Wavelet-based non-stationary response analysis of a friction base-isolated structure

Biswajit Basu ¹, Vinay K. Gupta ^{2 *}

¹Department of Civil Engineering, Jadavpur University, Calcutta 700032, India
²Department of Civil Engineering, Indian Institute of Technology, Kanpur 208016, India

Keywords

wavelet coefficients; Littlewood-Paley basis; frequency non-stationarity; base isolation; equivalent linear system; instantaneous damping

Abstract

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.