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 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...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1995-01-01
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| Series: | Shock and Vibration |
| Online Access: | http://dx.doi.org/10.3233/SAV-1995-2302 |
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| _version_ | 1832565312009011200 |
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| author | T. Ge A. Y. T. Leung |
| author_facet | T. Ge A. Y. T. Leung |
| author_sort | T. Ge |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-7ffe3921f16043cea6bcff3d7f16ddd1 |
| institution | Kabale University |
| issn | 1070-9622 1875-9203 |
| language | English |
| publishDate | 1995-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Shock and Vibration |
| spelling | doaj-art-7ffe3921f16043cea6bcff3d7f16ddd12025-02-03T01:08:06ZengWileyShock and Vibration1070-96221875-92031995-01-012320521810.3233/SAV-1995-2302A Toeplitz Jacobian Matrix/Fast Fourier Transformation Method for Steady-State Analysis of Discontinuous OscillatorsT. Ge0A. Y. T. Leung1Department of Civil and Structural Engineering, University of Hong Kong, Pokfulam Road, Hong KongDepartment of Civil and Structural Engineering, University of Hong Kong, Pokfulam Road, Hong KongA 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.http://dx.doi.org/10.3233/SAV-1995-2302 |
| spellingShingle | T. Ge A. Y. T. Leung A Toeplitz Jacobian Matrix/Fast Fourier Transformation Method for Steady-State Analysis of Discontinuous Oscillators Shock and Vibration |
| title | A Toeplitz Jacobian Matrix/Fast Fourier Transformation Method for Steady-State Analysis of Discontinuous Oscillators |
| title_full | A Toeplitz Jacobian Matrix/Fast Fourier Transformation Method for Steady-State Analysis of Discontinuous Oscillators |
| title_fullStr | A Toeplitz Jacobian Matrix/Fast Fourier Transformation Method for Steady-State Analysis of Discontinuous Oscillators |
| title_full_unstemmed | A Toeplitz Jacobian Matrix/Fast Fourier Transformation Method for Steady-State Analysis of Discontinuous Oscillators |
| title_short | A Toeplitz Jacobian Matrix/Fast Fourier Transformation Method for Steady-State Analysis of Discontinuous Oscillators |
| title_sort | toeplitz jacobian matrix fast fourier transformation method for steady state analysis of discontinuous oscillators |
| url | http://dx.doi.org/10.3233/SAV-1995-2302 |
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