Ultrabroadband Microresonators with Geometrically Nonlinear Stiffness and Dissipation

Potekin, Randi; Asadi, Keivan; Kim, Seok; Bergman, Lawrence A.; Vakakis, Alexander F.; Cho, Hanna

doi:10.1103/physrevapplied.13.014011

Cited by 8 publications

(4 citation statements)

References 39 publications

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“…The function g(x) is optimized using the proposed algorithm until the corresponding backbone curve passes through all target points. The validation is successful if g(x) is equal to the nonlinearity of the original system, i.e., either (12) or (13).…”

Section: Validation Of the Synthesis Methodologymentioning

confidence: 99%

“…For this latter absorber, the shaping of the two resonances of the coupled host structure-absorber system is based on the search for their equal magnitude as inspired by Den Hartog's linear design rule. Besides vibration absorption, a few other recent studies leveraged resonance tuning to meet design objectives that are less frequently addressed, like isochronicity [11], passive dynamical linearization [12] or extremely wide resonance patterns in microresonators [13]. Generally, a key step toward optimizing (in any sense) the behavior of a nonlinear resonance is the analysis of its parametric variability.…”

Section: Introductionmentioning

confidence: 99%

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Tailoring the resonances of nonlinear mechanical systems

2020

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In this work we propose a novel optimization-based methodology to tailor nonlinear resonances of mechanical systems according to specific design objectives. The objective pursued herein is the realization of a predetermined frequency-amplitude or frequency-energy dependence of a structural mode. The proposed methodology consists in synthesizing the nonlinearities automatically, from low to large relative displacements, by optimizing piecewise-linear segments. The methodology is illustrated using 2-degree-of-freedom nonlinear systems with modal interaction suppression and isochronicity design applications.

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Section: Validation Of the Synthesis Methodologymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Tailoring the resonances of nonlinear mechanical systems

2020

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“…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]. Even for single-mode nonlinear vibrations, a gap remains in the modeling and analysis of systems that exhibit higher-order nonlinear effects, particularly those resulting in non-monotonic amplitude-frequency characteristics [23][24][25].…”

Section: Introductionmentioning

confidence: 99%

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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“…As reviewed by Maamer et al [5], all these techniques have pros and cons. For example, the widely used Duffing-type oscillators have broad bandwidth due to their cubic nonlinear stiffness [15][16][17], which helps the resonance curve to follow the frequency sweep of external excitations. However, the performance of the Duffing-type system is affected by the hysteresis phenomenon depending on the initial condition.…”

Section: Introductionmentioning

confidence: 99%

A continuous broadband electromagnetic energy harvester based on amplitude and phase adjustments

Xu¹,

Xiang²

2022

Smart Mater. Struct.

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Broadening the bandwidth of vibration energy harvesters is a critical issue for their practical implementations. Although utilizing multi-degree-of-freedoms is a frequently used solution to widen the operating frequency range, the resultant effective bandwidth could consist of discrete peaks (existing local minimum points lower than the half-power level) if the modal amplitudes have large differences at different frequencies. To solve these problems, we designed a new electromagnetic multi-modal energy harvester, which works in a broad and continuous low-frequency bandwidth. This is achieved by attaching the magnet and the coil to a compliant frame integrated with two different kinked beams, respectively. In this way, the voltage can be generated in a continuous and wide frequency range by adjusting the amplitudes and phases of the magnet and the coil in different modes according to a proposed design requirement. Finite element re-sults and experimental results are in good agreement with each other, which validate the performance of the proposed harvester. The experimental results demonstrate that the half-power bandwidth can be achieved in the range of 15.0 Hz and the maximum peak power is 1.56 mW at the center frequency of 40.5 Hz under base excitation of the root-mean-square acceleration of 0.24 g. The broadband and high power density feature are also validated in a random excitation test, so that this harvester has great potential for practical applications.

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Ultrabroadband Microresonators with Geometrically Nonlinear Stiffness and Dissipation

Cited by 8 publications

References 39 publications

Tailoring the resonances of nonlinear mechanical systems

Tailoring the resonances of nonlinear mechanical systems

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

A continuous broadband electromagnetic energy harvester based on amplitude and phase adjustments

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