On the nonlinear primary resonances of a piezoelectric laminated micro system under electrostatic control voltage

Abstract

In this article, a comprehensive nonlinear analysis for a piezoelectric laminated micro system around its static deflection is presented. This static deflection is created by an electrostatic DC control voltage through an electrode plate. 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 a piezoelectrically actuated micro system it was showed that because of existence of curvature and inertia nonlinear terms a small change in excitation amplitude can lead to the formation and expansion of nonlinear response. In this paper, it is demonstrated that by applying an electrostatic DC control voltage, these nonlinearities can be controlled and altered to a linear domain. This model can be used to design a nano or micro-scale smart device.