Anomalous amplitude-frequency dependence in a micromechanical resonator under synchronization
It is well known that the oscillation frequency relates approximately quadratically with amplitude in a Duffing nonlinear oscillator while the frequency is independent of amplitude in a linear oscillator. In this article, the dynamics of a micromechanical oscillator during synchronization is studied...
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| Published in | Nonlinear dynamics Vol. 103; no. 1; pp. 467 - 479 |
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| Main Authors | , , , , , |
| Format | Journal Article |
| Language | English |
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Dordrecht
Springer Netherlands
01.01.2021
Springer Nature B.V |
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| Abstract | It is well known that the oscillation frequency relates approximately quadratically with amplitude in a Duffing nonlinear oscillator while the frequency is independent of amplitude in a linear oscillator. In this article, the dynamics of a micromechanical oscillator during synchronization is studied and anomalous amplitude-frequency (a-f) dependence in a micromechanical resonator is observed. We theoretically and experimentally observed that in a linear resonator the amplitude is tuned quadratically with frequency while tuned linearly in a hardening as well as a softening nonlinear resonator, when the self-sustained resonator is synchronized to an external weak perturbation. Further investigation shows that the tunable range of the oscillation amplitude of a certain oscillator directly relies on the synchronization bandwidth, perturbation amplitude and frequency difference. The slope of the dependence can be tuned by phase delay in the feedback loop, while the feedback force dominantly determines the properties of the dependence from nonlinear relation to linear relation. This anomalous a-f effect provides a convenient technique for precise amplitude control. |
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| AbstractList | It is well known that the oscillation frequency relates approximately quadratically with amplitude in a Duffing nonlinear oscillator while the frequency is independent of amplitude in a linear oscillator. In this article, the dynamics of a micromechanical oscillator during synchronization is studied and anomalous amplitude-frequency (a-f) dependence in a micromechanical resonator is observed. We theoretically and experimentally observed that in a linear resonator the amplitude is tuned quadratically with frequency while tuned linearly in a hardening as well as a softening nonlinear resonator, when the self-sustained resonator is synchronized to an external weak perturbation. Further investigation shows that the tunable range of the oscillation amplitude of a certain oscillator directly relies on the synchronization bandwidth, perturbation amplitude and frequency difference. The slope of the dependence can be tuned by phase delay in the feedback loop, while the feedback force dominantly determines the properties of the dependence from nonlinear relation to linear relation. This anomalous a-f effect provides a convenient technique for precise amplitude control. |
| Author | Huan, Ronghua Jiang, Zhuangde Pu, Dong Wang, Xuefeng Yang, Pengzhe Wei, Xueyong |
| Author_xml | – sequence: 1 givenname: Dong surname: Pu fullname: Pu, Dong organization: Department of Mechanics, Key Laboratory of Soft Machines and Smart Devices of Zhejiang Province, Zhejiang University, School of Micro-nano electronics, Zhejiang University, ZJU-Hangzhou Global Scientific and Technology Innovation Center, Zhejiang University – sequence: 2 givenname: Pengzhe surname: Yang fullname: Yang, Pengzhe organization: State Key Laboratory for Manufacturing Systems Engineering, Xi’an Jiaotong University, School of Social and Political Science, University of Edinburgh – sequence: 3 givenname: Xuefeng surname: Wang fullname: Wang, Xuefeng organization: Department of Mechanics, Key Laboratory of Soft Machines and Smart Devices of Zhejiang Province, Zhejiang University – sequence: 4 givenname: Ronghua orcidid: 0000-0003-4648-3805 surname: Huan fullname: Huan, Ronghua email: rhhuan@zju.edu.cn organization: Department of Mechanics, Key Laboratory of Soft Machines and Smart Devices of Zhejiang Province, Zhejiang University – sequence: 5 givenname: Zhuangde surname: Jiang fullname: Jiang, Zhuangde organization: State Key Laboratory for Manufacturing Systems Engineering, Xi’an Jiaotong University – sequence: 6 givenname: Xueyong surname: Wei fullname: Wei, Xueyong email: seanwei@mail.xjtu.edu.cn organization: State Key Laboratory for Manufacturing Systems Engineering, Xi’an Jiaotong University |
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| SubjectTerms | Amplitudes Automotive Engineering Classical Mechanics Control Control theory Dependence Dynamical Systems Engineering Feedback loops Mechanical Engineering Original Paper Perturbation Resonators Synchronism Vibration |
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| Title | Anomalous amplitude-frequency dependence in a micromechanical resonator under synchronization |
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