Bistability of curved microbeams actuated by fringing electrostatic fields

Abstract

In this work we investigate the feasibility of two-directional switching of an initially curved or pre-buckled electrostatically actuated microbeams using a single electrode fabricated from the same structural layer. The distributed electrostatic force, which is engendered by the asymmetry of the fringing fields in the deformed state, acts in the direction opposite to the deflection of the beam and can be effectively viewed as a reaction of a nonlinear elastic foundation with stiffness parameterized by the voltage. The reduced order model was built using the Galerkin decomposition with linear undamped modes of a straight beam as base functions and verified using the results of the numerical solution of the differential equation. The electrostatic force was approximated by means of fitting the results of three-dimensional numerical solution of the electrostatic problem. Static stability analysis reveals that the presence of the restoring electrostatic force may result in the suppression of the snapthrough instability as well as in the appearance of additional stable configurations associated with higher buckling modes of the beam that are not observed in "mechanically" loaded structures. We show that two-directional switching of a pre-buckled beam between two stable configurations cannot be achieved using quasistatic loading. Furthermore, we show that switching is both associated with the dynamic snapthrough mechanism and possible within certain interval of actuation voltages. Using a single-degree-offreedom (lumped) model, estimation voltage boundaries are obtained. Theoretical results illustrate the feasibility of the suggested operational principle as an efficient mechanism in the arena of non-volatile mechanical memory devices.

Dynamics of a clamped–clamped microbeam resonator considering fabrication imperfections

“…Krylov et al [13][14][15] examined experimentally and theoretically the various scenarios of snap-through motion and pull-in instability in deliberately fabricated MEMS arches of deep capacitive gaps. They used the Galerkin procedure to solve for the dynamic response including geometric and electric nonlinearities.…”

“…They also studied the transient response and escape from one potential well to the other one. In [15], Krylov et al demonstrated the actuation of clamped-clamped arches using fringing effect of the electrostatic forces.…”

Structural Behavior of a Multi-Layer Based Microbeam Actuator

“…The main problem with this approach is that the distributed electrostatic force comes in an integral form in the resulting ROM equations, and consequently this integral form is not easy to deal analytically due to nonlinearities arising from its denominator. As an attempt to overcome this challenge, some groups [31,32] used Taylor-series expansion procedure, which brings the nonlinearity to the numerator of the electrostatic force and hence simplifies the calculation of nonlinear ROM integrals. Others suggested multiplying the resultant equation of motion by the electrostatic force denominator and hence the evaluation of the integral in the ROM equation will not be problematic anymore [25].…”

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.…”