Quasi Static Investigation of Squeeze Film Damping on a Fully Clamped Micro-Beam

In this article a clamped-clamped type micro beam has been considered in an interaction with a thin film of air underneath the beam and its dynamic characteristics such as natural frequency and damping ratio have been discussed. Most important priority is to solve the dynamic motionof the beam due to electrical actuation considering pressure distribution of air within the gap. So a distributed model for both flexural deflection and pressure distribution has bean considered using Euler- Bernoulli beam model and ideal gas Reynolds equation. In that way a set of coupled nonlinear partial differential equations have been obtained that must be solved simultaneously. Because there is no analytic solution for any of equations some simplifications have been considered to linearize both of them. Assuming the actuation voltage to be compound of a finite DC component and an infinitesimally low AC component the quasi static conditions took place and the equations became linear. Application of Galerkin based reduced order model mass, spring and damping matrixes has been found so root locus, frequency and damping ratio diagrams of the system have been plotted and discussed in terms of some defined dimensionless parameters that are very reasonable and useful in designof MEMS.

Keywords:

MEMS , Squeeze Film Damping , Frequency Response , Dynamic Pull-in , Reynolds Equation , Fully Clamped Micro-beam