Modeling and nonlinear analysis of a micro-switch under electrostatic and piezoelectric excitations with curvature and piezoelectric nonlinearities

In this paper, a comprehensive model of a micro-switch with both electrostatic and piezoelectric excitations, which accounts for the nonlinearities due to inertia, curvature, electrostatic forces and piezoelectric actuator is presented to demonstrate the mechanical characteristics of such a micro-system. Dynamic equations of this model are derived by the Lagrange method. Static analysis of this model is performed with five modes through the Galerkin method. The micro-switch beam is assumed as an elastic Euler-Bernoulli beam with clamped-free end conditions. The electrostatic actuation results are compared with other existing experimental and numerical results. Whereas the major drawback of electrostatically actuated micro-switches is the high driving voltage, using the piezoelectric actuator in these systems can provide less driving voltage and control the pull-in voltage. The study demonstrates that when the ratio of electrostatic actuation distance to length of micro-switch is small, the nonlinear piezoelectric term has a significant effect on the pull-in phenomenon. There are three ways to influence the design and control of the mechanical characteristics of this micro-switch: the softening effect due to electrostatic actuation, the hardening effect due to piezoelectric actuation, and varying the length and thickness of the piezoelectric actuator.