Non-stationary seismic response of MDOF systems by wavelet transform

Biswajit Basu, Vinay K. Gupta ^*

Department of Civil Engineering, Indian Institute of Technology, Kanpur - 208016, India

Keywords

 wavelet transform; Littlewood-Paley basis; frequency non-stationarity; modal correlation; time-dependent PSDF; ordered peak amplitudes

Abstract

A wavelet-based formulation has been presented in this paper for the stochastic analysis of a linear multi-degree-of-freedom (MDOF) classically damped system subjected to earthquake ground motion. The ground motion has been modelled as a non-stationary process (both in amplitude and frequency) using wavelets. Closed-form expressions of the moments of the instantaneous Power Spectral Density Function (PSDF) of the response have been derived and used to predict the statistics of the response peak of any desired order. For illustration of the formulation, an example torsionally coupled multistoried building has been considered along with the twenty synthetically generated time-histories corresponding to an example ground motion process.