Non-Gaussian equivalent linearization for non-stationary random vibration of hysteretic system

Abstract

An approximate analytical technique is developed for obtaining the non-stationary response of a single-degree-of-freedom mechanical system with bilinear hysteresis subjected to amplitude modulated non-white random excitations. The hysteretic behavior is described by introducing an additional state variable and non-linear functions. The equivalent linear coefficients and also the moment equations of the equivalent linear systems are derived using a non-Gaussian probability density function which is composed of a truncated Gaussian probability density function and a couple of delta functions. The mean square responses and the mean dissipated hysteretic energy are calculated by solving the moment equations and are compared with the corresponding digital simulation results.