Quasi-periodic response and stability analysis for non-linear systems: A general approach

A modified FPA (Fixed Point Algorithm) is developed to analyze quasi-periodic responses of strongly non-linear dynamical systems with multi-input frequencies. An accurate and explicit form of the Jacobian matrix is used in the iteration process by selecting discrete integral points in the Poincare map. The monodromy matrix, obtained from discrete integral points on the second order Poincare domain, can accurately provide the stability condition as well as the bifurcation characteristics for the calculated quasi-periodic solution. Two examples are shown to illustrate the detailed application of the method. The proposed method can be utilized for obtaining the stable quasi-periodic responses as well as for analyzing the bifurcation characteristics of unstable solutions of general non-linear dynamical systems with multiple input excitation frequencies. (C) 1996 Academic Press Limited