The results presented show that a simple microstructure involving a plate supported by two tethers can exhibit varied dynamics due to its nonlinearities. The plate vibrates such that the tethers experience a torsional twisting and it is designed within the constraints imposed by the MetalMUMPs process. Each region of operation has different applications and one can traverse through these regions by adjusting the sensing and actuation voltages. As one would expect, the nonlinearities dominate at higher voltages, with the first signs of chaotic trajectories appearing at 75 V. Parameters of the nonlinear model are first determined from finite-element analysis responses, and results from subsequent numerical simulations for each region are presented.
Introduction:The drive to increase the functionality in portable devices is always increasing and one way of providing increased functionality is by having structures that can be applied for different applications. The MEMS device presented here is one such structure. Having a good mathematical model is instrumental in accurate prediction of the different modes of operation. Modelling of the dynamics of MEMS resonators is extensively covered in the literature [1][2][3][4]. Numerical solutions that involve distributed models and finite-element analysis (FEA) provide the best description of system behaviour, but are computationally expensive. Assumptions are taken to develop nonlinear systems of equations that are able to give a good enough approximation. It is common to ignore all modes of vibration and keep the most prominent one. Further assumptions are taken on modelling the spring behaviour. A linear, quadratic and cubic spring stiffness term is considered in [1], whereas in [2] only the linear and cubic terms are included. The inhomogeneity of the silicon structure and geometric nonlinearities are often responsible for this behaviour [1]. When it comes to damping, the behaviour is more complex. Damping can be divided into two categories: thermoelastic effects and fluid damping. The dominant form of damping is determined by the Knudsen number [5]. In [5], the nonlinear relationship between the viscous damping coefficient, gap and pressure is clearly seen, especially for gaps less than 800 nm. However, in much of the reviewed literature related to resonators with gaps larger than 800 nm, the effects of damping are assumed to be captured by a viscous damping coefficient.This Letter first presents the mathematical model of the structure and the parameters determined from the FEA simulations. Then, different regions of behaviour are identified from the nonlinear model. In the final Section, applications related to each region are discussed.