Stochastic Seismic Response of Hysteretic Structures

Abstract

An analytical procedure for the stochastic response analysis of hysteretic structures with strong nonlinearity to earthquake excitations is presented. For hysteretic nonlinear systems, statistical properties such as moments and probability densities of the responses cannot usually be obtained exactly. The present method is approximate but the solution is obtained without recourse to the equivalent linearization technique. The hysteretic characteristics such as bilinear and trilinear types are expressed in appropriate first-order differential forms with quasi-linear characteristics. These expressions give physical interpretation of hysteretic characteristics and make it possible to formulate the Fokker-Planck equation. The time-dependent statistics are then obtained as the solutions to a set of nonlinear first-order differential equations derived from the Fokker-Planck equation. As an illustration of the method, it is used to determine the response of a bilinear hysteretic system to a class of nonstationary excitations. Comparison of the results obtained here with those obtained by the simulation technique indicates that the proposed method is efficient for a stochastic seismic analysis of hysteretic systems, particularly for those with strong nonlinearity.