Analysis of the Chaotic Dynamics of MEMS/NEMS Doubly Clamped Beam Resonators with Two-Sided Electrodes

Abstract

We investigate the chaotic dynamics of micro- and nanoelectromechanical (MEMS/NEMS) beam resonators actuated electrostatically by two-sided electrodes, considering devices with realistic physical parameters. We model the resonators using the Euler–Bernoulli beam theory with the addition of viscous damping, midplane stretching and the electrostatic force. For the purpose of numerical simulations, the partial differential equation describing the system is reduced to a one degree of freedom model using the Galerkin method. The resulting nonlinear ordinary differential equation incorporates the main effects of the beam curvature. A comparison with the widely used parallel plate approximation (PPA) evidences the significant effects of the beam curvature. It is also concluded that in the case of resonators with two-sided electrodes special care must be taken when using the PPA. A detailed numerical analysis reveals the region in the relevant parameter space where chaos can be found. Phase portraits, Poincaré sections and bifurcation diagrams are used to characterize the chaotic attractors. The effects of gap asymmetry and damping are also investigated, showing that a stronger chaotic dynamics is favored by small asymmetries and smaller damping. In general, a more complex chaotic dynamics was found, compared to what was initially expected. The results are relevant in view of the potential practical applications in the generation of pseudo-random numbers and chaotic signals for secure communications. The proposed improved model can be easily implemented numerically, helping in the design and simulation of resonators, and the comparison between theoretical and experimental results.