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Wavelet‐based non‐stationary response analysis of a friction base‐isolated structure
Author(s) -
Basu Biswajit,
Gupta Vinay K.
Publication year - 2000
Publication title -
earthquake engineering and structural dynamics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.218
H-Index - 127
eISSN - 1096-9845
pISSN - 0098-8847
DOI - 10.1002/1096-9845(200011)29:11<1659::aid-eqe983>3.0.co;2-s
Subject(s) - wavelet , spectral density , response analysis , amplitude , series (stratigraphy) , frequency response , basis (linear algebra) , stochastic process , mathematics , superstructure , mathematical analysis , computer science , physics , structural engineering , engineering , geology , geometry , statistics , paleontology , artificial intelligence , electrical engineering , quantum mechanics
A wavelet‐based stochastic formulation has been presented in this paper for the seismic analysis of a base‐isolated structural system which is modelled as a two‐degree‐of‐freedom (2‐DOF) system. The ground motion has been modelled as a non‐stationary process (both in amplitude and frequency) by using modified Littlewood–Paley basis wavelets. The proposed formulation is based on replacing the non‐linear system by an equivalent linear system with time‐dependent damping properties. The expressions of the instantaneous damping and the power spectral density function (PSDF) of the superstructure response have been obtained in terms of the functionals of input wavelet coefficients. The proposed formulation has been validated by simulating a ground motion process. The effect of the frequency non‐stationarity on the non‐linear response has also been studied in detail, and it has been clearly shown how ignoring the frequency non‐stationarity in the ground motion leads to inaccurate non‐linear response calculations. Copyright © 2000 John Wiley & Sons, Ltd.