Forced harmonic response analysis of nonlinear structures using describing functions

Abstract

A semianalytical quasilinear method based on the describing function formulation is proposed for the harmonic response analysis of structures with symmetrical nonlinearities. The equations of motion are converted to a set of nonlinear algebraic equations. The linear and nonlinear parts of the structure are dealt with separately, the former being represented by the constant linear receptance matrix, and the latter by the generalized quasilinear matrix which is updated at each iteration. Several examples dealing with cubic stiffness, piecewise linear stiffness, and coulomb friction type of nonlinearities are presented