The Spreading Residue Harmonic Balance Method for Strongly Nonlinear Vibrations of a Restrained Cantilever Beam
The exact solutions of the nonlinear vibration systems are extremely complicated to be received, so it is crucial to analyze their approximate solutions. This paper employs the spreading residue harmonic balance method (SRHBM) to derive analytical approximate solutions for the fifth-order nonlinear...
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2017/5214616 |
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| author | Y. H. Qian J. L. Pan S. P. Chen M. H. Yao |
| author_facet | Y. H. Qian J. L. Pan S. P. Chen M. H. Yao |
| author_sort | Y. H. Qian |
| collection | DOAJ |
| description | The exact solutions of the nonlinear vibration systems are extremely complicated to be received, so it is crucial to analyze their approximate solutions. This paper employs the spreading residue harmonic balance method (SRHBM) to derive analytical approximate solutions for the fifth-order nonlinear problem, which corresponds to the strongly nonlinear vibration of an elastically restrained beam with a lumped mass. When the SRHBM is used, the residual terms are added to improve the accuracy of approximate solutions. Illustrative examples are provided along with verifying the accuracy of the present method and are compared with the HAM solutions, the EBM solutions, and exact solutions in tables. At the same time, the phase diagrams and time history curves are drawn by the mathematical software. Through analysis and discussion, the results obtained here demonstrate that the SRHBM is an effective and robust technique for nonlinear dynamical systems. In addition, the SRHBM can be widely applied to a variety of nonlinear dynamic systems. |
| format | Article |
| id | doaj-art-6e81eabc505849beae10036ae63cc2f3 |
| institution | OA Journals |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-6e81eabc505849beae10036ae63cc2f32025-08-20T02:06:28ZengWileyAdvances in Mathematical Physics1687-91201687-91392017-01-01201710.1155/2017/52146165214616The Spreading Residue Harmonic Balance Method for Strongly Nonlinear Vibrations of a Restrained Cantilever BeamY. H. Qian0J. L. Pan1S. P. Chen2M. H. Yao3College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua, Zhejiang 321004, ChinaCollege of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua, Zhejiang 321004, ChinaCollege of Mathematics, Xiamen University of Technology, Xiamen 361024, ChinaCollege of Mechanical Engineering, Beijing University of Technology, Beijing 100124, ChinaThe exact solutions of the nonlinear vibration systems are extremely complicated to be received, so it is crucial to analyze their approximate solutions. This paper employs the spreading residue harmonic balance method (SRHBM) to derive analytical approximate solutions for the fifth-order nonlinear problem, which corresponds to the strongly nonlinear vibration of an elastically restrained beam with a lumped mass. When the SRHBM is used, the residual terms are added to improve the accuracy of approximate solutions. Illustrative examples are provided along with verifying the accuracy of the present method and are compared with the HAM solutions, the EBM solutions, and exact solutions in tables. At the same time, the phase diagrams and time history curves are drawn by the mathematical software. Through analysis and discussion, the results obtained here demonstrate that the SRHBM is an effective and robust technique for nonlinear dynamical systems. In addition, the SRHBM can be widely applied to a variety of nonlinear dynamic systems.http://dx.doi.org/10.1155/2017/5214616 |
| spellingShingle | Y. H. Qian J. L. Pan S. P. Chen M. H. Yao The Spreading Residue Harmonic Balance Method for Strongly Nonlinear Vibrations of a Restrained Cantilever Beam Advances in Mathematical Physics |
| title | The Spreading Residue Harmonic Balance Method for Strongly Nonlinear Vibrations of a Restrained Cantilever Beam |
| title_full | The Spreading Residue Harmonic Balance Method for Strongly Nonlinear Vibrations of a Restrained Cantilever Beam |
| title_fullStr | The Spreading Residue Harmonic Balance Method for Strongly Nonlinear Vibrations of a Restrained Cantilever Beam |
| title_full_unstemmed | The Spreading Residue Harmonic Balance Method for Strongly Nonlinear Vibrations of a Restrained Cantilever Beam |
| title_short | The Spreading Residue Harmonic Balance Method for Strongly Nonlinear Vibrations of a Restrained Cantilever Beam |
| title_sort | spreading residue harmonic balance method for strongly nonlinear vibrations of a restrained cantilever beam |
| url | http://dx.doi.org/10.1155/2017/5214616 |
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