A TOEPLITZ JACOBIAN MATRIX FAST FOURIER TRANSFORMATION METHOD FOR STEADY-STATE ANALYSIS OF DISCONTINUOUS OSCILLATORS

A semianalytical algorithm is proposed for the solutions and their sta bility of a piecewise nonlinear system. The conventional harmonic bala nce method is modified by the introduction of Toeplitz Jacobian matric es (TJM) and by the alternative applications of fast Fourier transform ation (FFT) and its inverse. The TJM/FFT method substantially reduces the amount of computation and circumvents the necessary numerical diff erentiation for the Jacobian. An are-length algorithm anti a branch sw itching procedure are incorporated so that the secondary branches can be independently traced. Oscillators with piecewise nonlinear characte ristics are taken as illustrative examples. Flip, fold, and Hopf bifur cations are of interest. (C) 1995 John Wiley & Sons, Inc.