Equivalent viscous damping for a bilinear hysteretic oscillator

A bilinear hysteretic model is commonly used to study elastoplastic structu res. In this paper, a damped, bilinear hysteretic oscillator is studied und er harmonic loading. We show the existence of an equivalent viscous damping for small values of a loading parameter such that the associated linear st ructure and the hysteretic structure have the same frequency response curve s. We use the Kryloff-Bogoliuboff method of averaging to find the equivalen t viscous damping as a function of the steady stare amplitude. We present a model of a bilinear elastic oscillator which captures the steady-state dyn amics of the hysteretic oscillator for low values of the loading parameter. We also study the nature of the dependence of the equivalent viscous dampi ng on the kinematic hardening parameter.