FORCED HARMONIC RESPONSE ANALYSIS OF NONLINEAR STRUCTURES USING DESCRIBING FUNCTIONS

The dynamic response of multiple-degree-of-freedom nonlinear structure s is usually determined by numerical integration of the equations of m otion, an approach which is computationally very expensive for steady- state response analysis of large structures. In this paper, an alterna tive semianalytical quasilinear method based on the describing functio n formulation is proposed for the harmonic response analysis of struct ures with symmetrical nonlinearities. The equations of motion are conv erted to a set of nonlinear algebraic equations and the solution is ob tained iteratively. The linear and nonlinear parts of the structure ar e dealt with separately, the former being represented by the constant linear receptance matrix [alpha], and the latter by the generalized qu asilinear matrix [DELTA] which is updated at each iteration. A special technique that reduces the computation time significantly when the no nlinearities are localized is used with success to analyze large struc tures. The proposed method is fully compatible with standard modal ana lysis procedures. Several examples dealing with cubic stiffness, piece wise linear stiffness, and coulomb friction type of nonlinearities are presented in the case of a ten-degree-of-freedom structure.