On Approximate Treatment of Nonlinear Dynamical System of an Electrostatically Actuated Micro-Cantilever
This paper analyzed an approximate treatment of the nonlinear dynamical system of an electrostatically actuated micro-cantilever subjected to combined parametric and forcing excitations in MEMS. In this approximation, the nonlinearity is expanded into Taylor series. By retaining a number of terms, a modified system is obtained and then employed to study the real system indirectly. Bifurcations and sub-harmonic responses of the real system and of the modified system are obtained via numerical integrating methods. It was found, modified systems with only several terms cannot simulate multi-periodic and quasi-periodic responses of the real system. However, as long as enough terms are taken into account, the modified systems can give rise up the real responses no matter how complex they are.
Y.M. Chen et al., "On Approximate Treatment of Nonlinear Dynamical System of an Electrostatically Actuated Micro-Cantilever", Applied Mechanics and Materials, Vols. 29-32, pp. 2211-2218, 2010