Stochastic linearization coefficients of the Bouc-Wen oscillator

The Bouc-Wen oscillator has been popular in non-linear random vibration analysis because of its versatility and mathematical tractability but its stochastic linearization coefficients that have been presented in the literature have different forms and may cause some confusion. This paper presents a general form of the coefficients that is valid for the full range of possible values of the correlation coefficient between response velocity and hysteretic restoring force, and of the hysteresis shape parameter that controls the degree of non-linearity. The complete set of linearization coefficients are used in a random vibration analysis of a single-degree-of-freedom hysteretic, degrading and pinching system. Results under white noise excitation compare favourably with those from Monte Carlo simulation.