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

ABSTRACT 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 RayleighRitz 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 pullin 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