Stochastic Equivalent Linearization for Hysteretic, Degrading, Multistory Strutctures

A mathematical model for the response of multi-degree of freedom, hysteretic, and degrading systems under random base excitation is presented. A typical hysteretic element is described by a first order nonlinear differential equation. System degradation is governed by the total energy dissipation of the hysteresis. The model can represent multi-degree of freedom shear beam, or discrete hinge structures. Zero time lag covariance matrix response is obtained via equivalent linearization, and agrees more closely with Monte Carlo simulations than do other available approximate solutions. The response power spectral density function of the linearized system is obtained and several available first passage probability estimates are compared. Numerical studies are presented for shear beam models under stationary white noise, Kanai filtered white noise, and non-stationary excitations. Studies for framed structures with discrete hinge regions show that in addition to the usual covariance response, joint by joint energy dissipation requirements are provided.National Science Foundation Research Grant ENG 77-0909