Abstract
A wavelet-based stochastic formulation has been presented in this paper for the seismic analysis of a rigid block resting on a friction base. The ground motion has been modelled as a non-stationary process (both in amplitude and frequency) by using wavelets. The proposed formulation is based on replacing the non-linear system by an equivalent linear system with time-dependent properties. The expressions of the instantaneous damping, root mean square (r.m.s.) velocity response, and the power spectral density function (PSDF) of the velocity response have been obtained in terms of the input wavelet coefficients. For validation of the formulation, simulation based on twenty synthetically generated time-histories corresponding to an example ground motion process has been carried out. The effectiveness of the base-isolation system and the effect of the frequency non-stationarity on the non-linear response have also been studied in detail. It has been clearly shown how the frequency non-stationarity in the ground motion changes the non-linear response.
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