AN EFFICIENT NUMERICAL SCHEME TO DETERMINE THE PULL-IN PARAMETERS OF AN ELECTROSTATIC MICRO-ACTUATOR WITH CONTACT TYPE NONLINEARITY

摘要

In this article, we present an efficient numerical scheme based on the Rayleigh-Ritz method to determine the pull-in parameters of electrostatically actuated microbeams exploiting contact type nonlinearity. A case of an electrostatically actuated cantilevered microbeam is first analyzed using the Rayleigh-Ritz energy technique. The deflection of the microbeam is approximated by a polynomial trial function. The principle of the stationary potential energy leads to a highly nonlinear algebraic equation, which is solved to determine the deflected shape of the microbeam. A novel voltage iteration algorithm is implemented to determine the critical voltage at which the pull-in occurs. The analysis is then extended to the case of cantilever beam making use of the contact type nonlinearity to exhibit an extended travel range. The present case consists of a compression spring getting engaged at the cantilever tip at the critical point where the pull-in occurs. An increase in both travel range and pull-in voltage is observed with the introduction of the compression spring. A performance index is suggested, which combines the gain in the travel range together with the concomitant increase in the pull-in voltage. This index is used to determine the critical bound for the choice of the stiffness of the newly introduced compression member.