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This paper deals with analysis of the mechanical behavior of an electro-statically-actuated micro-beam resonator from the bifurcation view of point. The non-local constitutive relation has been used to obtain the governing deformation equations. The obtained static equation has been solved using two approaches. The dynamic equation of motion has been solved applying a Galerkin-reduced order model. Bifurcation behavior of the beam subjected to an electrostatic force has been analyzed using the both approaches. The fixed points of the beam for given voltages have been obtained and stability of them determined by studying the phase portraits for each fixed point.

Bifurcation Analysis of a Capacitive Micro-resonator Considering Non-local Elasticity Theory