Synchronization of electrically coupled micromechanical oscillators with a frequency ratio of 3:1

Pu, Dong; Wei, Xueyong; Xu, Liang; Jiang, Zhuangde; Huan, Ronghua

doi:10.1063/1.5000786

Cited by 45 publications

(26 citation statements)

References 22 publications

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“…Hopf bifurcations [27], synchronization [28][29][30], internal resonances [31][32][33], and veering [34][35][36] are examples of physical phenomena that were extensively investigated at the micro and nano scale. Also, significant research has been conducted recently on nonlinear mechanics of microsystems, such as dynamic integrity of electrostatic MEMS [37][38][39] and AFM [40,41], control of MEMS [42][43][44], reduced-order modeling and gyroscopes [45][46][47].…”

Section: Introductionmentioning

confidence: 99%

Linear and nonlinear dynamics of micro and nano-resonators: Review of recent advances

Hajjaj

Jaber

Ilyas

et al. 2020

International Journal of Non-Linear Mechanics

119

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Micro and nanoelectromechanical systems M/NEMS have been extensively investigated and exploited in the past few decades for various applications and for probing fundamental physical phenomena. Understanding the linear and nonlinear dynamical behaviors of the movable structures in these systems is crucial for their successful implementation in various novel technologies and to meet the long list of new sophisticated requirements. This paper presents a review for some of the recent topics pertaining to the dynamical behaviors, linear and nonlinear, of M/NEMS resonating structures. First, an overview is presented of the various used dynamical approaches to enhance the sensitivity of resonators for sensing applications. Then a summary is presented of the recent works on the linear and nonlinear mode coupling in M/NEMS resonator. Next, recent research is reviewed on coupled M/NEMS resonators, mechanically and electrically, leading to collective behaviors like mode localization. The final part of the paper discusses analytical approaches that have been developed to better understand and investigate the dynamical behavior of M/NEMS resonators focusing on the perturbation method the multiple time scales.

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Section: Introductionmentioning

confidence: 99%

Linear and nonlinear dynamics of micro and nano-resonators: Review of recent advances

Hajjaj

Jaber

Ilyas

et al. 2020

International Journal of Non-Linear Mechanics

119

View full text Add to dashboard Cite

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“…Energy transfer via internal resonance among various modes of vibration of micro and nano-electromechanical structures (MEMS and NEMS) has been explored for several potential applications, such as timing/synchronization [1,2], energy harvesting [3,4], mass sensing [5], and frequency stabilization [6,7]. Internal resonance, also called auto-parametric resonance, represents a nonlinear 2 mechanism for energy leakage from the targeted vibration mode to another mode.…”

Section: Introductionmentioning

confidence: 99%

Theoretical and experimental investigations of the crossover phenomenon in micromachined arch resonator: part II—simultaneous 1:1 and 2:1 internal resonances

et al. 2019

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We investigate in a silicon micromachined arch beam the activation of a one-to-one internal resonance between the first symmetric and first antisymmetric modes simultaneously with the activation of a two-to-one internal resonance between these modes and the second symmetric mode. The arch is excited electrically, using an antisymmetric partial electrode to activate both modes of vibrations, and tuned electrothermally via Joule's heating. Theoretically, we explore the dynamics of the beam using the Galerkin and multiple time scales methods. The simulation results are shown to have good agreement with the experimental data. The results show the merging of both modes at crossing, after which the first antisymmetric mode exchanges the nonlinear behavior with the first symmetric mode. The nonlinear behavior of the arch beam is demonstrated and analyzed experimentally and theoretically as experiencing the simultaneous 2:1 and 1:1 internal resonances.

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“…Mode coupling among various modes of vibration of micro-and nano-electromechanical systems (MEMS and NEMS) has been explored for several interesting capabilities and potential applications, such as mass sensing [1,2], signals filtering [3] and timing/synchronization [4][5][6]. The wide implementation of mode coupling in N/MEMS in the past decade has been sparked by the exciting results demonstrated in the classical structure dynamics.…”

Section: Introductionmentioning

confidence: 99%

Theoretical and experimental investigations of the crossover phenomenon in micromachined arch resonator: part I—linear problem

et al. 2019

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We investigate, experimentally and theoretically, the linear mode coupling between the first symmetric and antisymmetric modes of an electrothermally tuned and electrostatically actuated micromachined arch resonator. The arch is excited using an antisymmetric partial electrode to activate both modes of vibrations. Theoretically, we explore the static and dynamic behavior using the Galerkin method. When tuning the electrothermal voltage, the first symmetric frequency increases while the first antisymmetric frequency decreases until they cross. The results show linear coupling and hybridization of both modes near crossing only in the presence of the perturbation from the electrostatic force using the partial electrode. We show the linear merging of both modes at crossing. Also, the eigenfrequency variation around crossing shows a ratio of 2:1 between the second symmetric mode and the first symmetric/antisymmetric modes, which can lead to simultaneous 1:1 and 2:1 internal resonances.

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Synchronization of electrically coupled micromechanical oscillators with a frequency ratio of 3:1

Cited by 45 publications

References 22 publications

Linear and nonlinear dynamics of micro and nano-resonators: Review of recent advances

Linear and nonlinear dynamics of micro and nano-resonators: Review of recent advances

Theoretical and experimental investigations of the crossover phenomenon in micromachined arch resonator: part II—simultaneous 1:1 and 2:1 internal resonances

Theoretical and experimental investigations of the crossover phenomenon in micromachined arch resonator: part I—linear problem

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