Symmetry breaking, snap-through and pull-in instabilities under dynamic loading of microelectromechanical shallow arches

Abstract

Arch-shaped microelectromechanical systems (MEMS) have been used as mechanical memories, micro-relays, micro-valves, optical switches and digital micro-mirrors. A bi-stable structure, such as an arch, is characterized by a multivalued load deflection curve. Here we study the symmetry breaking, the snap-through instability and the pull-in instability of a bi-stable arch-shaped MEMS under static and dynamic electric loads. Unlike a mechanical load, the electric load is a nonlinear function of the a priori unknown deformed shape of the arch. The nonlinear partial differential equation governing transient deformations of the arch is solved numerically using the Galerkin method and a time integration scheme that adaptively adjusts the time step to compute the solution within the prescribed tolerance. For the static problem, the displacement control and the pseudo-arc-length continuation methods are used to obtain the bifurcation curve of the arch's displacement versus a load parameter. The displacement control method fails to compute the arch's asymmetric deformations that are found by the pseudo-arc-length continuation method. For the dynamic problem, two distinct mechanisms of the snap-through instability are found. It is shown that critical loads and geometric parameters for instabilities of an arch under an electric load with and without consideration of mechanical inertia effects are quite different. A phase diagram between a critical load parameter and the arch height is constructed to delineate different regions of instabilities. We compare results from the present model with those from a continuum mechanics based approach, and with results of other models and experiments available in the literature.

Asymmetric bifurcation of thermally and electrically actuated functionally graded material microbeam

“…It is shown in [35] that the numerical simulations using n w ≥ 6 in equation (2.23) are indistinguishable from each other. It is further stated that a reasonably accurate prediction of the symmetric snap-through behaviour can be given by considering only the 1st mode, and for the asymmetric deformations, the participation of the 2nd mode is more than that of the 4th and 6th modes.…”

Continuation-Based Pull-In and Lift-Off Simulation Algorithms for Microelectromechanical Devices

“…The algorithms in [25], [26], [28] require a priori knowledge about the path taken by parts of the design, which limits their generality. Standard continuation methods were employed to help estimate the pull-in voltages [29]- [31] based on some simplified MEMS models or for some specific devices. Such algorithms have been extensively investigated by the applied mathematics community [32]- [34] and have been successfully applied to circuit simulation [35].…”

“…yk - 3) Limitation in MEMS Simulation: Standard continuation methods have been employed to estimate the pull-in voltages [29]- [31] based on some simplified MEMS models or for some specific devices. In [31], multiple solution points are manually calculated to analyze the stability of a onedimensional MEMS model.…”

Influence of squeeze-film damping on the dynamic behavior of a curved micro-beam

“…In particular, curved micro-beams tend to unveil snap-through instabilities and symmetric/nonsymmetric buckling behaviors. [23][24][25][26][27][28][29][30][31][32][33] In this article, the influence of SQFD on oscillations of a slightly curved micro-beam is considered. The initial shape of the beam is assumed to have a sinusoidal profile.…”