Nonlinear Vibration Analysis of Nano to Micron Scale Beams Under Electric Force Using Nonlocal Theory

Electrostatically actuated beams are fundamental blocks of many different nano and micro electromechanical devices. Accurate design of these devices strongly relies on recognition of static and dynamic behavior and response of mechanical components. Taking into account the effect of internal forces between material particles nonlocal theories become highly important. In this paper nonlinear vibration of a micro\nano doubly clamped and cantilever beam under electric force is investigated using nonlocal continuum mechanics theory. Implementing differential form of nonlocal constitutive equation the nonlinear partial differential equation of motion is reformulated. The equation of motion is nondimentioanalized to study the effect of applied nonlocal theories. Galerkin decomposition method is used to transform governing equation to a nonlinear ordinary differential equation. Homotopy perturbation method is implemented to find semi-analytic solution of the problem. Size effect on vibration frequency for various applied voltages is studied. Results indicate as size decreases the dimensionless frequency increases for a cantilever beam and decreases for a doubly clamped beam. Size effect is specially significant as the beam size tends toward nano scale in the analysis.