Nonlinear dynamic analysis of a structure with a friction-based seismic base isolation system

Many dynamical systems are subject to some form of non-smooth or discontinuous nonlinearity. One eminent example of such a nonlinearity is friction. This is caused by the fact that friction always opposes the direction of movement, thus changing sign when the sliding velocity changes sign. In this paper, a structure with friction-based seismic base isolation is regarded. Seismic base isolation can be employed to decouple a superstructure from the potentially hazardous surrounding ground motion. As a result, the seismic resistance of the superstructure can be improved. In this case study, the base isolation system is composed of linear laminated rubber bearings and viscous dampers and nonlinear friction elements. The nonlinear dynamic modelling of the base-isolated structure with the aid of constraint equations, is elaborated. Furthermore, the influence of the dynamic characteristics of the superstructure and the nonlinear modelling of the isolation system, on the total system’s dynamic response, is examined. Hereto, the effects of various modelling approaches are considered. Furthermore, the dynamic performance of the system is studied in both nonlinear transient and steady-state analyses. It is shown that, next to (and in correlation with) transient analyses, steady-state analyses can provide valuable insight in the discontinuous dynamic behaviour of the system. This case study illustrates the importance and development of nonlinear modelling and nonlinear analysis tools for non-smooth dynamical systems.

[1]  Ahsan Kareem,et al.  Damping in structures: its evaluation and treatment of uncertainty , 1996 .

[2]  A. P. Jeary,et al.  Damping in tall buildings—a mechanism and a predictor , 1986 .

[3]  M. Bampton,et al.  Coupling of substructures for dynamic analyses. , 1968 .

[4]  K. Bathe.  Finite Element Procedures , 1995 .

[5]  Leon O. Chua,et al.  Practical Numerical Algorithms for Chaotic Systems , 1989 .

[6]  Anshel J. Schiff.  Hyogoken-Nanbu (Kobe) earthquake of January 17, 1995 : lifeline performance , 1999 .

[7]  Kazumi Yamane,et al.  Structures Paper: Isolation Story Structure of Umeda Tower, Osaka, Japan , 2003 .

[8]  Y. K. Wen,et al.  Random vibration of hysteretic systems under bi‐directional ground motions , 1986 .

[9]  Juan Carlos de la Llera,et al.  Analytical model of structures with frictional pendulum isolators , 2002 .

[10]  J. W. Tedesco,et al.  Structural Dynamics: Theory and Applications , 1998 .

[11]  Stephen A. Mahin,et al.  MODELING AND CHARACTERIZATION OF SEISMIC ISOLATION BEARINGS , 1998 .

[12]  Fabio Casciati,et al.  Stochastic dynamics of hysteretic media , 1989 .

[13]  Aleksej F. Filippov,et al.  Differential Equations with Discontinuous Righthand Sides , 1988, Mathematics and Its Applications.

[14]  Guowei Ma,et al.  Simulation of structural response under high‐frequency ground excitation , 2001 .

[15]  Reza Akbari,et al.  SEISMIC BEHAVIOUR FACTOR, R, FOR STEEL X-BRACED AND KNEE-BRACED RC BUILDINGS , 2003 .

[16]  H. Nijmeijer,et al.  Dynamics and Bifurcations ofNon - Smooth Mechanical Systems , 2006 .

[17]  Giuseppe Oliveto.  Innovative Approaches to Earthquake Engineering , 2002 .

[18]  Mario Paz,et al.  Structural Dynamics: Theory and Computation , 1981 .

[19]  Bram De Kraker.  A Numerical - Experimental Approach in Structural Dynamics , 2004 .

[20]  C. Glocker.  Set-valued force laws , 2001 .

[21]  Achilleas G. Papadimitriou,et al.  Multi‐variable relations for soil effects on seismic ground motion , 2003 .

[22]  Federico M. Mazzolani,et al.  Seismic resistant steel structures , 2000 .

[23]  Yi-Qing Ni,et al.  IDENTIFICATION OF NON-LINEAR HYSTERETIC ISOLATORS FROM PERIODIC VIBRATION TESTS , 1998 .

[24]  R. Craig.  A review of time-domain and frequency-domain component mode synthesis method , 1985 .

[25]  A. M. Abdel-Ghaffar,et al.  MODELING OF RUBBER AND LEAD PASSIVE-CONTROL BEARINGS FOR SEISMIC ANALYSIS , 1995 .

[26]  M. N. van den Heuvel.  Modeling and analysis of an automatic balancing unit with dry friction , 2002 .

[27]  Yukio Tamura,et al.  Field measurement of damping and natural frequency of an actual steel-framed building over a wide range of amplitudes , 1996 .

[28]  Hsiang-Chuan Tsai,et al.  Mechanical properties of isolation bearings identified by a viscoelastic model , 2001 .

[29]  Gary C. Hart,et al.  Earthquake Design of Buildings:Damping , 1975 .

[30]  Andreas J. Kappos,et al.  Evaluation of behaviour factors on the basis of ductility and overstrength studies , 1999 .

[31]  Jiahao Lin,et al.  An Introduction to Seismic Isolation , 1993 .

[32]  Jr. Roy Craig,et al.  Coupling of substructures for dynamic analyses - An overview , 2000 .

[33]  Shouchuan Hu.  Differential equations with discontinuous right-hand sides☆ , 1991 .

[34]  Jing Zhou,et al.  Aseismic designs based on artificial simulations , 1999 .

[35]  Fabio Casciati,et al.  Structural Control for Dynamic Hazard Mitigation , 2004 .

[36]  H. Langhaar.  Dimensional analysis and theory of models , 1951 .

[37]  E. J. Haug,et al.  Computer aided kinematics and dynamics of mechanical systems. Vol. 1: basic methods , 1989 .

[38]  C. S. Tsai,et al.  An advanced analytical model for high damping rubber bearings , 2003 .

[39]  Y. Wen.  Method for Random Vibration of Hysteretic Systems , 1976 .

[40]  Eric M. Lui.  Seismic Isolation for Earthquake Resistant Structures , 2001 .

[41]  Mahendra P. Singh,et al.  Design of yielding metallic and friction dampers for optimal seismic performance , 2003 .

[42]  V. Yakubovich,et al.  Stability of Stationary Sets in Control Systems With Discontinuous Nonlinearities , 2004, IEEE Transactions on Automatic Control.

[43]  T. W. Maver.  Principles of optimal design: modelling and computation: P.Y. Papalambros and D.J. Wilde, Cambridge University Press, Cambridge, (1988), 416 pages, £45.00 , 1991 .

[44]  P. B Lindley,et al.  Engineering design with natural rubber , 1968 .

[45]  Anil K. Chopra,et al.  Dynamics of Structures: Theory and Applications to Earthquake Engineering , 1995 .

[46]  Farzad Naeim,et al.  Design of seismic isolated structures : from theory to practice , 1999 .

[47]  Ian D. Aiken,et al.  AN ANALYTICAL HYSTERESIS MODEL FOR ELASTOMERIC SEISMIC ISOLATION BEARINGS , 1997 .

[48]  T W Lowe.  Principles of optimal design: Modelling and computation , 2001 .

[49]  van Dh Dick Campen,et al.  Stick-Slip Vibrations Induced by Alternate Friction Models , 1998 .

[50]  C. Van Amerongen,et al.  Model analysis of structures , 1974 .

[51]  James M. Kelly,et al.  Earthquake-Resistant Design with Rubber , 1993 .

[52]  R. Clough,et al.  Dynamics Of Structures , 1975 .

[53]  W. J. Hall,et al.  Dynamics of Structures—Theory and Applications to Earthquake Engineering , 1996 .

[54]  J. Baumgarte.  Stabilization of constraints and integrals of motion in dynamical systems , 1972 .

[55]  Yukio Tamura,et al.  Damping Evaluation Using Full-Scale Data of Buildings in Japan , 2003 .