On resonances in a weakly nonlinear microbeam due to an electric actuation

In this paper, the oscillations of an actuated, simply supported microbeam are studied for which it is assumed that electric load composed a small DC polarization voltage and small, harmonic AC voltage. Bending stiffness mid-plane stretching taken into account as well viscous or structural damping. No tensile axial force to be present. By using multiple time-scales perturbation method, approximations solutions initial-boundary value problem equation constructed. This analysis performed without truncating infinite series representation in advance usually done existing literature. It shown cases truncation allowed problem. Moreover, accurate explicit natural frequencies up order \(\varepsilon ^3\) actuated also obtained. Intriguing new modal vibrations found when frequency (near) half twice microbeam, i.e., near superharmonic subharmonic resonance.