Modelling and simulation of a cantilever-paddle beam under the effect of capillary, shock, and electrostatic forces

In this paper, we present a mathematical model and analysis for a microbeam fixed at one end and coupled to a microplate at its other end under the effect of capillary, shock and electrostatic forces. The model considers the microbeam as a flexible structure, the plate as a rigid body. First, we subject the system to capillary force via a drop of fluid which is trapped underneath the microplate. We derive closed-form solutions to the static and eigenvalue problems associated with the microbeam-microplate system. We then subject the system to shock loads for both case (capillary and electrostatic forces). The Galerkin procedure is used to derive a set of nonlinear ordinary-differential equations that describe the microsystem dynamics. We investigate the influence of the fluid volume ratio and the applied DC voltage on the microbeam response. We find that the effect of capillary force has much more dominant role compared to shock and electrostatic forces.