Effects of time step size on the response of a bilinear system, I: Numerical study

Abstract

Numerical simulations have been carried out to study the dynamic response of a bilinear structural system subjected to harmonic excitations. By using Newmark's average acceleration method with a very small time step, subharmonic and chaotic responses have been obtained for certain parameter values. Poincaré maps, a divergence analysis with respect to initial conditions, and a bifurcation diagram with respect to frequency are presented. The effects of time step size on the numerical solutions of chaos are discussed. Insufficiently small time steps can lead to spurious existence of subharmonics and incomplete chaotic attractors. With small time steps, the correct shape of the chaotic attractor can be obtained. However, the response time history is sensitive to the time step size. © 1991.