Time response dynamics of linear model of microcantilever

This paper presents analytic derivation of dynamic behavior of a liniearized micro-electro-mechanical resonator. The parametric oscillation results from a displacement-dependent electrostatic force generated by oscillation of a microbeam. The utilized device is a MEMS with a time-varying capacitor. The stability and steady state dynamic behavior of the MEMS has been analyzed without polarization voltage. The main characteristic of the no-polarization model is effects of parameters in stability of the system. A set of stability charts is provided for prediction of the boundary between the stable and unstable domains for the principal resonance. Applying perturbation method, analytical equations are derived to describe both the steady state and time response of the system