The Elliptic Harmonic Balance Method for the Performance Analysis of a Two-Stage Vibration Isolation System with Geometric Nonlinearity
This study develops a modified elliptic harmonic balance method (EHBM) and uses it to solve the force and displacement transmissibility of a two-stage geometrically nonlinear vibration isolation system. Geometric damping and stiffness nonlinearities are incorporated in both the upper and lower stage...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Shock and Vibration |
| Online Access: | http://dx.doi.org/10.1155/2021/6690686 |
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| _version_ | 1832553999751970816 |
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| author | Weilei Wu Bin Tang |
| author_facet | Weilei Wu Bin Tang |
| author_sort | Weilei Wu |
| collection | DOAJ |
| description | This study develops a modified elliptic harmonic balance method (EHBM) and uses it to solve the force and displacement transmissibility of a two-stage geometrically nonlinear vibration isolation system. Geometric damping and stiffness nonlinearities are incorporated in both the upper and lower stages of the isolator. After using the relative displacement of the nonlinear isolator, we can numerically obtain the steady-state response using the first-order harmonic balance method (HBM1). The steady-state harmonic components of the stiffness and damping force are modified using the Jacobi elliptic functions. The developed EHBM can reduce the truncation error in the HBM1. Compared with the HBM1, the EHBM can improve the accuracy of the resonance regimes of the amplitude-frequency curve and transmissibility. The EHBM is simple and straightforward. It can maintain the same form as the balancing equations of the HBM1 but performs better than it. |
| format | Article |
| id | doaj-art-2a6fda710e254a5bae098a5e1e209eda |
| institution | Kabale University |
| issn | 1070-9622 1875-9203 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Shock and Vibration |
| spelling | doaj-art-2a6fda710e254a5bae098a5e1e209eda2025-02-03T05:52:37ZengWileyShock and Vibration1070-96221875-92032021-01-01202110.1155/2021/66906866690686The Elliptic Harmonic Balance Method for the Performance Analysis of a Two-Stage Vibration Isolation System with Geometric NonlinearityWeilei Wu0Bin Tang1Key Laboratory of Ocean Energy Utilization and Energy Conservation of Ministry of Education, Dalian University of Technology, Dalian 116023, ChinaKey Laboratory of Ocean Energy Utilization and Energy Conservation of Ministry of Education, Dalian University of Technology, Dalian 116023, ChinaThis study develops a modified elliptic harmonic balance method (EHBM) and uses it to solve the force and displacement transmissibility of a two-stage geometrically nonlinear vibration isolation system. Geometric damping and stiffness nonlinearities are incorporated in both the upper and lower stages of the isolator. After using the relative displacement of the nonlinear isolator, we can numerically obtain the steady-state response using the first-order harmonic balance method (HBM1). The steady-state harmonic components of the stiffness and damping force are modified using the Jacobi elliptic functions. The developed EHBM can reduce the truncation error in the HBM1. Compared with the HBM1, the EHBM can improve the accuracy of the resonance regimes of the amplitude-frequency curve and transmissibility. The EHBM is simple and straightforward. It can maintain the same form as the balancing equations of the HBM1 but performs better than it.http://dx.doi.org/10.1155/2021/6690686 |
| spellingShingle | Weilei Wu Bin Tang The Elliptic Harmonic Balance Method for the Performance Analysis of a Two-Stage Vibration Isolation System with Geometric Nonlinearity Shock and Vibration |
| title | The Elliptic Harmonic Balance Method for the Performance Analysis of a Two-Stage Vibration Isolation System with Geometric Nonlinearity |
| title_full | The Elliptic Harmonic Balance Method for the Performance Analysis of a Two-Stage Vibration Isolation System with Geometric Nonlinearity |
| title_fullStr | The Elliptic Harmonic Balance Method for the Performance Analysis of a Two-Stage Vibration Isolation System with Geometric Nonlinearity |
| title_full_unstemmed | The Elliptic Harmonic Balance Method for the Performance Analysis of a Two-Stage Vibration Isolation System with Geometric Nonlinearity |
| title_short | The Elliptic Harmonic Balance Method for the Performance Analysis of a Two-Stage Vibration Isolation System with Geometric Nonlinearity |
| title_sort | elliptic harmonic balance method for the performance analysis of a two stage vibration isolation system with geometric nonlinearity |
| url | http://dx.doi.org/10.1155/2021/6690686 |
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