Actuation of Higher Harmonics in Large Arrays of Micromechanical Cantilevers for Expanded Resonant Peak Separation

Abstract

A large array of elastically coupled micro cantilevers of variable length is studied experimentally and numerically. Full-scale finite element modal analysis is implemented to determine the spectral behavior of the array and to extract a global coupling matrix. A compact reduced order model is used for numerical investigation of the array’s dynamic response. Our model results show that at a given excitation frequency within a propagation band, only a finite number of beams respond. Spectral characteristics of individual cantilevers, inertially excited by an external piezoelectric actuator, were measured in vacuum using laser interferometry. The theoretical and experimental results collectively show that the resonant peaks corresponding to individual beams are clearly separated when operating in vacuum at the 3rd harmonic. Distinct resonant peak separation, coupled with the spatially-confined modal response, make higher harmonic operation of tailored, variable-length cantilever arrays well suited for a variety of resonant based sensing applications.

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

“…For the sake of clarity of the mapping, the experimental modal pattern was specifically chosen to consist only of the normal modes of the system and to exhibit no NPR. (f) Normalized amplitudes of various spatially localized modes generated from a full-scale FE modal analysis [34]. Spatial overlap of the opposing arrays’ modes is a necessary condition for NPR excitation in the system.…”

“…To explain the dynamics more rigorously, a reduced-order (RO) model was developed using the Galerkin decomposition under the direction of Euler-Bernoulli beam theory [26, 34, 44, 45]. Full details of the RO model are described in the Supplemental Material.…”

Modal Behavior of Microcantilevers Arrays with Tunable Electrostatic Coupling

“…The array shown in Figure 1 is composed of N interdigitated cantilevers and is configured as two partially overlapping half-arrays with the voltage difference V applied between them. Each half-array contains N/2 beams with the rectangular cross section of the width b and thickness h. The length L n of the cantilevers can be uniform along the array [17,21] or may vary between L min and L max [7,32]. The beams, designed to deflect in the vertical, z direction, are attached to a compliant overhang of the length L o and of the thickness h identical to that of the beams.…”

“…The length of the overlap between the beams of the opposite half-arrays (the electrode length) is L e , and the gap between the beams is g. Unmovable fixed beams positioned at the ends of the array serve as the end electrodes and are provided to enforce the zero-deflection of the endpoints of the array [12,17]. The devices reported in [7,17,32] were fabricated from single crystal silicon using a silicon-on-insulator (SOI) wafer with the device layer of the thickness h. One of the key, distinguishing, features of the device shown in Figure 1 is the way it combines, in an unusual manner, both the elastic and the ES couplings. Specifically, in absence of the voltage, the cantilevers of the opposite half-arrays are decoupled while the beams of the same half-arrays are coupled only elastically.…”

On the response of MEMS resonators under generic electrostatic loadings: experiments and applications

“…Enhancing the dynamic range of NEMS cantilevers for gas sensing applications is discussed in [12]. Furthermore, the actuation of higher harmonics in arrays of MEMS cantilevers is investigated to achieve distinct resonance peak separation for a variety of resonance-based sensing applications [13]. Resonance-based mass sensing is recently demonstrated to be capable of sensing traumatic brain injury protein biomarkers [3].…”