Dynamics of bistable initially curved shallow microbeams: Effects of the electrostatic fringing fields

Effects of fringing electrostatic fields on the behavior of a double clamped initially curved microbeam are investigated. Galerkin´s decomposition method is applied on the governing Euler-Bernoulli equation with distributed electrostatic force to obtain the lumped-parameter model of the system. The resulting single degree of freedom model is obtained with the Palmer´s formula as a model for the fringing field effects. To derive an applied form of the fringing field effect in lumped model, we have used Genetic Algorithms as an optimization method. Then using the lumped model, we have investigated the system nonlinear dynamics. Comparison of the obtained bifurcation diagrams with the experimental results confirms that neglecting the fringing field effects results in a significant error which should be avoided for accurate molding purposes.