Steady‐State Dynamic Analysis of Hysteretic Systems

Abstract

A great many hysteretic models have been recently introduced in the analysis of dynamic behavior of structures and structural elements. This paper considers the steady‐state oscillations of single‐degree‐of‐freedom systems with different force‐deflection relationships. Three types of constitutive laws are covered: bilinear, stiffness degrading, and stiffness‐strength degrading. An approximate solution to the equation of motion under sinusoidal excitations is obtained by an analytical procedure and the frequency response curves are drawn. All the models exhibit softening behavior but while the bilinear and the Ramberg‐Osgood type models give stable and single‐valued response curves, the stiffness and the stiffness‐strength degrading models exhibit a multi‐valued curve in a certain frequency range. The results obtained are verified by numerically integrating the equation of motion. Numerical solutions are also used to predict the actual response of systems with unstable frequency response curve to general excitation.