Frequency stabilization by synchronization of Duffing oscillators

Zanette, Damián H.

doi:10.1209/0295-5075/115/20009

Cited by 9 publications

(4 citation statements)

References 17 publications

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“…Investigations on synchronization trace back to Huygens' work in 1677 [12]. Presently, synchronization exhibits remarkable performance in sensing, attributed to exceptional frequency stability [13][14][15][16] and the ease of frequency recognition [17]. This has found significant application in microelectromechanical systems (MEMS) owing to their compact size and compatibility with integrated circuit fabrication [18][19][20][21].…”

Section: Introductionmentioning

confidence: 95%

Nonlinearity-Induced Asymmetric Synchronization Region in Micromechanical Oscillators

Liu,

Qin,

Shi

et al. 2024

Micromachines

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Synchronization in microstructures is a widely explored domain due to its diverse dynamic traits and promising practical applications. Within synchronization analysis, the synchronization bandwidth serves as a pivotal metric. While current research predominantly focuses on symmetric evaluations of synchronization bandwidth, the investigation into potential asymmetries within nonlinear oscillators remains unexplored, carrying implications for sensor application performance. This paper conducts a comprehensive exploration employing straight and arch beams capable of demonstrating linear, hardening, and softening characteristics to thoroughly scrutinize potential asymmetry within the synchronization region. Through the introduction of weak harmonic forces to induce synchronization within the oscillator, we observe distinct asymmetry within its synchronization range. Additionally, we present a robust theoretical model capable of fully capturing the linear, hardening, and softening traits of resonators synchronized to external perturbation. Further investigation into the effects of feedback strength and phase delay on synchronization region asymmetry, conducted through analytical and experimental approaches, reveals a consistent alignment between theoretical predictions and experimental outcomes. These findings hold promise in providing crucial technical insights to enhance resonator performance and broaden the application landscape of MEMS (Micro-Electro-Mechanical Systems) technology.

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Section: Introductionmentioning

confidence: 95%

Nonlinearity-Induced Asymmetric Synchronization Region in Micromechanical Oscillators

Liu,

Qin,

Shi

et al. 2024

Micromachines

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“…Substituting Equation (26) into Equation (24) yields the following: Figure 13 shows the variation of the detection error under different quality factors. It was found that the damping is crucial to the accuracy of mass detection.…”

Section: Parameter Identification Based On Frequency Stabilization Anmentioning

confidence: 99%

“…Experimental results showed that the interdependence between the resonance frequency and the vibration amplitude can be limited by the mode interaction in nonlinear micromechanical resonators [ 25 ]. Zanette [ 26 ] studied the joint dynamics of coupled Duffing oscillators with a nonlinearity of opposite signs. Results showed that the frequency stabilization of nonlinear coupled systems can be achieved under appropriate parameter conditions.…”

Section: Introductionmentioning

confidence: 99%

A Novel Frequency Stabilization Approach for Mass Detection in Nonlinear Mechanically Coupled Resonant Sensors

Liu

Shao

et al. 2021

Micromachines

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Frequency stabilization can overcome the dependence of resonance frequency on amplitude in nonlinear microelectromechanical systems, which is potentially useful in nonlinear mass sensor. In this paper, the physical conditions for frequency stabilization are presented theoretically, and the influence of system parameters on frequency stabilization is analyzed. Firstly, a nonlinear mechanically coupled resonant structure is designed with a nonlinear force composed of a pair of bias voltages and an alternating current (AC) harmonic load. We study coupled-mode vibration and derive the expression of resonance frequency in the nonlinear regime by utilizing perturbation and bifurcation analysis. It is found that improving the quality factor of the system is crucial to realize the frequency stabilization. Typically, stochastic dynamic equation is introduced to prove that the coupled resonant structure can overcome the influence of voltage fluctuation on resonance frequency and improve the robustness of the sensor. In addition, a novel parameter identification method is proposed by using frequency stabilization and bifurcation jumping, which effectively avoids resonance frequency shifts caused by driving voltage. Finally, numerical studies are introduced to verify the mass detection method. The results in this paper can be used to guide the design of a nonlinear sensor.

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“…This simple model has been used to model memory and logic devices [15,16], neural networks [17,18], the recurrence of Earth's ice ages [20], piezoelectric buckled beams [21] and many other systems. Different aspects of the system were investigated, including the effect of noise on the hysteresis of a single oscillator [22], the noise-induced intermittency of two coupled oscillators [23], chaos and routes to chaos [24,25], synchronization [26,27] and others. Here, using numerical continuation, we found the bifurcation diagram and identified a bistability region of oscillations with the driving period and with the doubled period.…”

mentioning

confidence: 99%

Double-period breathers in a driven and damped lattice

et al. 2018

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Spatially localized and temporally oscillating solutions, known as discrete breathers, have been experimentally and theoretically discovered in many physical systems. Here, we consider a lattice of coupled damped and driven Helmholtz-Duffing oscillators in which we found a spatial coexistence of oscillating solutions with different frequencies. Specifically, we demonstrate that stable perioddoubled solutions coexist with solutions oscillating at the frequency of the driving force. Such solution represents period-doubled breathers resulting from a stability overlap between subharmonic and harmonic solutions and exist up to a certain strength of the lattice coupling. Our findings suggest that this phenomenon can occur in any driven lattice where the nonlinearity admits bistability (or multi-stability) of subharmonic and harmonic solutions.

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Frequency stabilization by synchronization of Duffing oscillators

Cited by 9 publications

References 17 publications

Nonlinearity-Induced Asymmetric Synchronization Region in Micromechanical Oscillators

Nonlinearity-Induced Asymmetric Synchronization Region in Micromechanical Oscillators

A Novel Frequency Stabilization Approach for Mass Detection in Nonlinear Mechanically Coupled Resonant Sensors

Double-period breathers in a driven and damped lattice

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