Monostable Dynamic Analysis of Microbeam-Based Resonators via an Improved One Degree of Freedom Model
Monostable vibration can eliminate dynamic bifurcation and improve system stability, which is required in many microelectromechanical systems (MEMS) applications, such as microbeam-based and comb-driven resonators. This article aims to theoretically investigate the monostable vibration in size-effec...
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| Format: | Article |
| Language: | English |
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MDPI AG
2018-02-01
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| Series: | Micromachines |
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| Online Access: | http://www.mdpi.com/2072-666X/9/2/89 |
| _version_ | 1811259246695677952 |
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| author | Lei Li Qichang Zhang Wei Wang Jianxin Han |
| author_facet | Lei Li Qichang Zhang Wei Wang Jianxin Han |
| author_sort | Lei Li |
| collection | DOAJ |
| description | Monostable vibration can eliminate dynamic bifurcation and improve system stability, which is required in many microelectromechanical systems (MEMS) applications, such as microbeam-based and comb-driven resonators. This article aims to theoretically investigate the monostable vibration in size-effected MEMS via a low dimensional model. An improved single degree of freedom model to describe electrically actuated microbeam-based resonators is obtained by using modified couple stress theory and Nonlinear Galerkin method. Static displacement, pull-in voltage, resonant frequency and especially the monostable dynamic behaviors of the resonators are investigated in detail. Through perturbation analysis, an approximate average equation is derived by the application of the method of Multiple Scales. Theoretical expressions about parameter space and maximum amplitude of monostable vibration are then deduced. Results show that this improved model can describe the static behavior more accurately than that of single degree of freedom model via traditional Galerkin Method. This desired monostable large amplitude vibration is significantly affected by the ratio of the gap width to mircobeam thickness. The optimization design results show that reasonable decrease of this ratio can be beneficial to monostable vibration. All these analytical results are verified by numerical results via Differential Quadrature method, which show excellent agreement with each other. This analysis has the potential of improving dynamic performance in MEMS. |
| first_indexed | 2024-04-12T18:28:39Z |
| format | Article |
| id | doaj.art-cce7f5e1c67b48dd9a94b382f5fb7e7d |
| institution | Directory Open Access Journal |
| issn | 2072-666X |
| language | English |
| last_indexed | 2024-04-12T18:28:39Z |
| publishDate | 2018-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Micromachines |
| spelling | doaj.art-cce7f5e1c67b48dd9a94b382f5fb7e7d2022-12-22T03:21:10ZengMDPI AGMicromachines2072-666X2018-02-01928910.3390/mi9020089mi9020089Monostable Dynamic Analysis of Microbeam-Based Resonators via an Improved One Degree of Freedom ModelLei Li0Qichang Zhang1Wei Wang2Jianxin Han3School of Transportation and Vehicle Engineering, Shandong University of Technology, Zibo 255049, ChinaDepartment of Mechanics, School of Mechanical Engineering, Tianjin University, Tianjin 300350, ChinaDepartment of Mechanics, School of Mechanical Engineering, Tianjin University, Tianjin 300350, ChinaTianjin Key Laboratory of High Speed Cutting and Precision Machining, Tianjin University of Technology and Education, Tianjin 300222, ChinaMonostable vibration can eliminate dynamic bifurcation and improve system stability, which is required in many microelectromechanical systems (MEMS) applications, such as microbeam-based and comb-driven resonators. This article aims to theoretically investigate the monostable vibration in size-effected MEMS via a low dimensional model. An improved single degree of freedom model to describe electrically actuated microbeam-based resonators is obtained by using modified couple stress theory and Nonlinear Galerkin method. Static displacement, pull-in voltage, resonant frequency and especially the monostable dynamic behaviors of the resonators are investigated in detail. Through perturbation analysis, an approximate average equation is derived by the application of the method of Multiple Scales. Theoretical expressions about parameter space and maximum amplitude of monostable vibration are then deduced. Results show that this improved model can describe the static behavior more accurately than that of single degree of freedom model via traditional Galerkin Method. This desired monostable large amplitude vibration is significantly affected by the ratio of the gap width to mircobeam thickness. The optimization design results show that reasonable decrease of this ratio can be beneficial to monostable vibration. All these analytical results are verified by numerical results via Differential Quadrature method, which show excellent agreement with each other. This analysis has the potential of improving dynamic performance in MEMS.http://www.mdpi.com/2072-666X/9/2/89MEMSmonostable vibrationNonlinear Galerkin methodoptimization |
| spellingShingle | Lei Li Qichang Zhang Wei Wang Jianxin Han Monostable Dynamic Analysis of Microbeam-Based Resonators via an Improved One Degree of Freedom Model Micromachines MEMS monostable vibration Nonlinear Galerkin method optimization |
| title | Monostable Dynamic Analysis of Microbeam-Based Resonators via an Improved One Degree of Freedom Model |
| title_full | Monostable Dynamic Analysis of Microbeam-Based Resonators via an Improved One Degree of Freedom Model |
| title_fullStr | Monostable Dynamic Analysis of Microbeam-Based Resonators via an Improved One Degree of Freedom Model |
| title_full_unstemmed | Monostable Dynamic Analysis of Microbeam-Based Resonators via an Improved One Degree of Freedom Model |
| title_short | Monostable Dynamic Analysis of Microbeam-Based Resonators via an Improved One Degree of Freedom Model |
| title_sort | monostable dynamic analysis of microbeam based resonators via an improved one degree of freedom model |
| topic | MEMS monostable vibration Nonlinear Galerkin method optimization |
| url | http://www.mdpi.com/2072-666X/9/2/89 |
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