Dynamic Response of Initially Deformed and Imperfect Bi-stable Microbeams to Mechanical Shocks and Electrostatic Forces

The principal aim of the proposed research is to develop computational methods and exploit them to examine the dynamical behavior of electrostatically actuated bi-stable MEMS arches under mechanical shock loads. A critical issue for the development of MEMS devices is their performance, reliability and survivability when subjected to mechanical shock, such as when dropped on a hard surface. These active forces can lead to tremendous destruction in these tiny mechanisms, such stiction and all related short circuit problems in MEMS devices. Investigating numerically the dynamics of micro-structures under mechanical shock loads is a challenging job, driven, in part, by the large deflections that exacerbate system nonlinearities, such as those due to geometric (initial curvature) and electrostatic effects. The proposed work aims to establish computationally efficient approaches that are capable of analyzing the transient dynamics of microstructures due to shock in various applications and under a variety of conditions. These include quasi-static and dynamic shock loading, moderate and high-g shock loading, and combined shock and nonlinear electrostatic loading. Another objective of this research is to improve the understanding of how mechanical shock loads can deteriorate the bi-stability of MEMS arches. In fact, elastic beams with an initial rise (imperfect) are commonly found in MEMS due to residual stresses and stress gradient during the fabrication process. While attempting to fabricate perfect and straight clamped-clamped microbeams, MEMS engineers obtained many initially buckled and deformed beams, mainly used as bi-stable switches and actuators. The snap-through action of such microbeams can be utilized for fact actuation in large stroke. The reliability and response of clamped-clamped buckled and imperfect microbeams when subjected to dynamic loading have not been investigated before. The response of these structures to mechanical shocks and electrostatic forces has not been analyzed. Such an investigation can shed light on the potential of utilizing imperfect microbeams as reliable micro-scale devices and actuators. Therefore, in this research project, we will focus on two commonly used clamped-clamped microbeams: perfectly straight and initially curved (arches). Several examples of microbeams, of various natural frequencies, of real devices in the literature will be studied to span a variety of quasi-static and dynamic loads situations. The first computationally efficient approach we will explore is the Galerkin expansion reduced-order modeling (ROM). We will investigate the validity, accuracy, and computational efficiency of the ROM to investigate the response of microbeams under mechanical shock loads. We propose to investigate the capability of RO modeling in simulating the response of microbeams to the combined effect of electrostatic force and shock load. In each case, we will examine the number of modes needed for the ROM to converge within an acceptable accuracy. The second approach we will investigate is to use ANSYS (as finite-element software) and then compare the outcomes with those of the ROM. After we complete our investigation on the proposed approaches, we utilize them to explore the effect of several design parameters on the dynamic response of curved microbeams to shock loads. These include shock profile, shock duration, damping ratio, beam initial, and the DC voltage. We will generate universal curves for the snap-through and pull-in voltages thresholds versus shock amplitude for various values of the nondimensional design constraints of the ROM. These curves will present valuable information about the interaction between the shock and electrostatic forces and how to utilize this interaction to build new devices and propose new technologies.