A study of the nonlinear primary resonances of a micro-system under electrostatic and piezoelectric excitations

Abstract

In this article, a nonlinear analysis for a micro-system under electrostatic and piezoelectric excitations is presented. The micro-system beam is assumed as an elastic Euler-Bernoulli beam with clamped-free end conditions. The dynamic equations of this model have been derived by using the Hamilton method and considering the nonlinear inertia, curvature, piezoelectric and electrostatic terms. The static and dynamic solutions have been achieved by using the Galerkin method and the multiple-scales perturbation approach, respectively. The results are compared with numerical and other existing experimental results. By studying the primary resonance excitation, the effects of different parameters such as geometry, material, and excitations voltage on the system’s softening and hardening behaviors are evaluated. In an electrostatically actuated micro-system, it was showed that the nonlinear behavior occurs in frequency response as softening effect. In this paper, it is demonstrated that by applying a suitable piezoelectric DC voltage, this nonlinear effects can be controlled and altered to a linear domain. This model can be used to design a nano- or micro-scale smart device.