Nonlinear Dynamics and Its Applications in Micro- and Nanoresonators

Abstract

This review provides a summary of the work completed to date on the nonlinear dynamics of resonant micro- and nanoelectromechanical systems (MEMS/NEMS). This research area, which has been active for approximately a decade, involves the study of nonlinear behaviors arising in small scale, vibratory, mechanical devices that are typically integrated with electronics for use in signal processing, actuation, and sensing applications. The inherent nature of these devices, which includes low damping, desired resonant operation, and the presence of nonlinear potential fields, sets an ideal stage for the appearance of nonlinear behavior, and this allows engineers to beneficially leverage nonlinear dynamics in the course of device design. This work provides an overview of the fundamental research on nonlinear behaviors arising in micro/nanoresonators, including direct and parametric resonances, parametric amplification, impacts, selfexcited oscillations, and collective behaviors, such as localization and synchronization, which arise in coupled resonator arrays. In addition, the work describes the active exploitation of nonlinear dynamics in the development of resonant mass sensors, inertial sensors, and electromechanical signal processing systems. The paper closes with some brief remarks about important ongoing developments in the field.

Optimization of nonlinear structural resonance using the incremental harmonic balance method

“…As shown in Figure 11, where ϕ 1 denotes the deformation w for the first linear mode of a doubly clamped beam, the bending strain energy is proportional to ( ∂ 2 ϕ 1 ∂x 2 ) 2 and the strain energy associated with midplane stretching is proportional to ( ∂ϕ 1 ∂x ) 4 . The strongest midplane stretching effect occurs where ( ∂ϕ 1 ∂x ) 4 reaches the local maximum and ( ∂ 2 ϕ 1 ∂x 2 ) 2 reaches the local minimum. So as the load increases, the coupling effect will lead to an …”

“…Rhoads et al gave a comprehensive review of the application of nonlinear dynamics in Micro-and Nanoresonators concerning theoretical and experimental investigation of modeling, analysis and optimization [1]. A well known phenomenon in nonlinear vibration is the hardening and softening nonlinear effects [2,3].…”

Investigation of dynamic instability of three plates switch under step DC voltage actuation using modified couple stress theory

“…Simulating the mechanical behavior of these devices, particularly their static and dynamic behavior, is required for design and manufacturing purposes. Therefore, electrostatically actuated MEM/NEM devices such as, micro switches [1,2] micro-mirrors [3,4], nano-switches [5,6], nano-tweezers [7,8], micro capacitors [9][10][11], sensors [12,13], resonators [14,15] and oscillators [16,17] are widely designed, fabricated, used and analyzed.…”

Perturbation analysis of an electrostatic Micro-Electro-Mechanical System (MEMS) subjected to external and non-linear parametric excitations

“…Batra et al [28] and Kacem et al [29][30][31] studied respectively nonlinear multi-physics models including both mechanical and electrostatic nonlinearities and the fringing field effect. A more comprehensive review up to 2010 about the work on the non-linear dynamics of micro resonators is presented in literature [32].…”