Approximate Super- and Sub-harmonic Response of a Multi-DOFs System with Local Cubic Nonlinearities under Resonance
A multi-degree-of-freedom dynamical system with local cubic nonlinearities subjected to super/subharmonic excitation is considered in this paper. The purpose of this paper is to approximate the nonlinear response of system at super/sub harmonic resonance. For many situations, single resonance mode i...
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| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/531480 |
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| author | Yang CaiJin |
| author_facet | Yang CaiJin |
| author_sort | Yang CaiJin |
| collection | DOAJ |
| description | A multi-degree-of-freedom dynamical system with local cubic nonlinearities subjected to super/subharmonic excitation is considered in this paper. The purpose of this paper is to approximate the
nonlinear response of system at super/sub harmonic resonance. For many situations, single resonance mode is often observed to be leading as system enters into super/sub harmonic resonance. In this case, the single modal natural resonance theory can be applied to reduce the system model and a simplified model with only a single DOF is always obtained. Thus, an approximate solution and the analytical expression of frequency response relation are then derived using classical perturbation analysis. While the system is controlled by multiple modes, modal analysis for linearized system is used to decide dominant modes. The reduced model governed by these relevant modes is found and results in an approximate numerical solutions. An illustrative example of the discrete mass-spring-damper nonlinear vibration system with ten DOFs is examined. The approximation results are validated by comparing them with the calculations from direct numerical integration of the equation of motion of the original nonlinear system. Comparably good agreements are obtained. |
| format | Article |
| id | doaj-art-d8feb7cc7bc6430a9e8d5b6a0b892edc |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-d8feb7cc7bc6430a9e8d5b6a0b892edc2025-02-03T01:23:48ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/531480531480Approximate Super- and Sub-harmonic Response of a Multi-DOFs System with Local Cubic Nonlinearities under ResonanceYang CaiJin0Department of Engineering Mechanics, Tsinghua University, Beijing 100084, ChinaA multi-degree-of-freedom dynamical system with local cubic nonlinearities subjected to super/subharmonic excitation is considered in this paper. The purpose of this paper is to approximate the nonlinear response of system at super/sub harmonic resonance. For many situations, single resonance mode is often observed to be leading as system enters into super/sub harmonic resonance. In this case, the single modal natural resonance theory can be applied to reduce the system model and a simplified model with only a single DOF is always obtained. Thus, an approximate solution and the analytical expression of frequency response relation are then derived using classical perturbation analysis. While the system is controlled by multiple modes, modal analysis for linearized system is used to decide dominant modes. The reduced model governed by these relevant modes is found and results in an approximate numerical solutions. An illustrative example of the discrete mass-spring-damper nonlinear vibration system with ten DOFs is examined. The approximation results are validated by comparing them with the calculations from direct numerical integration of the equation of motion of the original nonlinear system. Comparably good agreements are obtained.http://dx.doi.org/10.1155/2012/531480 |
| spellingShingle | Yang CaiJin Approximate Super- and Sub-harmonic Response of a Multi-DOFs System with Local Cubic Nonlinearities under Resonance Journal of Applied Mathematics |
| title | Approximate Super- and Sub-harmonic Response of a Multi-DOFs System with Local Cubic Nonlinearities under Resonance |
| title_full | Approximate Super- and Sub-harmonic Response of a Multi-DOFs System with Local Cubic Nonlinearities under Resonance |
| title_fullStr | Approximate Super- and Sub-harmonic Response of a Multi-DOFs System with Local Cubic Nonlinearities under Resonance |
| title_full_unstemmed | Approximate Super- and Sub-harmonic Response of a Multi-DOFs System with Local Cubic Nonlinearities under Resonance |
| title_short | Approximate Super- and Sub-harmonic Response of a Multi-DOFs System with Local Cubic Nonlinearities under Resonance |
| title_sort | approximate super and sub harmonic response of a multi dofs system with local cubic nonlinearities under resonance |
| url | http://dx.doi.org/10.1155/2012/531480 |
| work_keys_str_mv | AT yangcaijin approximatesuperandsubharmonicresponseofamultidofssystemwithlocalcubicnonlinearitiesunderresonance |