders and controllable dampers on the basis of oil dampers with controlled bypass valve or magnetorheological fluids [4–7]. Controllable dampers F.Weber ( ) Maurer Switzerland GmbH, Neptunstrasse 25, 8032 Zurich, Switzerland e-mail: F.Weber@maurer.eu H. Distl Maurer Söhne Engineering GmbH & Co. KG, Frankfurter Ring 193, 80807 Munich, Germany e-mail: Distl@maurer.eu C. Braun MAURER SE, Frankfurter Ring 193, 80807 Munich, Germany e-mail: Braun@maurer.eu © The Society for Experimental Mechanics, Inc. 2017 J. Caicedo, S. Pakzad (eds.), Dynamics of Civil Structures, Volume 2, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-54777-0_1 1

2 F. Weber et al. are seen to provide a promising solution as the resulting closed-loop is unconditionally stable and their power consumption is very low compared to hydraulic actuators. This paper describes a novel approach of a semi-active isolator with the following main features: • controlled dynamic stiffness depending on the actual displacement amplitude of the pendulum, • optimum viscous damping, and • collocated control based on one displacement sensor. 1.2 Systems Under Consideration 1.2.1 Friction Pendulum The common way to decouple the building/structure from the shaking ground is to support the building by FPs. The effective radius Reff DR h of the FP is selected to shift the time period T of the non-isolated structure from the region of amplification, i.e. T is typically in the region 0.5–2.0 s, to the region of attenuation with associated isolation time period Tiso of typically 3–4 s. Subsequent to the design of the effective radius the friction coefficient of the sliding surface is optimized for minimum absolute structural acceleration for given Tiso. As friction damping is nonlinear, the optimal value of depends on the bearing displacement amplitude and consequently on PGA. As a result, is commonly optimized for the PGA of the DBE. Finally, the structure with the designed FP is computed for the PGA due to the MCE to check if the absolute structural acceleration resulting from the MCE is acceptable and to know the displacement capacity of the FP that is required for the MCE. 1.2.2 Viscous Pendulum In addition to the passive FP an “ideal” pendulum without friction but with linear viscous damping is considered as benchmark for passive isolators. Its effective radius is equal to that of the FP to ensure the same isolation time period Tiso. Its viscous damping coefficient c is optimized for minimum absolute structural acceleration. Thanks to the linear behavior of viscous dampingthe optimization of c inindependent of the bearing displacement amplitude and therefore independent of PGA. 1.2.3 Semi-Active Isolator The semi-active isolator consists of a passive FP and a semi-active damper that is installed between ground and top bearing plate of the pendulum (Fig. 1.1). The design of the effective radius will be explained in the section “CONTROL LAW” as it is related to the formulation of the control law. The sliding surface of the passive FP is lubricated to minimize the passive and therefore uncontrollable friction damping of the semi-active isolator and thereby to maximize the controllability of the total isolator force. The dissipative force of the semi-active damper is controlled by the electromagnetic bypass valve. The desired control force is computed by the real-time controller based on the measured bearing displacement which is identical to the relative motion between damper cylinder and damper piston. Based on the desired control force a force tracking module computes the valve command signal such that the actual force of the semi-active damper tracks closely its desired counterpart in real-time. 1.3 Modelling Due to the large isolation time period Tiso D3.5 s of the building with isolator the building may be modelled as a single degree-of-freedom system [1]. The according equation of motion becomes ms Rus Ccs .Pus Pu/ Cks .us u/ D ms Rug (1.1)

1 Semi-Active Base Isolation of Civil Engineering Structures Based on Optimal Viscous Damping and Zero Dynamic Stiffness 3 ms ks cs μ us u us .. ug .. semi-active damper controller disp. sensor ground ground cylinder piston spherical hinge valve m h R ground ground Fig. 1.1 Schematic of structure with semi-active isolator where ms, cs, ks denote the modal mass, the viscous damping coefficient and the stiffness of the building, Rus, Pus and us denote the acceleration, velocity and displacement of the structure relative to the ground, Pu and u are the velocity and displacement of the top bearing plate relative to the ground and Rug is the ground acceleration given by the accelerogram of the El Centro North-South earthquake. The mass ms is determined by the typical vertical load of WD6 MN on the isolator, cs D2 s pks ms is computed based on the damping ratio s D1%and ks D24.15 MN/m is selected such that the natural frequency of the building without isolator is 1 Hz representing a typical value for structures that require base isolation. The equation of motion of the top plate of the isolator with mass mand with actual forcef actual semi active of the semi-active oil damper is m RuCfh C W Reff u Dcs .Pus Pu/ Cks .us u/ f actual semi active ms Rug (1.2) where fh is the friction force of the curved sliding surface and W/Reff is the restoring stiffness due to the effective radius Reff DR h of the pendulum. The force fh is modelled by the hysteretic damper modelling approach [8] fh D kh u W pre sliding W sign.Pu/ W sliding (1.3) where kh is the pre-sliding stiffness that is selected two orders of magnitude greater than W/Reff . In case of the passive pendulum without any friction but linear viscous damping fh in (1.2) is replaced by the termc opt Pu where copt denotes the optimal viscous damping coefficient of the isolator. 1.4 Control Law 1.4.1 General Formulation The desired active control force is formulated as follows f desired active D kcontrol uC c opt c Pu W c c 0 kcontrol u W c c <0 (1.4)

4 F. Weber et al. in order to produce: 1. the controlled stiffness kcontrol that is controlled as function of the bearing displacement amplitude Uto compensate for the passive stiffness of the curved surface given by W/Reff and thereby produce zero dynamic stiffness by kcontrol <0 for maximum decoupling of the structure from the ground, and 2. the controlled damping force copt c Pu that dissipates the same amount of damping as resulting from optimal linear viscous damping. The desired optimal viscous damping coefficient copt is reduced by the viscous damping coefficient c that is energy equivalent to the friction damping of the lubricated curved surface [2] c 4 W !iso U (1.5) in order to dissipate the cycle energy of optimal viscous damping. Since c is inversely proportional to the displacement amplitude U of the isolator, i.e. c U 1, c may become greater than c opt at small U which necessitates the distinction of cases in (1.4). Notice that (1.5) represents an approximation because c according to Eq. (1.5) is derived based on the constant isolation radial frequency !iso Dr g Reff (1.6) but the actual frequency of the bearing displacement due to earthquake excitation is time-variant and therefore not detectable in real-time. However, the approximation (1.5) represents a good engineer’s solution as the actual frequency is in the vicinity of !iso. The actual force of the semi-active oil damper can only produce the dissipative forces of the desired active control force f desired active , that is f actual semi active D f desired active W Pu f desired active 0 0 W Pu f desired active <0 (1.7) The formulation (1.7) assumes that control force constraints such as minimum and maximum forces of the semi-active oil damper and control force tracking errors do not exist. Hence, the formulation (1.7) of the semi-active force represents the ideal behavior of a controllable damper. 1.4.2 Adaptive Controlled Stiffness The maximum decoupling of the structure from the shaking ground and therefore minimum absolute structural acceleration Rus C Rug is obtained fromzero dynamic stiffness of the isolator [9]. Since the passive (and positive) stiffness of the isolator is given by W/Reff , the controlled stiffness kcontrol must be negative to reduce the total stiffness ktotal of the isolator to zero under dynamic operation. However, ktotal D0 for the entire bearing displacement range could not re-center the structure sufficiently. Hence, four adaptive stiffness control laws are suggested that produce zero dynamic stiffness either at UD0 or at U Umax due to the MCE: • Control law #1 (CL #1, Fig. 1.2a): The effective radius Reff of the curved surface is 50% of the nominal effective radius Reff nominal generating the targeted isolation time period Tiso D3.5 s. The controlled stiffness is formulated to produce ktotal Dkcontrol CW/Reff DkR eff nominal DW/Reff nominal at UD0 and zero dynamic stiffness, i.e. ktotal D0, at U Umax D0.25 m. Between UD0 and UDUmax the controlled stiffness is a linear function of U. • Control law #2 (CL #2, Fig. 1.2b): The effective radius Reff of the curved surface is 50% of Reff nominal. The controlled stiffness is formulated to produce zero total stiffness at UD0andktotal DW/Reff nominal at U Umax D0.25 m. Between UD0 and UDUmax the controlled stiffness is a linear function of U. • Control law #3 (CL #3, Fig. 1.3a): The effective radius Reff of the curved surface is equal to Reff nominal. The controlled stiffness is formulated to produce ktotal DW/Reff nominal at U D0 and zero dynamic stiffness at U Umax D0.25 m. Between UD0 and UDUmax the controlled stiffness is a linear function of U.

1 Semi-Active Base Isolation of Civil Engineering Structures Based on Optimal Viscous Damping and Zero Dynamic Stiffness 5 0.10 0.15 0.2 0.25 0.3 0.35 stiffness coefficient (kN/m) -2000 -1000 1000 2000 3000 ktotal = kR-eff-nominal 0 0.05 kcontrol ktotal = kcontrol + kR-eff ktotal = 0 kcontrol =kR-eff control law #1 (CL #1) -3000 kcontrol= kR-eff (kR-eff = 0.5kR-eff-nominal) 0 - 0.10 0.15 0.2 0.25 0.3 0.35 stiffness coefficient (kN/m) -2000 -1000 1000 2000 3000 0 0.05 kcontrol ktotal = kcontrol + kR-eff ktotal = 0 -3000 kcontrol = kR-eff (kR-eff = 0.5kR-eff-nominal) 0 kcontrol =kR-eff control law #2 (CL #2) - ktotal = kR-eff-nominal a b bearing displacement amplitude U (m) bearing displacement amplitude U (m) Fig. 1.2 Controlled stiffness and total bearing stiffness due to (a) control law #1 and (b) control law #2 0.10 0.15 0.2 0.25 0.3 0.35 stiffness coefficient (kN/m) -3000 -2000 -1000 1000 2000 3000 ktotal = kR-eff-nominal 0 0 0.05 kcontrol = kR-eff kcontrol ktotal = kcontrol + kR-eff ktotal = 0 kcontrol = 0 (kR-eff = kR-eff-nominal) control law #3 (CL #3) - 0.10 0.15 0.2 0.25 0.3 0.35 stiffness coefficient (kN/m) -3000 -2000 -1000 1000 2000 3000 0 0 0.05 kcontrol ktotal = kcontrol + kR-eff kcontrol = 0 kcontrol = - kR-eff ktotal = 0 (kR-eff = kR-eff-nominal) control law #4 (CL #4) ktotal = kR-eff-nominal a b bearing displacement amplitude U (m) bearing displacement amplitude U (m) Fig. 1.3 Controlled stiffness and total bearing stiffness due to (a) control law #3 and (b) control law #4 • Control law #4 (CL #4, Fig. 1.3b): The effective radius Reff of the curved surface is equal to Reff nominal. The controlled stiffness is formulated to produce zero dynamic stiffness at UD0andktotal DW/Reff nom at U Umax D0.25 m. Between UD0 and UDUmax the controlled stiffness is a linear function of U. The main difference between CL #1 and CL #3 (and between CL #2 and CL #4) is that the maximum (positive) and minimum (negative) controlled stiffness coefficients due to CL #1 (and CL #2) are only 50% of the maximum negative controlled stiffness of CL #3 (and CL #4) due to the different designs of Reff for CL #1 (and CL #2) and CL #3 (and CL #4). The control law leading to smaller controlled stiffness is more suitable for controllable dampers since the emulation of large stiffness with semi-active dampers is inherently combined with the generation of damping that is larger than the desired viscous damping given in (1.4) whereby the actual stiffness and damping of the actual semi-active force are far from their desired counterparts. Detailed information on the emulation errors of desired stiffness and damping with controllable dampers is beyond the scope of this paper but can found in [10]. The main difference between CL #1 (and CL #3) and CL #2 (and CL #4) is that CL #1 (and CL #3) results in zero dynamic stiffness at UDUmax which improves the isolation of the structure at large PGAs due to earthquakes between DBE and MCE while CL #2 (and CL #4) generate zero dynamic stiffness at UD0 which improves the isolation of the structure due to earthquakes up to DBE.

6 F. Weber et al. 1.5 Results 1.5.1 Optimized Friction Pendulums The effective radius of the passive FP is designed to produce the targeted isolation time period Tiso D3.5 s. Given this effective radius the friction coefficient is optimized for minimum max jRus C Rugj for the PGA of the DBE that is assumed to be 5 m/s2 (Fig. 1.4b). The optimization of is also performed for PGAD3.5 m/s2 and PGAD6.5 m/s2 (Fig. 1.4a, c) to demonstrate that the best performance of the optimized FP is only obtained at the PGA value used for optimization highlighted by the green circles Fig. 1.4e. 1.5.2 Pendulum with Optimized Linear Viscous Damping The effective radius of the pendulum is the same as for the FP in order to guarantee equal time periods. The viscous damping coefficient is optimized for minimum max jRus C Rugj (Fig. 1.4d) which does not depend on the PGA of the ground acceleration as can be seen from the linear behavior of max jRus C Rugj as function of PGA depicted in Fig. 1.4e. 1.5.3 Semi-Active Pendulum The isolation performance in terms of absolute structural acceleration of the semi-active pendulum with passive friction of 1.5% (lubricated) resulting from the four suggested control laws is depicted in Fig. 1.5a. The main observations are: • CL #1 and CL #2 perform better than CL #3 and CL #4 because the maximum controlled stiffness of CL #1 and CL #2 are only 50% of the maximum value due to CL #3 and CL #4 whereby the actual stiffness and actual damping produced by the semi-active damper are closer to their desired counterparts for CL #1 and CL #2 than for CL #3 and CL #4; further information on stiffness and damping emulations with semi-active dampers are available in [10]. • CL #1 performs better than CL #2 at large PGAs because CL #1 is formulated to produce zero dynamic stiffness at U Umax D0.25 m whereas CL #2 outperforms CL #1 at smaller PGAs because CL #2 produces zero dynamic stiffness at UD0. In order to select the “best performing control law” not only the maximum reduction of the absolute structural acceleration should be considered but also the maximum force of the isolator (costs!, Fig. 1.5b), the maximum bearing displacement 2.2 2.4 2.6 2.8 0.60 0.62 0.64 0.66 PGA=3.5m/s2 PGA=6.5m/s2 µ (%) 3.4 3.6 3.8 4.0 4.2 0.86 0.88 0.90 4.6 4.8 5.0 5.2 1.12 1.13 1.14 1.15 c (kNs/m) 650 700 750 0.76 0.77 0.78 0.79 3.0 µ (%) 3.2 µ (%) PGA=5.0m/s2 independent of PGA 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 0 1 2 3 4 5 6 7 8 FP, optimized @ PGA=3.5m/s2 pendulum with optimized linear viscous damping FP, optimized @ PGA=5.0m/s2 FP, optimized @ PGA=6.5m/s2 optimization points of FPs (e.g. DBE) (e.g. MCE) e a b c d PGA (m/s2) max( | üs+üg | ) (m/s 2) max( | üs+üg | ) (m/s 2) max( | üs+üg | ) (m/s 2) max( | üs+üg | ) (m/s 2) max( | üs+üg | ) (m/s 2) Fig. 1.4 Optimal friction coefficients (a–c) of passive FPs and optimal viscous coefficient (d) of passive pendulum with viscous damping; absolute structural acceleration (e) due to optimized passive FPs and pendulum with optimized viscous damping

1 Semi-Active Base Isolation of Civil Engineering Structures Based on Optimal Viscous Damping and Zero Dynamic Stiffness 7 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 0 1 2 3 4 5 6 7 8 pendulum with opt. lin. viscous damping semi-active, CL #3 semi-active, CL #4 semi-active, CL #1 semi-active, CL #2 (e.g. DBE) (e.g. MCE) 0 200 400 600 800 1000 1200 max( | f | ) (kN) 0 1 2 3 4 5 6 7 8 (e.g. DBE) (e.g. MCE) FP, PGAopt=3.5m/s2 pendulum with opt. lin. viscous damping FP, PGAopt=5.0m/s2 FP, PGAopt=6.5m/s2 semi-active, CL #1 semi-active, CL #2 semi-active, CL #3 semi-active, CL #4 a b PGA (m/s2) PGA (m/s2) max( | üs+üg | ) (m/s 2) Fig. 1.5 Absolute structural acceleration (a) due to semi-active pendulums and (b) maximum total forces of all considered isolators max( | u | ) (mm) 0 50 100 150 200 250 300 350 400 450 500 0 1 2 3 4 5 6 7 8 (e.g. DBE) (e.g. MCE) FP, PGAopt=3.5m/s2 pendulum with opt. lin. viscous damping FP, PGAopt=5.0m/s2 FP, PGAopt=6.5m/s2 semi-active, CL #1 semi-active, CL #2 semi-active, CL #3 semi-active, CL #4 residual | u | (mm) 0 2 4 6 8 10 12 14 16 18 20 0 1 2 3 4 5 6 7 8 (e.g. DBE) (e.g. MCE) FP, PGAopt=3.5m/s2 pendulum with opt. lin. viscous damping FP, PGAopt=5.0m/s2 FP, PGAopt=6.5m/s2 semi-active, CL #1 semi-active, CL #2 semi-active, CL #3 semi-active, CL #4 a b PGA (m/s2) PGA (m/s2) Fig. 1.6 Maximum displacements (a) and residual displacements (b) of all considered isolators (costs!, Fig. 1.6a), the re-centering capability (Fig. 1.6b, re-centering error must not be larger than 50% of the bearing displacement capacity, i.e. 50% of 250 mm) and the maximum force of the semi-active damper (costs!, Figs. 1.7 and 1.8). The review of all these results reveals that CL #1 and CL #2 represent promising solutions. None of these two control laws can be denoted as superior as the project specifications alone determine if CL #1 or CL #2 is more appropriate for the isolation task, i.e. if the absolute structural acceleration should be minimized for PGAs corresponding to DBE and earthquakes beyond of DBE (CL #1) or for PGAs corresponding to DBE and earthquakes below DBE (CL #2). 1.6 Summary This paper presents a novel semi-active base isolator based on a pendulum with uncontrollable lubricated friction of 1.5% and a semi-active oil damper in parallel. Four different control laws are formulated that target to control the total stiffness of the semi-active isolator in real-time as function of the actual bearing displacement amplitude and to produce optimal viscous damping. The numerical results demonstrate that the semi-active isolator significantly improves the isolation of the structure

8 F. Weber et al. bearing displacement u (mm) 㻙300 −200 100 100 200 300 −0.10 −0.08 −0.06 −0.04 −0.02 0 0.02 0.04 0.06 0.08 0.10 0 negative kR-eff during 1/2 cycle (with viscous damping superimposed) due to U >= 250 mm positive stiffness due to U < 125 mm (plus kR-eff at U close to zero) control law #1 (CL #1) bearing displacement u (mm) −300 −200 100 100 200 300 −0.10 −0.08 −0.06 −0.04 −0.02 0 0.02 0.04 0.06 0.08 0.10 0 control law #1 (CL #1) zero dynamic stiffness during 1/2 cycle (with viscous damping superimposed) due to U >= 250 mm positive stiffness due to U < 125 mm (kR-eff-nominal at U close to zero) a b total isolator force f / W (−) fsemi-active / W (−) Fig. 1.7 Force displacement trajectories of (a) semi-active control force and (b) total force of semi-active isolator due to control law #1 bearing displacement u (mm) −300 −200 100 100 200 300 −0.10 −0.08 −0.06 −0.04 −0.02 0 0.02 0.04 0.06 0.08 0.10 0 bearing displacement u (mm) −300 −200 100 0 100 200 300 control law #2 (CL #2) −0.10 −0.08 −0.06 −0.04 −0.02 0 0.02 0.04 0.06 0.08 0.10 control law #2 (CL #2) kR-eff-nominal during 1/2 cycle (with viscous damping superimposed) due to U >= 250 mm zero dynamic stiffness during 1/2 cycle at U close to zero total isolator force f / W (−) positive kR-eff during 1/2 cycle (with viscous damping superimposed) due to U >= 250 mm negative kR-eff during 1/2 cycle due to U close to zero a b fsemi-active / W (−) Fig. 1.8 Force displacement trajectories of (a) semi-active control force and (b) total force of semi-active isolator due to control law #2 compared to optimized friction pendulums and a hypothetical pendulum without friction but optimal viscous damping. This result is achieved without getting larger bearing displacements and forces and the re-centering requirement is also fulfilled semi-active base isolator. Acknowledgements The authors gratefully acknowledge the financial support of MAURER SE. References 1. Tsai, C.S., Chiang, T.-C., Chen, B.-J.: Experimental evaluation of piecewise exact solution for predicting seismic responses of spherical sliding type isolated structures. Earthq. Eng. Struct. Dyn. 34, 1027–1046 (2005) 2. Weber, F., Boston, C.: Energy based optimization of viscous-friction dampers on cables. Smart Mater. Struct. 19, 045025 (11pp) (2010) 3. Fenz, D.M., Constantinou, M.C.: Spherical sliding isolation bearings with adaptive behavior: theory. Earthq. Eng. Struct. Dyn. 37, 163–183 (2008) 4. Feng, M.Q., Shinozuka, M., Fujii, S.: Friction-controllable sliding isolation system. J. Eng. Mech. (ASCE). 119(9), 1845–1864 (1993)

1 Semi-Active Base Isolation of Civil Engineering Structures Based on Optimal Viscous Damping and Zero Dynamic Stiffness 9 5. Kobori, T., Takahashi, M., Nasu, T., Niwa, N.: Seismic response controlled structure with active variable stiffness system. Earthq. Eng. Struct. Dyn. 22, 925–941 (1993) 6. Ramallo, J.C., Johnson, E.A., Spencer Jr., B.F.: ‘Smart’ base isolation systems. J. Eng. Mech. (ASCE). 128(10), 1088–1100 (2002) 7. Nagarajaiah, S., Sahasrabudhe, S.: Seismic response control of smart sliding isolated buildings using variable stiffness systems: an experimental and numerical study. Earthq. Eng. Struct. Dyn. 35(2), 177–197 (2006) 8. Ruderman, M.: Presliding hysteresis damping of LuGre and Maxwell-slip friction models. Mechatronics. 30, 225–230 (2015) 9. Preumont, A.: Vibration Control of Active Structures, Chapter 6. Kluwer Academic Publishers, Dordrecht (2002) 10. Weber, F., Mas´lanka, M.: Precise stiffness and damping emulation with MR dampers and its application to semi-active tuned mass dampers of Wolgograd Bridge. Smart Mater. Struct. 23, 015019 (2014)

Chapter 2 Long-Term Performance of Specialized Fluid Dampers Under Continuous Vibration on a Pedestrian Bridge Alan R. Klembczyk Abstract In 2001, Taylor Devices Inc. developed special Viscous Dampers for use on the Millennium Bridge in London, England. These dampers were specified and designed to be used for mitigating the dynamic response of the bridge due to pedestrian traffic. Prior to the integration of the dampers, the bridge had experienced unacceptable movements, especially during periods when larger crowds of people were on the bridge. The result was that the bridge had to be closed until a solution was found. Much research was done and several papers were published about the nature of that problem and the ensuing solution. After successful component level testing and the installation of 37 Taylor Viscous Dampers, the bridge was re-opened to the public in February, 2002. Tests with approximately 2000 people demonstrated a much improved dynamic response. Since that time, the dampers have been subjected to almost constant dynamic input, some more than others. Due to the location of the bridge in central London, there has been nearly constant pedestrian traffic on the bridge each day and even throughout the night. However, because of the specialized nature of the damper design, no degradation in damper performance or in the dynamic response of the bridge itself has been experienced. This paper will outline the specifics in quantifying the continued damper performance through an intermediate inspection after 7 years, followed by a successful comprehensive inspection after 11 years. This included the removal, dynamic testing, and re-installation of three selected dampers. Keywords Millennium Bridge • Bridge damper test results • Fluid viscous dampers • Continuous vibration • Vibration damper 2.1 Introduction The unique design and the resulting unacceptable response of the Millennium Bridge in central London (see Fig. 2.1) have been well publicized and documented. The specifics of this dynamic response and the resulting solution will not be reiterated within the context of this paper. However, in order to provide a necessary background, a short summary is presented here. In June 2000, the bridge was first opened to the public. Shortly thereafter, with substantial pedestrian traffic present, the bridge began to sway in a lateral motion to the discomfort of many of the pedestrians. The bridge was subsequently shut down and significant studies were performed to provide solutions to stop the excessive swaying. Since the response frequency was near the frequency of human footfalls during walking, it was determined that stiffening of the structure was not a practical solution. The unique design and its aesthetic appearance would have been sacrificed if structural modifications were made to keep the various modal frequencies away from walking frequencies. A more acceptable solution was determined to substantially increase the damping level of the bridge over all input conditions in order to prevent pedestrian traffic from exciting the bridge. The required amount of added damping was determined to be nearly 20% critical, a value that is effectively unachievable with typical solutions, such as tuned mass dampers, frictional elements, or structural modifications. Many challenges became immediately apparent when proposing a damping solution for this unique structure. One of the most significant was the fact that the owner of the bridge required a permanent and maintenance-free solution that would last throughout the life of the bridge; this being in excess of 50 years. Since the expected pedestrian traffic was such that the dampers would cycle nearly continuously at 1.3 Hz, it was necessary to specify a cycle life of 2 109 cycles minimum. Due to this stringent requirement, Taylor Devices proposed the use of specialized Fluid Dampers that employed the use of flexing metal bellows seals, rather than traditional sliding seals that are elastomeric in nature and therefore subject to wear and degradation over long-term environmental and cyclic conditions. A.R. Klembczyk ( ) Taylor Devices, Inc., 90 Taylor Drive, North Tonawanda, NY, 14120-0748, USA e-mail: alanklembczyk@taylordevices.com © The Society for Experimental Mechanics, Inc. 2017 J. Caicedo, S. Pakzad (eds.), Dynamics of Civil Structures, Volume 2, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-54777-0_2 11

12 A.R. Klembczyk Fig. 2.1 The Millennium Bridge 2.2 Specialized Damper Design [1] Taylor Devices’ Fluid Dampers with metal bellows seals had been previously used exclusively by NASA and other U.S. Government agencies for space based optical systems. These previous applications had similar requirements for long life and high resolution at low amplitudes, but required relatively low damper forces from small, lightweight design envelopes. Figure 2.2 is a photograph of a pair of typical dampers of this design, used in space on more than 70 satellites to protect delicate solar array panels. This figure also shows the metal bellows seals; one in the compressed position and one in the extended position. This type of seal does not slide, but rather flexes without hysteresis as the damper moves. This patented design is known as a Frictionless Hermetic Damper. A cutaway of a typical damper of this type is shown in Fig. 2.3. Two metal bellows seals are used to seal fluid in each damper, one at each end of the damping chamber. As the damper moves, the two metal bellows alternately extend and retract, by flexure of the individual bellows segments. Since the seal element elastically flexes rather than slides, seal hysteresis is nearly zero. The volume displaced by the compressing bellows passes through the crossover ports to the extending bellows at the opposite end of the damper. While this is occurring, damping forces are being produced by orifices in the damping head, and the pressures generated are kept isolated from the metal bellows by high restriction hydrodynamic labyrinth bushings. Because hydrodynamic bushings are used, no sliding contact with the piston rod occurs, assuring near-frictionless performance. Adapting this basic design for use on the Millennium Bridge largely involved simply scaling the small satellite Dampers to the required size range. All parts, including the metal bellows seals, were designed with low stress levels to provide an endurance life in excess of 2 109 cycles. The metal bellows and other moving parts were constructed from stainless steel for corrosion resistance. To assure a high resolution output, it was required that all damper attachment clevises be fabricated with fitted spherical bearings and fitted mounting pins, such that zero net end play existed in the attachment brackets. A total of 37 dampers of this design were manufactured, component-level tested, and installed on the bridge in late 2001. There are three basic types of dampers. These are referred to as the Pier Dampers, the Deck Dampers, and the Vertical Dampers and are described below: Damper Nomenclature: Pier Damper Quantity on the Bridge: 16 Description: Two Pier Dampers are located on each side of each of two piers on both the east and west side of the bridge, for a total of eight dampers per pier. Damping coefficient values for the eight dampers connected directly to the center span of the bridge are significantly higher than the other Pier Dampers. Dampers have varying over-all lengths due to the

2 Long-Term Performance of Specialized Fluid Dampers Under Continuous Vibration on a Pedestrian Bridge 13 Fig. 2.2 Space satellite dampers Fig. 2.3 Cutaway of frictionless hermetic damper location of the attachment points, the longest being 8.3 m long. These dampers are quite apparent to pedestrians when crossing the bridge as illustrated in Figs. 2.4 and 2.5 below. Damper Nomenclature: Deck Damper Quantity on the Bridge: 17 Description: The Deck Dampers are located under various deck sections. A very limited number can be seen from under the north end of the bridge. Most deck dampers are not visible since they are situated directly under the deck panels. Lateral motions of the bridge are transmitted to the dampers through pairs of relatively long V-shaped chevron braces as shown in Figs. 2.6 and 2.7 below. Damper Nomenclature: Vertical Damper Quantity on the Bridge: 4 Description: Vertical Dampers are located in two pairs under the south end of the bridge with damper ends connected between a structural arm and the ground. As illustrated below in Figs. 2.8 and 2.9, the dampers are directly accessible to pedestrian traffic. Nearly continuous damped motion is felt and observed with even low to moderate pedestrian traffic on the bridge overhead.

14 A.R. Klembczyk Fig. 2.4 4 of 16 pier dampers Fig. 2.5 Moving end of pier damper over the River Thames Fig. 2.6 Deck damper shown with chevron connection

2 Long-Term Performance of Specialized Fluid Dampers Under Continuous Vibration on a Pedestrian Bridge 15 Fig. 2.7 Deck panels removed deck damper showing Fig. 2.8 Inspection of vertical damper pair Fig. 2.9 Vertical damper pair with pedestrian access

16 A.R. Klembczyk 2.3 Intermediate Inspection After 7 Years in Service A visual inspection of each damper was performed looking for corrosion, damage to the unit from use or the surrounding environment, and for fluid leakage. The units were all found to be in 100% working condition with minimal signs of physical damage or deterioration, as well as no signs of fluid leakage. There were only minor signs of corrosion and some external contamination noted. The units had been subjected to nearly constant cycling for a period of use of over 7 years at the time of this inspection. The total estimated cycles after 7 years was as many as 2.0 108. The owner required no formal testing of installed dampers at this time. 2.4 Principal Inspection and Testing After 11 Years in Service The Principal Inspection after 11 years of service included two phases. The first was a visual inspection of all Pier Dampers and all four Vertical Dampers. All dampers appeared to be in 100% working order. A sample of five of the seventeen deck dampers were inspected per the owner’s request to minimize deck panel removal costs. Similar to the case for the Intermediate Inspection 4 years earlier, there were only minor signs of corrosion and some external contamination noted. This minor corrosion and contamination appears to have been caused by caustic chemicals from the exhaust plumes from boats and ships navigating under the bridge. Dampers located under the deck of the bridge near the shore or over land exhibited nearly new appearance. Two of the five Deck Dampers and one of the four Vertical Dampers were temporarily removed for testing purposes as outlined below. The second phase of the Principal Inspection consisted of performing dynamic tests on the three dampers that were removed. These three dampers were shipped to the Taylor Devices facility in North Tonawanda, New York so that they could be tested to the original Acceptance Test Procedure and compared to the original acceptance tests from 2001. This was done to determine if any of the performance outputs had deteriorated in any way. This Acceptance Test Procedure consisted of two types of tests. The first type consisted of subjecting the dampers to a series of sinusoidal input tests throughout the specified velocity range. These tests are referred to as the “Force vs. Velocity” tests. The second type of test was performed at approximately 0.50 mm amplitude. These tests are referred to as the “Low Amplitude” tests. The Low Amplitude test demonstrates the ability of each Damper to produce substantial damping force for very small vibrations, and demonstrate that there has been no loss of fluid. If any loss of fluid had occurred, the damper would demonstrate an inability to produce any substantial force for these small displacements. Figures 2.10, 2.11, and 2.12 show the results of the Force versus Velocity tests for each Damper, measuring the output force at several velocity inputs. These plots also show the data points recorded through the same testing methods 11 years prior. The graphical data illustrates the fact that there is virtually no difference in output characteristics when comparing the results from 2001 to the results from 2012. Figures 2.13, 2.14 and 2.15 demonstrate the results of the Low Amplitude Tests for each of the three dampers that were tested. Note that in each case, the hysteresis loops (force vs. displacement) show no signs of free-play, loss of fluid, excessive friction, wear or degradation of any sort. It should be noted that the dampers were tested with their spherical bearings in place and their end attachment brackets still connected. Therefore, no degradation to these components has occurred and the bearings have maintained their tight fit requirement that is necessary to produce damping for very low displacements. Subsequent to the successful testing of these three dampers, they were sent back to London and reinstalled on the bridge in January 2013. 2.5 Conclusions The results of the 7-year Intermediate Inspection, the 11-year Principal Inspection, and dynamic testing show that the Millennium Bridge dampers have experienced no physical or functional deterioration. The dampers displayed no measurable change in output, as well as no signs of leakage after 11 years of continuous service and nearly constant cycling.

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