Analysis of the chaotic regime of MEMS/NEMS fixed-fixed beam resonators using an improved 1DOF model

The Galerkin's method is used to derive a consistent one degree of freedom (1DOF) model for a suspended fixed-fixed beam micro/nanoelectromechanical resonator including the contributions of geometric nonlinearity and the Casimir force. This model goes beyond the parallel plate approximation by including the main correction to the electrostatic and Casimir forces due to the beam curvature. The chaotic regime found in a small region of the parameter space, close to the dynamic pull-in, is fully characterized by means of the calculation of the Lyapunov exponent and bifurcation diagrams. The comparison with results presented in the literature, obtained using a much more computationally demanding approach, evidences the reliability of the proposed 1DOF model. It also evidences the relevance of incorporating the effects of beam curvature in simplified models of the beam dynamics when large displacements are expected, and the effect of the Casimir force when low operating voltages and small gaps are involved.