Static characterization and pull-in voltage of a micro-switch under both electrostatic and piezoelectric excitations

In this paper, a comprehensive model of a micro-switch with both electrostatic and piezoelectric actuators, 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 have been derived by the Lagrange method and solved by the Galerkin method using five modes. The micro-switch beam has been 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 although the effect of nonlinearity due to electrostatic forces on the deflection is larger than other ones, yet a linear behavior can be observed through the balance between nonlinear terms. 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.