Nonlinear tuning of microresonators for dynamic range enhancement

Abstract

This paper investigates the development of a novel framework and its implementation for the nonlinear tuning of nano/microresonators. Using geometrically exact mechanical formulations, a nonlinear model is obtained that governs the transverse and longitudinal dynamics of multilayer microbeams, and also takes into account rotary inertia effects. The partial differential equations of motion are discretized, according to the Galerkin method, after being reformulated into a mixed form. A zeroth-order shift as well as a hardening effect are observed in the frequency response of the beam. These results are confirmed by a higher order perturbation analysis using the method of multiple scales. An inverse problem is then proposed for the continuation of the critical amplitude at which the transition to nonlinear response characteristics occurs. Pathfollowing techniques are employed to explore the dependence on the system parameters, as well as on the geometry of bilayer microbeams, of the magnitude of the dynamic range in nano/microresonators.

On the geometrically exact low-order modelling of a flexible beam: formulation and numerical tests

“…Note that there is some slight difference between the two results in the 9.5-10 Hz range; however, due to the speed of decay it is unlikely that either method closely captures the localized backbone structure in this region. For the precise tracking of this backbone curve, one could employ more sophisticated methods based upon shooting or pseudo-arclength continuation [42][43][44], however, this is not pursued here.…”

Nonlinear dynamics of micromechanical resonator arrays for mass sensing

“…combined with a reduced size, a target application being the measure of infinitesimal mass in biological environment: 5 biomolecule, DNA, protein, enzyme, etc. A lot of research works focus on improving the sensitivity of a single mass sensor by reducing the sensor size, increasing the signal-tonoise ratio or exciting the sensor in nonlinear regime [1,2,3]. Some researchers considered higher bending modes of 10 vibration [4,5] while other researchers showed that using the first torsional mode is more efficient than the first bending mode [6].…”

Tailoring the nonlinear response of MEMS resonators using shape optimization

“…13 For example, it has been shown that one can relax the constraints in mode mismatch in MEMS gyroscopes due to fabrication errors by independently tuning the linear and/or cubic stiffness coefficients of the capacitive drive, 4,14,15 and one can achieve optimal drive conditions for micro-resonators in order to enhance their dynamic range. 16,17 Although a large number of research efforts are focused on the understanding of nonlinear dynamics in MEMS and their applications to sensors and actuators, only a few have focused on the systematic optimization of nonlinearities in MEMS to achieve desirable outputs. Ye et al demonstrated optimization of interdigitated comb finger actuators to achieve linear, quadratic, and cubic driving force profiles, 18 and, more recently, Guo designed quadratic shaped comb fingers to achieve large displacement parametric resonance, overcoming the limited movement in non-interdigitated comb drive.…”