Response of a Hysteretic System Under Non-Stationary Earthquake Excitations

Abstract

Under strong earthquake excitations, a structure is likely to become nonlinear and inelastic. The term hysteresis is used to describe a type of inelastic behavior in which the restoring force depends not only on the instantaneous deformation, but also the past history of the deformation. Consider an engineering structure idealized as a single-degree-of-freedom system governed by

$$ \ddot X\, + \,2\zeta \dot X\, + \,aX\, + \,\eta Z(t)\, = f_k (X,\dot X)\xi _k (t) $$

(1)

where ξ_k(t) are ground accelerations, and Z(t) is a hysteretic restoring force, described by the Bouc-Wen model (Bouc, 1967; Wen, 1976, 1980)