Size Dependent Nonlinear Dynamics of a Piezoelectrically Actuated MEMS Near Primary Resonance

Size dependent nonlinear static and dynamic behavior of a piezoelectrically actuated micro electromechanical system is investigated in this paper. A clamped-clamped microbeam sandwiched between two layers of piezoelectric, under electrostatic actuation is considered. The governing equation of motion is derived using Hamilton s principle, under the assumptions of Euler Bernoulli beam theory. The size effect is considered using strain gradient theory. In the proposed model nonlinearities due to midplane stretching, electrostatic actuation and the fringing field effect are taken into account. Axial residual stress is also considered in the formulation. Reduced order model is obtained via Galerkin scheme. The frequency response of the system near primary resonance is captured by means of shooting method, a numerical approach capable of finding both stable and unstable periodic attractors of the system. The proposed nonlinear model is verified with the experimental data available in the literature. The effect of piezoelectric voltage and its polarization is investigated on the nonlinear behavior and pull-in voltage of the system. The results show that the classical continuum theory underestimates the stiffness of the system and consequently a lower pull-in voltage for the system. By changing the piezoelectric voltage and its polarity on the other hand, one is able to tune the pull-in voltage and also the pull-in instability frequency band of the system in the unstable region.