A Toeplitz Jacobian Matrix/Fast Fourier Transformation Method for Steady-State Analysis of Discontinuous Oscillators. (1995)

• Record Type: Journal Article
• Authors: Ge, T.; Leung, A. Y. T.
• Is Part Of: Shock and vibration. Volume 1995(1995)
• Page Start: 205
• Page End: 218
• Publication Date: 1995
• Subjects: Shock (Mechanics) -- Periodicals; Vibration -- Periodicals; 534.5
• DOI: 10.3233/SAV-1995-2302
• Languages: English
• ISSNs: 1070-9622

Abstract

Abstract : A semianalytical algorithm is proposed for the solutions and their stability of a piecewise nonlinear system. The conventional harmonic balance method is modified by the introduction of Toeplitz Jacobian matrices (TJM) and by the alternative applications of fast Fourier transformation (FFT) and its inverse. The TJM/FFT method substantially reduces the amount of computation and circumvents the necessary numerical differentiation for the Jacobian. An arc-length algorithm and a branch switching procedure are incorporated so that the secondary branches can be independently traced. Oscillators with piecewise nonlinear characteristics are taken as illustrative examples. Flip, fold, and Hopf bifurcations are of interest.