Periodic Oscillations in MEMS under Squeeze Film Damping Force

We provide sufficient conditions for the existence of periodic solutions for an idealized electrostatic actuator modeled by the Lienard-type equation x+FDx,x?+x=beta V2t/1-x2,x similar to-infinity,1 with beta is an element of R+, V is an element of CDouble-struck capital R/TDOUBLE-STRUCK CAPITAL Z, and FDx,x?=kappa x?/1-x3, kappa is an element of R+ (called squeeze film damping force), or FDx,x?=cx?, c is an element of R+ (called linear damping force). If FD is of squeeze film type, we have proven that there exists at least two positive periodic solutions, one of them locally asymptotically stable. Meanwhile, if FD is a linear damping force, we have proven that there are only two positive periodic solutions. One is unstable, and the other is locally exponentially asymptotically stable with rate of decay of c/2. Our technique can be applied to a class of Lienard equations that model several microelectromechanical system devices, including the comb-drive finger model and torsional actuators.