Approximate analytical expressions for the stochastic response of a bilinear hysteretic oscillator with low yield levels

Differential equations are derived which exactly govern the evolution of th e second order response moments of a single-degree-of-freedom (SDOF) biline ar hysteretic oscillator subject to stationary Gaussian white noise excitat ion. Then, considering cases for which response stationarity will be achiev ed, i.e., excluding the case of an elastic-perfectly-plastic oscillator, al gebraic equations for the response moments are found. By the nature of the problem, these moments depend on the probability of the oscillator being in the plastic state. Upon considering oscillators with low yield levels and using analytically available information, physical reasoning, and approxima tions supported by empirical observation, an equation for the probability o f the oscillator being in the plastic state is derived. Upon numerical solu tion of this equation, analytical approximations to the response moments ca n be obtained. All analytical, approximate, and numerical results are verif ied by extensive Monte Carlo simulations. (C) 1999 Academic Press.