Snap-Through and Pull-In Instabilities of an Arch-Shaped Beam Under an Electrostatic Loading

Abstract

Abstract-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 snapthrough 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.

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.…”

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

“…The snap-through instability has been extensively explored and utilized in the micro-actuator and transducer design of arch (Ko et al 2002;Qiu et al 2004;Vangbo 1998;Zhang et al 2007) and chevron/V-shaped structures (Hwang et al 2003;Kugel et al 1998;Sulfridge et al 2002). For the arch and chevron/V-shaped structures as shown in Fig.…”

“…The snap-through is the instability phenomenon that the system experiences a discontinuous displacement between the two separated stable equilibria. When the loading is the electrostatic type, the system will have another instability called pull-in (Francais et al 1997;Nemirovsky and Bochobza-Degani 2001;Zhang et al 2007). The mathematical analysis (Zhang et al 2007) shows that when pull-in occurs, the system is also in a bistable state and tries to jump to the other stable equilibrium configuration, which is exactly the same scenario of snap-through.…”

“…When the loading is the electrostatic type, the system will have another instability called pull-in (Francais et al 1997;Nemirovsky and Bochobza-Degani 2001;Zhang et al 2007). The mathematical analysis (Zhang et al 2007) shows that when pull-in occurs, the system is also in a bistable state and tries to jump to the other stable equilibrium configuration, which is exactly the same scenario of snap-through. The only difference between the pull-in and snap-through instabilities is that for the pull-in instability the other equilibrium is physically unreachable unless the structure penetrates the electrode.…”

“…As shown in Fig. 2 the consequence of pull-in is that the structure hits Y. Zhang State Key Laboratory of Nonlinear Mechanics (LNM), Institute of Mechanics, Chinese Academy of Science, Beijing 100190, China the electrode and adheres to it (Francais et al 1997;Zhang et al 2007). The snap-through and pull-in instabilities are the same type of instability termed as fold catastrophe (Thompson 1982), which in energy perspective involves the coalescence and extinction of a minimum and a maximum (Adams et al 1998;Thompson 1982).…”