Steady‐State Oscillation of Hysteretic Differential Model. I: Response Analysis

Abstract

This study considers the periodic forced vibration of nonlinear hysteretic system. Multiharmonic steady‐state responses of a general hysteretic system adopting the Bouc‐Wen differential model, subjected to arbitrary periodic excitation, are analyzed by the Galerkin/Levenberg‐Marquardt method. The frequency/ time domain alternation and the fast Fourier transform (FFT) techniques are introduced in this frequency domain solution procedure. The frequency‐controlled and amplitude‐controlled algorithms are simultaneously formulated to obtain complete, probably multivalued, frequency response curves. This approach gives possible harmonic, superharmonic, and subharmonic responses of the Bouc‐Wen hysteretic system. The response characteristics of softening, hardening, and quasilinear hysteretic systems are studied through numerical computations. The proposed procedure is also extended to analyze the periodic vibration of degrading hysteretic system with amplitude‐dependent stiffness deterioration. In addition, a verification is given by comparing with the results obtained by a numerical integration procedure.