Impacts of Small-Scale Effect and Nonlinear Damping on the Nonlinear Vibrations of Electrostatic Microresonators
Although the small-scale effect and nonlinear damping on the nonlinear vibration of microbeam electrostatic resonators are important, they have been overlooked by researchers. We use the slender beam model including the small-scale effect and nonlinear damping to investigate the nonlinear vibrations...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-01-01
|
| Series: | Micromachines |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2072-666X/14/1/170 |
| _version_ | 1797438575219834880 |
|---|---|
| author | Dayao Meng Kun Huang Wei Xu |
| author_facet | Dayao Meng Kun Huang Wei Xu |
| author_sort | Dayao Meng |
| collection | DOAJ |
| description | Although the small-scale effect and nonlinear damping on the nonlinear vibration of microbeam electrostatic resonators are important, they have been overlooked by researchers. We use the slender beam model including the small-scale effect and nonlinear damping to investigate the nonlinear vibrations of the electrostatic resonators in the present paper. We apply the Galerkin method on a nonlinear partial differential equation to obtain the nonlinear ordinary differential equations for the first and third modes. The two equations include constant terms. The multiple-scale method is used to obtain the approximate analytical solutions of the two equations. The approximate analytical solutions discover the effects of driving electric field, small-scale effect, and nonlinear damping on structural vibrations. The results suggest that the small-scale effect, the direct current (DC) voltage, and the alternating current (AC) voltage have some critical effects on the vibrations of microresonators. |
| first_indexed | 2024-03-09T11:40:03Z |
| format | Article |
| id | doaj.art-26945ec763e04d98bd87406cabadd396 |
| institution | Directory Open Access Journal |
| issn | 2072-666X |
| language | English |
| last_indexed | 2024-03-09T11:40:03Z |
| publishDate | 2023-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Micromachines |
| spelling | doaj.art-26945ec763e04d98bd87406cabadd3962023-11-30T23:34:10ZengMDPI AGMicromachines2072-666X2023-01-0114117010.3390/mi14010170Impacts of Small-Scale Effect and Nonlinear Damping on the Nonlinear Vibrations of Electrostatic MicroresonatorsDayao Meng0Kun Huang1Wei Xu2Department of Engineering Mechanics, Faculty of Civil Engineering and Mechanics, Kunming University of Science and Technology, Kunming 650500, ChinaDepartment of Engineering Mechanics, Faculty of Civil Engineering and Mechanics, Kunming University of Science and Technology, Kunming 650500, ChinaDepartment of Engineering Mechanics, Faculty of Civil Engineering and Mechanics, Kunming University of Science and Technology, Kunming 650500, ChinaAlthough the small-scale effect and nonlinear damping on the nonlinear vibration of microbeam electrostatic resonators are important, they have been overlooked by researchers. We use the slender beam model including the small-scale effect and nonlinear damping to investigate the nonlinear vibrations of the electrostatic resonators in the present paper. We apply the Galerkin method on a nonlinear partial differential equation to obtain the nonlinear ordinary differential equations for the first and third modes. The two equations include constant terms. The multiple-scale method is used to obtain the approximate analytical solutions of the two equations. The approximate analytical solutions discover the effects of driving electric field, small-scale effect, and nonlinear damping on structural vibrations. The results suggest that the small-scale effect, the direct current (DC) voltage, and the alternating current (AC) voltage have some critical effects on the vibrations of microresonators.https://www.mdpi.com/2072-666X/14/1/170microbeam resonatorselectric actuationscale effectnonlinear vibrationprimary resonancemultiple-scale method |
| spellingShingle | Dayao Meng Kun Huang Wei Xu Impacts of Small-Scale Effect and Nonlinear Damping on the Nonlinear Vibrations of Electrostatic Microresonators Micromachines microbeam resonators electric actuation scale effect nonlinear vibration primary resonance multiple-scale method |
| title | Impacts of Small-Scale Effect and Nonlinear Damping on the Nonlinear Vibrations of Electrostatic Microresonators |
| title_full | Impacts of Small-Scale Effect and Nonlinear Damping on the Nonlinear Vibrations of Electrostatic Microresonators |
| title_fullStr | Impacts of Small-Scale Effect and Nonlinear Damping on the Nonlinear Vibrations of Electrostatic Microresonators |
| title_full_unstemmed | Impacts of Small-Scale Effect and Nonlinear Damping on the Nonlinear Vibrations of Electrostatic Microresonators |
| title_short | Impacts of Small-Scale Effect and Nonlinear Damping on the Nonlinear Vibrations of Electrostatic Microresonators |
| title_sort | impacts of small scale effect and nonlinear damping on the nonlinear vibrations of electrostatic microresonators |
| topic | microbeam resonators electric actuation scale effect nonlinear vibration primary resonance multiple-scale method |
| url | https://www.mdpi.com/2072-666X/14/1/170 |
| work_keys_str_mv | AT dayaomeng impactsofsmallscaleeffectandnonlineardampingonthenonlinearvibrationsofelectrostaticmicroresonators AT kunhuang impactsofsmallscaleeffectandnonlineardampingonthenonlinearvibrationsofelectrostaticmicroresonators AT weixu impactsofsmallscaleeffectandnonlineardampingonthenonlinearvibrationsofelectrostaticmicroresonators |