Summary
Micro- and nanoelectromechanical systems (MEMS and NEMS) can exhibit rich nonlinear dynamics. Therefore, they have been studied extensively over the last decades in various areas of academic research ranging from engineering over physics to fundamental mathematics. In addition to its intriguing fundamental phenomena, nonlinear dynamics also found interest in rather applied industrial domains such as MEMS sensors and actuators where it shows the ability to disturb many devices based on linear system concepts. In either case, being able to tailor the nonlinear dynamical effects by design is certainly of great use. A main source of nonlinear system behavior in MEMS originates from geometric nonlinearities. In this work, we apply node-based shape optimization to tune the geometrically nonlinear 3-wave coupling coefficients using a custom FE and optimization code. On the example of an industrial level MEMS gyroscope, we demonstrate that individual coupling coefficients can be both decreased and increased over several orders of magnitude by shape optimization, while satisfying typical constraints on manufacturability and operability of the device. The optimized designs contain unintuitive geometrical features which can only be found using a computer implemented algorithm. Our work demonstrates the power of shape optimization for tailoring the complex nonlinear dynamic properties of MEMS and NEMS resonators of arbitrary geometries. Therefore, we believe that our work finds applications in various areas of mechanical engineering.
