Bifurcation Analysis of a Micro-Machined Gyroscope with Nonlinear Stiffness and Electrostatic Forces
The bifurcation of the periodic response of a micro-machined gyroscope with cubic supporting stiffness and fractional electrostatic forces is investigated. The pull-in phenomenon is analyzed to show that the system can have a stable periodic response when the detecting voltage is kept within a certa...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-01-01
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| Series: | Micromachines |
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| Online Access: | https://www.mdpi.com/2072-666X/12/2/107 |
| _version_ | 1827598747355316224 |
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| author | Huabiao Zhang Xinye Li Lijuan Zhang |
| author_facet | Huabiao Zhang Xinye Li Lijuan Zhang |
| author_sort | Huabiao Zhang |
| collection | DOAJ |
| description | The bifurcation of the periodic response of a micro-machined gyroscope with cubic supporting stiffness and fractional electrostatic forces is investigated. The pull-in phenomenon is analyzed to show that the system can have a stable periodic response when the detecting voltage is kept within a certain range. The method of averaging and the residue theorem are employed to give the averaging equations for the case of primary resonance and 1:1 internal resonance. Transition sets on the driving/detecting voltage plane that divide the parameter plane into 12 persistent regions and the corresponding bifurcation diagrams are obtained via the singularity theory. The results show that multiple solutions of the resonance curves appear with a large driving voltage and a small detecting voltage, which may lead to an uncertain output of the gyroscope. The effects of driving and detecting voltages on mechanical sensitivity and nonlinearity are analyzed for three persistent regions considering the operation requirements of the micro-machined gyroscope. The results indicate that in the region with a small driving voltage, the mechanical sensitivity is much smaller. In the other two regions, the variations in the mechanical sensitivity and nonlinearity are analogous. It is possible that the system has a maximum mechanical sensitivity and minimum nonlinearity for an appropriate range of detecting voltages. |
| first_indexed | 2024-03-09T03:59:20Z |
| format | Article |
| id | doaj.art-40e7a0bbaf9d47d6992c57cf8d1d951f |
| institution | Directory Open Access Journal |
| issn | 2072-666X |
| language | English |
| last_indexed | 2024-03-09T03:59:20Z |
| publishDate | 2021-01-01 |
| publisher | MDPI AG |
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| series | Micromachines |
| spelling | doaj.art-40e7a0bbaf9d47d6992c57cf8d1d951f2023-12-03T14:15:01ZengMDPI AGMicromachines2072-666X2021-01-0112210710.3390/mi12020107Bifurcation Analysis of a Micro-Machined Gyroscope with Nonlinear Stiffness and Electrostatic ForcesHuabiao Zhang0Xinye Li1Lijuan Zhang2School of Mechanical Engineering, Tianjin University of Commerce, Tianjin 300134, ChinaSchool of Mechanical Engineering, Hebei University of Technology, Tianjin 300401, ChinaSchool of Automobile and Transportation, Tianjin University of Technology and Education, Tianjin 300222, ChinaThe bifurcation of the periodic response of a micro-machined gyroscope with cubic supporting stiffness and fractional electrostatic forces is investigated. The pull-in phenomenon is analyzed to show that the system can have a stable periodic response when the detecting voltage is kept within a certain range. The method of averaging and the residue theorem are employed to give the averaging equations for the case of primary resonance and 1:1 internal resonance. Transition sets on the driving/detecting voltage plane that divide the parameter plane into 12 persistent regions and the corresponding bifurcation diagrams are obtained via the singularity theory. The results show that multiple solutions of the resonance curves appear with a large driving voltage and a small detecting voltage, which may lead to an uncertain output of the gyroscope. The effects of driving and detecting voltages on mechanical sensitivity and nonlinearity are analyzed for three persistent regions considering the operation requirements of the micro-machined gyroscope. The results indicate that in the region with a small driving voltage, the mechanical sensitivity is much smaller. In the other two regions, the variations in the mechanical sensitivity and nonlinearity are analogous. It is possible that the system has a maximum mechanical sensitivity and minimum nonlinearity for an appropriate range of detecting voltages.https://www.mdpi.com/2072-666X/12/2/107micro-machined gyroscopenonlinear dynamicsstatic pull-in analysissingularity analysisbifurcation of periodic solutions |
| spellingShingle | Huabiao Zhang Xinye Li Lijuan Zhang Bifurcation Analysis of a Micro-Machined Gyroscope with Nonlinear Stiffness and Electrostatic Forces Micromachines micro-machined gyroscope nonlinear dynamics static pull-in analysis singularity analysis bifurcation of periodic solutions |
| title | Bifurcation Analysis of a Micro-Machined Gyroscope with Nonlinear Stiffness and Electrostatic Forces |
| title_full | Bifurcation Analysis of a Micro-Machined Gyroscope with Nonlinear Stiffness and Electrostatic Forces |
| title_fullStr | Bifurcation Analysis of a Micro-Machined Gyroscope with Nonlinear Stiffness and Electrostatic Forces |
| title_full_unstemmed | Bifurcation Analysis of a Micro-Machined Gyroscope with Nonlinear Stiffness and Electrostatic Forces |
| title_short | Bifurcation Analysis of a Micro-Machined Gyroscope with Nonlinear Stiffness and Electrostatic Forces |
| title_sort | bifurcation analysis of a micro machined gyroscope with nonlinear stiffness and electrostatic forces |
| topic | micro-machined gyroscope nonlinear dynamics static pull-in analysis singularity analysis bifurcation of periodic solutions |
| url | https://www.mdpi.com/2072-666X/12/2/107 |
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