Snap-through and pull-in instabilities of an arch-shaped beam under an electrostatic loading

The snap-through and pull-in instabilities of the micromachined arch-shaped beams under an electrostatic loading are studied both theoretically and experimentally. The pull-in instability that results in a system collision with an electrode substrate may lead to a system failure and, thus, limits the system maximum displacement. The beam/plate structure with a flat initial configuration under an electrostatic loading can only experience the pull-in instability. With the different arch configurations, the structure may experience either only the pull-in instability or the snap-through and pull-in instabilities together. As shown in our computation and experiment, those arch-shaped beams with the snap-through instability have the larger maximum displacement compared with the arch-shaped beams with only the pull-in stability and those with the flat initial configuration. The snap-through occurs by exerting a fixed load, and the structure experiences a discontinuous displacement jump without consuming power. Furthermore, after the snap-through jump, the structures are demonstrated to have the capacity to withstand further electrostatic loading without pull-in. Those properties of consuming no power and increasing the structure deflection range without pull-in is very useful in microelectromechanical systems design, which can offer better sensitivity and tuning range.

Asymmetric structure of an isolated flux arch

This paper extends two-dimensional model of symmetric magnetostatic flux arches confined in stratified atmospheres (Zhang and Hu, 1992, 1993) to asymmetric models. Numerical results show that the flux structure is influenced greatly by the boundary condition of magnetic field, the force-free factor, the atmospheric pressure distribution and the position of footpoints (especially the width ratio of outlet to entrance, which differs from symmetric case).

Analytical method of predicating the instabilities of a micro arch-shaped beam under electrostatic loading

An arch-shaped beam with different configurations under electrostatic loading experiences either the direct pull-in instability or the snap-through first and then the pull-in instability. When the pull-in instability occurs, the system collides with the electrode and adheres to it, which usually causes the system failure. When the snap-through instability occurs, the system experiences a discontinuous displacement to flip over without colliding with the electrode. The snap-through instability is an ideal actuation mechanism because of the following reasons: (1) after snap-through the system regains the stability and capability of withstanding further loading; (2) the system flips back when the loading is reduced, i.e. the system can be used repetitively; and (3) when approaching snap-through instability the system effective stiffness reduces toward zero, which leads to a fast flipping-over response. To differentiate these two types of instability responses for an arch-shaped beam is vital for the actuator design. For an arch-shaped beam under electrostatic loading, the nonlinear terms of the mid-plane stretching and the electrostatic loading make the analytical solution extremely difficult if not impossible and the related numerical solution is rather complex. Using the one mode expansion approximation and the truncation of the higher-order terms of the Taylor series, we present an analytical solution here. However, the one mode approximation and the truncation error of the Taylor series can cause serious error in the solution. Therefore, an error-compensating mechanism is also proposed. The analytical results are compared with both the experimental data and the numerical multi-mode analysis. The analytical method presented here offers a simple yet efficient solution approach by retaining good accuracy to analyze the instability of an arch-shaped beam under electrostatic loading.