Investigation of the Effect of Nonlinearities on the Response of Cantilever Microbeams under Mechanical Shock and Electrostatic Loading Mohammad I Younis* and Haider N. Arafat ‡ * Assistant Professor, Department of Mechanical Engineering, State University of New York at Binghamton, Binghamton, NY 13902, myounis@binghamton.edu (corresponding author). ‡ Senior Engineer, Dynamic Loads, Cessna Aircraft Company, Wichita, KS 67215, hnarafat@cessna.textron.com . ABSTRACT We present an investigation into the effect of nonlinearities on the response of cantilever microbeams under mechanical shock and electrostatic loading. The nonlinear Euler-Bernoulli beam theory is used to model the microbeam, accounting for cubic geometric and inertia nonlinearities, in addition to the nonlinear electrostatic forces in the case of electrostatic actuation. The influences of the different components of nonlinearity are examined. The results of the nonlinear model are compared to results obtained from linear beam theory and finite-element simulations (ANSYS). For mechanical shock loading, both quasi-static and dynamic responses of a microbeam are considered. The effect of nonlinearity is found to be significant when the deflection of the microbeam exceeds around 30% of its length. The consequence of the large deflection is that the geometric nonlinearity has a much stronger influence on the response in comparison to the inertia nonlinearity. For electrostatic actuation, it is found that using a nonlinear beam model to predict the pull-in and the deflection produces a slight improvement over using a linear beam model. 1. Introduction Cantilever beams are basic structures that are used numerously in micro-electro-mechanical systems (MEMS). For example, they are employed in mass sensors for bio and gas sensing, as switching elements in RF microswitches and optical fibers, and probe elements in atomic force microscope (AFM). Also, they form a basic element in nano-scale devices and carbon nano tubes (CNT). Cantilever microbeams can be exposed to shock during fabrication, shipping, storage, and end-use, such as in space applications and military scenarios. When implemented in portable electronic devices, such as cell phones, these microbeams have to survive impact and drop testing. Cantilever microbeams are characterized by having low stiffness compared to beams with other boundary conditions. Therefore, under dynamic shock loading, they can deflect significantly. This deflection can cause a hard contact of the microbeam with other stationary components on the MEMS chip, which may break the beam or cause other kinds of damages. In optical fiber applications, where the microbeam is used as a switch, this accidental deflection can cause undesirable alignment for the cantilever optical fiber with other fibers, hence, passing an erroneous light signal [1]. In applications such as capacitive sensors, this large deflection can result in a contact with the substrate, which may lead to short circuit and stiction problems [2]. Many microstructures experience mechanical shock as quasi-static loads [1-4]. This is because these small structures have high natural frequencies and hence, their natural periods are much smaller than the typical duration of shock loads. On the other hand, because of the low natural frequencies of cantilever microbeams, they can experience mechanical shock as a dynamic load, which can dangerously amplify their response. Another cause of failure for microbeams that are actuated electrostatically is through the pull-in instability. In this case, the electrostatic force acting on the microbeam overcomes its elastic restoring force causing it to collapse Proceedings of the XIth International Congress and Exposition June 2-5, 2008 Orlando, Florida USA ©2008 Society for Experimental Mechanics Inc.