Characterization of extensional multi-layer microbeams in pull-in phenomenon and vibrations

This paper presents an analysis of the pull-in instability and vibrational behaviors for a multi-layer microbeam actuated electrostatically. Based on the accurate geometrically nonlinear theory of Euler-Bernoulli beams, a distributed electromechanical model that accounts for finite deformation and residual stress is proposed. The governing differential equations are established in the form similar to those of the single-layer beam theory by re-determination of the neutral axis. These equations, in conjunction with corresponding boundary conditions, are transformed into two two-point boundary value problems. The geometrical nonlinearity is taken into account in static deformation research. The pull-in parameters are obtained using the shooting method through taking the applied voltage as an unknown and the central deflection as a control parameter. The same algorithm is applied to the small-amplitude free vibration around the predeformed bending configuration following an assumed harmonic time mode. The corresponding fundamental natural frequency is presented. The proposed method is validated by comparing several case studies with available published simulations. The influences of pivotal parameters on the pull-in instability behavior and natural frequency are examined, including the length, thickness and residual stress of the microbeam. (C) 2011 Elsevier Ltd. All rights reserved.