Equivalent Linearization For Simplified Hysteretic Systems Of Stochastic Seismic Response

Due to the uncertainty of the seismic activity and the randomness ofthe spread of seismic waves in the Earth’s crust, the ground shakeparameters such as ground displacement, velocity and acceleration are allrandom, the process of movement is very irregular waveform. Back andforth under seismic loading, curve of the components resilience and thedeformation doesn’t change along the same path in the process of loadingand unloading, showing significant hysteretic characteristics. To betterunderstand the hysteretic dynamic characteristics of structures underrandom seismic excitation, the random equivalent linearization methodand the Monte-Carlo numerical simulation method is applied to theanalysis of random seismic response of hysteretic systems in this article.In this paper, response characteristics of the structure under the mostcommonly used stationary random process model (including the Gaussianwhite noise model, the Kanai-Tajimi smooth spectrum model, and theClough-Penzien model), and modulation non-stationary random process model is discussed. For the Bouc-Wen hysteretic model to derive theexpression of the equivalent linearization parameters for hystereticsystems under random excitation, and use the stochastic equivalentlinearization method to study the structure response characteristics underthe stationary random process model and the non-stationary randomprocess model.At the same time, for the hysteretic model reaction under thestationary random process model and the non-stationary random processmodel, the Monte-Carlo numerical simulation method has also beenadopted to calculate, and were compared with the random equivalentlinearization method to illustrate the feasibility of equivalent linearizationmethod to solve random response problem of the hysteretic system.