Modelling of nonlinearities in MEMS devices

Shows how mode shapes of vibration, obtained from a linear analysis of a structure (as determined by finite element analysis or otherwise), can be used as generalised co-ordinates for a nonlinear model. This procedure has been well tested in many mechanical engineering problems and allows the partial differential equations of motion to be transformed into a set of ordinary differential equations. An electrostatically excited beam structure will be examined to illustrate the approach. Parametric and nonlinear vibrations are discussed and situations which lead to phenomenon such as combination resonance and `jump´ resonance will be described. Although the nonlinear system of equations generated by this approach can be readily solved numerically using the many simulation packages available today greater insight into behaviour can be obtained by seeking solutions based upon perturbation schemes. The basic ideas of the perturbation approach are discussed