Nonlinearity-Induced Synchronization Enhancement in Micromechanical Oscillators

Guest, Jeffrey R.; Antonio, Dario; Czaplewski, David A.; 'opez, Daniel L; Arroyo, Sebasti 'an I.; Zanette, Damián H.

doi:10.1103/physrevlett.114.034103

Cited by 61 publications

(48 citation statements)

References 16 publications

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“…In modern clocks, oscillators are built from synthetic quartz crystals and feedback is implemented electronically. At the micro-and nanoscale, quartz crystals are expected to be replaced by simpler mechanical oscillators such as tiny vibrating silica beams [2,3], which are easily built during circuit printing and can be actuated by very small electric fields [4,5].…”

Section: Introductionmentioning

confidence: 99%

Self-sustained oscillations with delayed velocity feedback

Zanette

2017

Pap. Phys.

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We study a model for a nonlinear mechanical oscillator, relevant to the dynamics of microand nanomechanical time-keeping devices, where periodic motion is sustained by a feedback force proportional to the oscillation velocity. Specifically, we focus our attention on the effect of a time delay in the feedback loop, assumed to originate in the electric circuit that creates and injects the self-sustaining force. Stationary oscillating solutions to the equation of motion, whose stability is insured by the crucial role of nonlinearity, are analytically obtained through suitable approximations. We show that a delay within the order of the oscillation period can suppress self-sustained oscillations. Numerical solutions are used to validate the analytical approximations.

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Section: Introductionmentioning

confidence: 99%

Self-sustained oscillations with delayed velocity feedback

Zanette

2017

Pap. Phys.

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“…A similar behavior is observed in this experiment as well, with a difference that, when the 3h mode is driven at a larger amplitude, the synchronization range increases but the range when sweeping down is smaller than when sweeping up. An asymmetric synchronization range is observed when the resonance modes have nonlinearities and this asymmetry has been previously reported in injection-locked oscillators 9,10 and mutual synchronization. 20 To study the theoretical behavior of the coupled oscillators, we introduce a model which explains this behavior.…”

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confidence: 94%

“…The range of frequencies over which this locking can occur is called the synchronization range, and this range increases with the amplitude of the reference oscillator and with certain types of amplitude-dependent nonlinearities in the first oscillator. 9,10 Synchronization can also occur when the two frequencies have a harmonic relationship, f 2 ¼ nf 1 , where n is an integer, a phenomenon known as subharmonic synchronization. [11][12][13][14] Distinct from injection locking, mutual synchronization and mutual subharmonic synchronization occur when there is mutual, bidirectional coupling between the two oscillators.…”

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confidence: 99%

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Mutual 3:1 subharmonic synchronization in a micromachined silicon disk resonator

Taheri-Tehrani

Guerrieri

Defoort

et al. 2017

Applied Physics Letters

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We demonstrate synchronization between two intrinsically coupled oscillators that are created from two distinct vibration modes of a single micromachined disk resonator. The modes have a 3:1 subharmonic frequency relationship and cubic, non-dissipative electromechanical coupling between the modes enables their two frequencies to synchronize. Our experimental implementation allows the frequency of the lower frequency oscillator to be independently controlled from that of the higher frequency oscillator, enabling study of the synchronization dynamics. We find close quantitative agreement between the experimental behavior and an analytical coupled-oscillator model as a function of the energy in the two oscillators. We demonstrate that the synchronization range increases when the lower frequency oscillator is strongly driven and when the higher frequency oscillator is weakly driven. This result suggests that synchronization can be applied to the frequency-selective detection of weak signals and other mechanical signal processing functions.

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“…The high structural quality of those materials combined with the reduced effective mass allows such beams to operate at very high resonance frequencies with extremely high Q factors (i.e., low damping). These beneficial attributes provide the basis for exceptional performance of MEMS applications such as extremely sensitive sensors [1][2][3][4], mechanical energy harvesters [5][6][7], nano/micro-relays [8,9], logic memory and computation [10][11][12], field effect transistors [13], and a high frequency reference in oscillators [14][15][16]. The MEMS devices implemented in these applications were mostly designed to operate in their linear resonant modes with the above-mentioned benefits.…”

Section: Introductionmentioning

confidence: 99%

Mechanism of geometric nonlinearity in a nonprismatic and heterogeneous microbeam resonator

Asadi

Peshin

et al. 2017

Phys. Rev. B

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Implementation of geometric nonlinearity in micro-electro-mechanical system (MEMS) resonators offers a flexible and efficient design to overcome the limitations of linear MEMS by utilizing beneficial nonlinear characteristics not attainable in a linear setting. Integration of nonlinear coupling elements into an otherwise purely linear microcantilever is one promising way to intentionally realize geometric nonlinearity. Here, we demonstrate that a nonlinear, heterogeneous micro-resonator system, consisting of a silicon micro-cantilever with a polymer attachment exhibits strong nonlinear hardening behavior not only in the first flexural mode but also in the higher modes (i.e., second and third flexural modes). In this design, we deliberately implement a drastic and reversed change in the axial vs. bending stiffness between the Si and polymer components by varying the geometric and material properties. By doing so, the resonant oscillations induce the large axial stretching within the polymer component, which effectively introduces the geometric stiffness and damping nonlinearity. The efficacy of the design and the mechanism of geometric nonlinearity are corroborated through a comprehensive experimental, analytical, and numerical (Finite Element) analysis on the nonlinear dynamics of the proposed system. 2

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Nonlinearity-Induced Synchronization Enhancement in Micromechanical Oscillators

Cited by 61 publications

References 16 publications

Self-sustained oscillations with delayed velocity feedback

Self-sustained oscillations with delayed velocity feedback

Mutual 3:1 subharmonic synchronization in a micromachined silicon disk resonator

Mechanism of geometric nonlinearity in a nonprismatic and heterogeneous microbeam resonator

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