On Equivalent Linearization Using Wavelet Transform

Abstract

This paper proposes a wavelet-based formulation for linearizing a base-excited single-degree-of-freedom nonlinear system to a time-variant linear (TVL) system. The given system is assumed to be nonlinear in stiffness, and the time-dependent natural frequency of the equivalent system is proposed to he estimated through instantaneous minimization of the mean-square error. A duffing oscillator has been considered to illustrate the performance of the proposed TVL system.