Dynamic pull-in instability of geometrically nonlinear actuated micro-beams based on the modified couple stress theory

Abstract

This paper investigates the dynamic pull-in instability of vibrating micro-beams undergoing large deflection under electrosatically actuation. The governing equation of motion is derived based on the modified couple stress theory. Homotopy Perturbation Method is employed to produce the high accuracy approximate solution as well as the second-order frequency-amplitude relationship. The nonlinear governing equation of micro beam vibrations predeformed by an electric field includes both even and odd nonlinearities. The influences of basic non-dimensional parameters on the pull-in instability as well as the natural frequency are studied. It is demonstrated that two terms in series expansions are sufficient to produce high accuracy solution of the micro-structure. The accuracy of proposed asymptotic approach is validated via numerical results. The phase portrait of the system exhibits periodic and homoclinic orbits.

Analytical determination of size-dependent natural frequencies of fully clamped rectangular microplates based on the modified couple stress theory

“…Most of the published results in this area are related to beam-type microstructures, and only a limited number of works have explored plate-type ones [27][28][29][30][31][32][33][34]. A number of works concerning plate models are reviewed in this paper.…”

Study of squeeze film damping in a micro-beam resonator based on micro-polar theory

“…Latin By adding a term representing the force acting on the micro-beam owing to the pressure of the squeeze gas film, the equation of motion governing the transverse deflection of the beam is as follow (Li et al, 2007;Asghar et al, 2010;Arbind et al, 2014, Sedighi et al, 2014 (EI) eq 4 ( , )…”

The size-dependent electromechanical instability of double-sided and paddle-type actuators in centrifugal and Casimir force fields

“…This size e ect cannot be modeled by classic continuum mechanics. In order to overcome this shortcoming, the non-classical theories, such as nonlocal elasticity [35], Couple Stress Theory (CST) [36][37][38], strain gradient theory [39], modi ed couple stress theory [40], etc., have been developed to consider the size e ect on theoretical continuum models. Despite other size-dependent theories, limited research has been conducted on modeling the ultra-small structures using the CST [41][42][43].…”