Nondegenerate Parametric Resonance in Large Ensembles of Coupled Micromechanical Cantilevers with Varying Natural Frequencies

Abstract

We investigate the collective dynamics and nondegenerate parametric resonance (NPR) of copla-nar, interdigitated arrays of microcantilevers distinguished by their cantilevers having linearly expanding lengths and thus varying natural frequencies. Within a certain excitation frequency range, the resonators begin oscillating via NPR across the entire array consisting of 200 single-crystal silicon cantilevers. Tunable coupling generated from fringing electrostatic fields provides a mechanism to vary the scope of the NPR. Our experimental results are supported by a reduced-order model that reproduces the leading features of our data including the NPR band. The potential for tailoring the coupled response of suspended mechanical structures using NPR presents new possibilities in mass, force, and energy sensing applications, energy harvesting devices, and optomechanical systems.

Multiple electrically tunable parametric resonances in a capacitively coupled electromechanical resonator for broadband energy harvesting

“…Note that the mechanical response of the CMUT is quite damped, with a −3 dB bandwidth of roughly 2.5 MHz around 2.4 MHz. This is significant as the electrical resonator-based approach here enables PR without the need for lightly damped mechanical resonators or experiments in vacuum chambers [16]. The static capacitance C var of the custom CMUT is measured in FC-70 using a network analyzer and is found to be 38 pF.…”

“…The instability tongue in which a PE energy harvester is driven into PR is limited to a narrow band around two times the natural frequency of the system and this places a significant restriction on the operational bandwidth of the harvester. Different approaches have been proposed to overcome this limitation, including using systems with multiple mechanical degrees of freedom (DOF) [15][16][17][18][19]. However, such an approach leads to an increase in the size of the energy harvester without a significant increase in the energy density.…”

Mode Localization and Tunable Overlap in a Closed-Chain Micromechanical Resonator Array

“…Coupled micromechanical resonators have received significant attention over the last decade for both their ability to enhance measurement sensitivity in sensors and to demonstrate complex nonlinear behavior that may be useful for both classical and quantum computing [1][2][3][4][5][6][7][8][9][10][11][12]. Mode localization in coupled resonators has in particular been shown to be a powerful approach for improving the precision of microelectromechanical (MEMS) sensors, where the relative vibration amplitudes between resonators are used to measure external perturbations [1,2].…”

“…Parametric resonance and amplification have also been explored in coupled resonators, resulting in nonlinear frequency conversion and classical dynamics that are analogous to Rabi oscillations found in two-level quantum systems [6]. Finally, coupled nonlinear dynamics have been shown to yield complex bifurcations that can drive oscillations across large arrays including more than 100 resonators [7] and generate phononic frequency combs with fixed frequency spacing around a parametric resonance [8]. Due to this wide range of applications for coupled resonators, there is a continued need to develop new resonator geometries that can better leverage the dynamic behaviors described above.…”

Self-organized synchronization of mechanically coupled resonators based on optomechanics gain-loss balance

“…A lot of attention has been paid to these optomechanical arrays owing to their capabilities to promote new phenomena and applications. These include collective nonlinear dynamics [4,5], quantum many-body dynamics of photons and phonons [6], long-range coupling of phonon modes [7,8], photons and phonons transport [9,10], Anderson localization [11], as well as topological phases of sound and light [12,13].…”