Chaos in MEMs/NEMs resonators

The Galerkin's method is used to derive a consistent one degree of freedom (1DOF) model for a suspended fixed-fixed beam micro/nanoelectromechanical (MEM/NEM) resonator including the contributions of geometric non-linearity and the Casimir force. This model goes beyond the parallel plate approximation by including the main correction to the electrostaic 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 much more computationally demanding approaches, evidences the reliability of the proposed 1DOF model, and the relevance of incorporating the effects of beam curvature in simplified models of beam dynamics when large displacements are involved. We go further on that analysis studying similar systems and trying to stablish the sources to the appearing of this chaotic regime in such devices. A systematic analysis has been carried out in order to understand all possible regimes to the vibration of those resonators using as control parameters three typical quantities in those devices. Some modifications in its architecture or in the dissipation mechanism modelling are made, trying to stablish the robustness of each dynamical regime.