Vibration of electrically actuated MEMS Timoshenko microbeams based on a hierarchical beam element
In this paper, vibration of Timoshenko microbeams with an axial force in micro-electromechanical systems (MEMS) is studied for the first time by using a nonlinear finite element procedure. Based on the von Kármán geometric nonlinearity and the modified couple stress theory (MCST), a beam element is...
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| Language: | English |
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Publishing House for Science and Technology
2022-12-01
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| Series: | Vietnam Journal of Mechanics |
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| Online Access: | https://vjs.ac.vn/index.php/vjmech/article/view/17909 |
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| author | Cong Ich Le Dinh Kien Nguyen |
| author_facet | Cong Ich Le Dinh Kien Nguyen |
| author_sort | Cong Ich Le |
| collection | DOAJ |
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In this paper, vibration of Timoshenko microbeams with an axial force in micro-electromechanical systems (MEMS) is studied for the first time by using a nonlinear finite element procedure. Based on the von Kármán geometric nonlinearity and the modified couple stress theory (MCST), a beam element is formulated by employing hierarchical functions to interpolate the displacement field. Using the derived element, the discretized equation of motion for the microbeam is constructed and then solved by the Newton-Raphson iterative procedure in conjunction with the Newmark method. The natural frequencies, pull-in voltages and dynamic deflections are computed for a clamped-clamped microbeam under electrostatic actuation of a given direct current (DC) voltage. The numerical result reveals that the axial force and the microsize effect have a significant influence on the vibration, and the fundamental frequency of the microbeams is underestimated by ignoring the size effect. The effects of the axial force, the applied voltage and the material length scale parameter on the vibration of the beam are studied in detail and highlighted.
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| format | Article |
| id | doaj-art-3208530ff5fc47b7b4569d3319f12472 |
| institution | OA Journals |
| issn | 0866-7136 2815-5882 |
| language | English |
| publishDate | 2022-12-01 |
| publisher | Publishing House for Science and Technology |
| record_format | Article |
| series | Vietnam Journal of Mechanics |
| spelling | doaj-art-3208530ff5fc47b7b4569d3319f124722025-08-20T02:10:38ZengPublishing House for Science and TechnologyVietnam Journal of Mechanics0866-71362815-58822022-12-0144410.15625/0866-7136/17909Vibration of electrically actuated MEMS Timoshenko microbeams based on a hierarchical beam elementCong Ich Le0https://orcid.org/0000-0002-5367-0054Dinh Kien Nguyen1https://orcid.org/0000-0001-9356-8401Le Quy Don Technical University, 236 Hoang Quoc Viet street, Hanoi, Vietnam\(^1\)Graduate University of Science and Technology, VAST, Hanoi, Vietnam<br>\(^2\)Institute of Mechanics, VAST, Hanoi, Vietnam In this paper, vibration of Timoshenko microbeams with an axial force in micro-electromechanical systems (MEMS) is studied for the first time by using a nonlinear finite element procedure. Based on the von Kármán geometric nonlinearity and the modified couple stress theory (MCST), a beam element is formulated by employing hierarchical functions to interpolate the displacement field. Using the derived element, the discretized equation of motion for the microbeam is constructed and then solved by the Newton-Raphson iterative procedure in conjunction with the Newmark method. The natural frequencies, pull-in voltages and dynamic deflections are computed for a clamped-clamped microbeam under electrostatic actuation of a given direct current (DC) voltage. The numerical result reveals that the axial force and the microsize effect have a significant influence on the vibration, and the fundamental frequency of the microbeams is underestimated by ignoring the size effect. The effects of the axial force, the applied voltage and the material length scale parameter on the vibration of the beam are studied in detail and highlighted. https://vjs.ac.vn/index.php/vjmech/article/view/17909Timoshenko microbeamMCSTelectrostatic actuationhierarchical interpolationnonlinear finite element analysis |
| spellingShingle | Cong Ich Le Dinh Kien Nguyen Vibration of electrically actuated MEMS Timoshenko microbeams based on a hierarchical beam element Vietnam Journal of Mechanics Timoshenko microbeam MCST electrostatic actuation hierarchical interpolation nonlinear finite element analysis |
| title | Vibration of electrically actuated MEMS Timoshenko microbeams based on a hierarchical beam element |
| title_full | Vibration of electrically actuated MEMS Timoshenko microbeams based on a hierarchical beam element |
| title_fullStr | Vibration of electrically actuated MEMS Timoshenko microbeams based on a hierarchical beam element |
| title_full_unstemmed | Vibration of electrically actuated MEMS Timoshenko microbeams based on a hierarchical beam element |
| title_short | Vibration of electrically actuated MEMS Timoshenko microbeams based on a hierarchical beam element |
| title_sort | vibration of electrically actuated mems timoshenko microbeams based on a hierarchical beam element |
| topic | Timoshenko microbeam MCST electrostatic actuation hierarchical interpolation nonlinear finite element analysis |
| url | https://vjs.ac.vn/index.php/vjmech/article/view/17909 |
| work_keys_str_mv | AT congichle vibrationofelectricallyactuatedmemstimoshenkomicrobeamsbasedonahierarchicalbeamelement AT dinhkiennguyen vibrationofelectricallyactuatedmemstimoshenkomicrobeamsbasedonahierarchicalbeamelement |