Equivalent Viscous Damping for a Bilinear Hysteretic Oscillator

A bilinear hysteretic model is commonly used to study elastoplastic structures. In this paper, a damped, bilinear hysteretic oscillator is studied under harmonic loading. We show the existence of an equivalent viscous damping for small values of a loading parameter such that the associated linear structure and the hysteretic structure have the same frequency response curves. We use the Kryloff-Bogoliuboff method of averaging to find the equivalent viscous damping as a function of the steady state amplitude. We present a model of a bilinear elastic oscillator which captures the steady-state dynamics of the hysteretic oscillator for low values of the loading parameter. We also study the nature of the dependence of the equivalent viscous damping on the kinematic hardening parameter.