Dynamic instability analysis of electrostatic functionally graded doubly-clamped nano-actuators

This paper is dedicated to investigate the dynamic instability of functionally graded nano-bridges considering Casimir attraction and electric filed actuation. The nano-bridge is initially at rest and actuated by suddenly DC voltage. The fundamental frequency of the system is obtained asymptotically by employing modern approach namely Parameter Expansion Method (PEM). The effects of actuation voltage, properties of FGM materials and intermolecular force on the dynamic pull-in behavior are studied. It is exhibited that in order to achieve the acceptable approximations for fundamental frequency as well as the analytic solution, six terms in series expansions should be taken into account. Comparison between the obtained results based on the asymptotic analysis and the reported results in the literature, verify the strength of the analytical procedure. Finally, the influences of applied voltage and gradient power of functionally graded materials on the dynamic pull-in voltage and pull-in time of vibrating nano-actuators are explained.