T. Ge et Ayt. Leung, A TOEPLITZ JACOBIAN MATRIX FAST FOURIER TRANSFORMATION METHOD FOR STEADY-STATE ANALYSIS OF DISCONTINUOUS OSCILLATORS, Shock and vibration, 2(3), 1995, pp. 205-218
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.