A Toeplitz Jacobian Matrix/Fast Fourier Transformation Method for Steady-State Analysis of Discontinuous Oscillators | Zendy

T. Ge | Zendy; A. Y. T. Leung | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Open Access

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

Author(s) -

T. Ge,

A. Y. T. Leung

Publication year - 1995

Publication title -

shock and vibration

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.418

H-Index - 45

eISSN - 1875-9203

pISSN - 1070-9622

DOI - 10.1155/1995/973431

Subject(s) - toeplitz matrix , jacobian matrix and determinant , mathematics , fast fourier transform , nonlinear system , piecewise , inverse , harmonic balance , matrix (chemical analysis) , computation , transformation (genetics) , mathematical analysis , algorithm , geometry , pure mathematics , physics , biochemistry , chemistry , materials science , quantum mechanics , composite material , gene

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.

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research