Dynamic pull-in instability of a micro-actuator made from nonlinear elasticity materials

Abstract

This paper investigates the dynamic pull-in instability of a micro-actuator made from nonlinear elasticity materials. The theoretical formulations are based on Bernoulli–Euler beam theory and include the effects of both material nonlinearity and mid-plane stretching due to large deformation. By employing the Galerkin method, the nonlinear partial differential governing equation is decoupled into a set of nonlinear ordinary differential equations which are then solved using the Runge–Kutta method. Numerical results show that the linear constitutive relationship used in previous studies is valid for small deformation only, whereas for large deformation the nonlinear elasticity constitutive relationship must be used for accurate analysis. The effects of material nonlinearity, initial gap, beam length, and beam width on the pull-in instability of the micro-actuator are studied.