Amplifying the response of a driven resonator via nonlinear interaction with a secondary resonator

Rosenberg, Sahar; Shoshani, Oriel

doi:10.1007/s11071-021-06659-x

Cited by 8 publications

(5 citation statements)

References 41 publications

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“…Figure 1). Instead, these distributions shown in Figures 6(d, e), with additional resonators activated to a high-amplitude state, exist because of the interplay between the coupling and nonlinearity (Rosenberg and Shoshani 2021). Note that although the coupling parameters (α, β) are identical for each distribution, the Global Coupling Force G is distinct for each solution.…”

Section: Bifurcation Diagramsmentioning

confidence: 94%

Multiple Equilibrium States in Large Arrays of Globally Coupled Resonators

Borra

Bajaj

Rhoads

et al. 2022

Preprint

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This work considers the response of a globally coupled array of oscillators, each with cubic nonlinear stiffness, in the presence of global reactive and dissipative coupling. Based on the continuum formulation for this system first presented in C. Borra et al (Journal of Sound and Vibration, 393:232–239, 2017), in the present work the individual resonators are excited to sufficient amplitude to allow for multiple coexisting equilibrium distributions. The method of multiple scales is then applied to the system to describe evolution equations for the amplitude and phase of each resonator. Because of the global nature of the coupling, this leads to an integro-differential equation for the stationary populations. Moreover, the characteristic equation used to determine the stability of these states is also an integral equation and admits both a discrete and continuous spectrum for its eigenvalues. The equilibrium structure of the system is studied as the reactive and dissipative coupling parameters are varied. For specific families of the equilibrium distributions two-parameter bifurcation sheets can be constructed. These sheets are connected as individual resonators transition between different branches for the corresponding individual resonators. The resulting one-parameter bifurcation curves are then understood in terms of the collections of these identified bifurcation sheets. The analysis is demonstrated for a system of N = 10 coupled resonators with mass detuning and extended results with N = 100 coupled resonators are illustrated.

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Section: Bifurcation Diagramsmentioning

confidence: 94%

Multiple Equilibrium States in Large Arrays of Globally Coupled Resonators

Borra

Bajaj

Rhoads

et al. 2022

Preprint

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“…Rosenberg et al. [ 513 ] analytically and numerically demonstrated that nonlinear interaction between two resonators with large difference in the relaxation times can significantly enhance the driven response of the slowly decaying (primary) resonator. They found that when the excitation frequency of the relatively fast decaying (secondary) resonator becomes near to the resonance frequency of the primary one, the linear coupling between the pair of driven resonators results in increasing the direct drive of the primary resonator.…”

Section: Fundamental Concepts Of Nano/micromechanical Resonatorsmentioning

confidence: 99%

Section: Fundamental Concepts Of Nano/micromechanical Resonatorsmentioning

confidence: 99%

“…Signal amplification of driven M/NEMS resonators, which can be performed by electrical [510,511] and mechanical [395,512,513] means, is crucial for achieving a large signal-to-noise ratio in engineering applications. Rosenberg et al [513] analytically and and c) indicating frequency response curves just before (at V Th = 5 • 5 V) and after veering (at V Th = 6 • 5 V), respectively, showing the amplification of the vibrational amplitude of the 3rd resonance due to the coupling between the modes after veering. Reproduced with permission.…”

Section: Nonlinear Coupled Resonator Arrays: Ncrasmentioning

confidence: 99%

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A Comprehensive Categorization of Micro/Nanomechanical Resonators and Their Practical Applications from an Engineering Perspective: A Review

Ghaemi

Nikoobin

Ashory

2022

Adv Elect Materials

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Micro/nanoelectromechanical systems (M/NEMS), especially micro/nanomechanical resonators, provide an unprecedented platform for investigating a wide range of applications in both fundamental physical phenomena (such as quantum‐level problems) and engineering and applied sciences (like sensing physical quantities and signal processing). In sensing context, these tiny resonators are invaluable tools for detecting weak forces and single molecules. Measuring such small variations in sub‐nanometer amplitudes at high frequencies has created many practical challenges. Therefore, maximizing the responsivity to a specified input parameter and minimizing the responsivity to other inputs such as noise are considered as the optimal design for the excellent performance in nanoresonators. The present review aims to summarize some of the recent progress in this rapidly advancing field. Specifically, more attention is paid to the topics related to the dynamical behaviors of micro/nanoresonator and their practical applications. First, the theory behind micro/nanoresonators is described. Then a summary is presented of the basic concepts in resonant devices. In addition, several commonly dynamical techniques to enhance sensitivity are introduced. Finally, the devices are classified based on linear and nonlinear, single and array, symmetric and asymmetric, and frequency shift‐based and amplitude shift‐based resonators, along with the relative advantages and disadvantages of each one in engineering applications.

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“…Recently, the vibrations of micro-and nano-electromechanical resonators have provided a new realm of applications for nonlinear vibrations [1][2][3][4]. Many significant advances have been made in theory [5][6][7], experiments [8][9][10], and applications [11][12][13], including exploring new phenomena uncovered in previously unattainable parameter regimes [14][15][16]. The dynamics of these systems range from simple Duffing responses [17][18][19] to more exotic responses, sometimes involving two or more interacting vibration modes [20][21][22].…”

Section: Introductionmentioning

confidence: 99%

A hybrid averaging and harmonic balance method for weakly nonlinear asymmetric resonators

2022

Self Cite

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Models for nonlinear vibrations commonly employ polynomial terms that arise from series expansions about an equilibrium point. The analysis of symmetric systems with cubic terms is very common, and the inclusion of asymmetric quadratic terms is known to modify the effective cubic nonlinearity in weakly nonlinear systems. The net effect is a monotonic dependence of the vibration frequency on the amplitude squared in both cases. However, in many applications, such a monotonic dependence is not observed, necessitating the use of techniques for strongly nonlinear systems or the inclusion of higher-order terms in a weakly nonlinear formulation. In either case, the analysis involves very tedious and/or numerical approaches for determining the system response. In the present work, we propose a method that is a hybrid of the methods of averaging and harmonic balance, which provides, with relatively straightforward calculations, good approximations for the amplitude-frequency dependence and for the steady-state response of damped, driven vibrations, including information about overtone harmonics and stability. The method is described, and general results are obtained for an asymmetric system with up to quintic nonlinear terms. The results are applied to a numerical example and validated using simulations. This approach will be useful for analyzing various systems with higher-order polynomial nonlinearities.

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Amplifying the response of a driven resonator via nonlinear interaction with a secondary resonator

Cited by 8 publications

References 41 publications

Multiple Equilibrium States in Large Arrays of Globally Coupled Resonators

Multiple Equilibrium States in Large Arrays of Globally Coupled Resonators

A Comprehensive Categorization of Micro/Nanomechanical Resonators and Their Practical Applications from an Engineering Perspective: A Review

A hybrid averaging and harmonic balance method for weakly nonlinear asymmetric resonators

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