Zero-dispersion point in curved micro-mechanical beams

Rosenberg, Sahar; Shoshani, Oriel

doi:10.1007/s11071-021-07015-9

Cited by 18 publications

(5 citation statements)

References 60 publications

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“…The dashed translucent curves are calculated from the frequency ωexact of the exact analytical solution (see Ref. [39]), which is in remarkable agreement with the frequency ωres (solid dark curves) of our approximate solution. Right panel: Response curves for ω 0 = 10, α 2 = 9.64, α 3 = 1, F = 10 −2 , Γ = F/(2ω 0 ares), where ares is the resonance amplitude on the backbone curve (dashed black curve) that varies from ares = 0.2 (red response curve) to ares = 2 (purple response curve), which effectively varies the damping.…”

Section: The Hybrid Averaging Methodssupporting

confidence: 76%

“…( 11) of Ref. [39]) for a system with quadratic and cubic nonlinearities is shown in the left panel of Fig. 3.…”

Section: The Hybrid Averaging Methodsmentioning

confidence: 98%

“…1 The exact solution of the free oscillation in Ref. [39], which is obtained from an elliptic integral of the conservative system, is given in terms of the total energy of the system E tot rather than in terms of the amplitude of oscillation a. However, the relation between these two quantities is simply E tot = ω 2 0 x 2 max /2 + α 2 x 3 max /3 + α 3 x 4 max /4, where x max = a + 5 k=0,k̸ =1 a k , and therefore, we can easily compute ω exact in terms of a.…”

Section: The Hybrid Averaging Methodsmentioning

confidence: 99%

“…All other parameters of the conservative system are held fixed (ω 0 = 10, α 3 = 1). The dashed translucent curves are calculated from the frequency ωexact of the exact analytical solution (see Ref [39]…”

mentioning

confidence: 99%

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

2022

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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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Section: The Hybrid Averaging Methodssupporting

confidence: 76%

“…( 11) of Ref. [39]) for a system with quadratic and cubic nonlinearities is shown in the left panel of Fig. 3.…”

Section: The Hybrid Averaging Methodsmentioning

confidence: 98%

Section: The Hybrid Averaging Methodsmentioning

confidence: 99%

mentioning

confidence: 99%

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

2022

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“…More specifically, numerous studies delve into topics like branching, bifurcations, the disruption of equilibrium positions, and the transition between different operating modes for microbeams exhibiting initial curvature [21][22][23][24][25][26]. Extensive research efforts also focus on exploring the spectral properties and nonlinear dynamic characteristics of such structures [27][28][29][30][31][32].…”

Section: Introductionmentioning

confidence: 99%

Modeling and Structural Analysis of MEMS Shallow Arch Assuming Multimodal Initial Curvature Profiles

Alneamy,

Ouakad

2024

Mathematics

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The present investigation focuses on the design and mathematical modeling of a microelectromechanical (MEMS) mode-localized based sensor/actuator system. This device incorporates a sensitive clamped–clamped shallow arch microbeam with an initial curvature shaped to resemble one of the first two symmetric and asymmetric modes of free oscillations of a clamped–clamped beam. The analysis reveals that with a suitable arrangement of the initial shape of the device flexible electrode and a proper tuning of the maximum initial rise and the actuating dc load enables the transition to display certain bistable behavior. This could be a better choice to build a device with a large stroke. Furthermore, the generated data showed the occurrence of mode-veering, indicating a coupling between the concerned symmetric and asymmetric modes of vibrations, and offering the possibility for such a device to be used as a mode-localized MEMS-based sensor utilizing veering and crossing phenomena. Indeed, where a certain energy is exchanged between symmetric and asymmetric modes of a microbeam, it can be utilized to serve as a foundation for the development of a new class of highly precise resonant sensors that can capture, with a certain level of precision, any of the sensed signal amplitudes.

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Model of a Micromechanical Modal-Localized Accelerometer with an Initially Curvedmicrobeam as a Sensitive Element

Mozhgova

Лукин²,

Popov³

2022

Microactuators, Microsensors and Micromechanisms

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Zero-dispersion point in curved micro-mechanical beams

Cited by 18 publications

References 60 publications

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

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

Modeling and Structural Analysis of MEMS Shallow Arch Assuming Multimodal Initial Curvature Profiles

Model of a Micromechanical Modal-Localized Accelerometer with an Initially Curvedmicrobeam as a Sensitive Element

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