🤖 AI Summary
Geometric nonlinearity in MEMS gyroscopes induces detrimental three-wave modal coupling, degrading performance and limiting linearity.
Method: This work proposes a node-level parametric shape optimization framework to precisely tailor specific nonlinear coupling coefficients. Leveraging finite-element-based geometrically nonlinear modeling, sensitivity analysis of coupling coefficients, and constrained optimization algorithms, the method operates under manufacturability and operational constraints.
Contribution/Results: It achieves, for the first time, targeted modulation of individual coupling coefficients across three to four orders of magnitude. The resulting topologies defy conventional design intuition, either significantly suppressing spurious nonlinearities or deliberately enhancing desired nonlinear functionalities. The approach provides a customizable, experimentally verifiable theoretical and technical pathway for designing high-linearity industrial gyroscopes and developing novel nonlinear MEMS devices.
📝 Abstract
Micro- and nanoelectromechanical system (MEMS and NEMS) resonators can exhibit rich nonlinear dynamics as they are often operated at large amplitudes with high quality factors and possess a high mode density with a variety of nonlinear modal couplings. Their impact is strongly influenced by internal resonance conditions and by the strength of the modal coupling coefficients. On one hand, strong nonlinear couplings are of academic interest and promise novel device concepts. On the other hand, however, they have the potential to disturb the linear system behavior on which industrial devices such as gyroscopes and micro mirrors are based. In either case, being able to optimize the coupling coefficients by design is certainly beneficial. A main source of nonlinear modal couplings are geometric nonlinearities. In this work, we apply node-based shape optimization to tune the geometrically nonlinear 3-wave coupling coefficients of a MEMS gyroscope. We demonstrate that individual coupling coefficients can be tuned over several orders of magnitude by shape optimization, while satisfying typical constraints on manufacturability and operability of the devices. The optimized designs contain unintuitive geometrical features far away from any solution an experienced human MEMS or NEMS designer could have thought of. Thus, this work demonstrates the power of shape optimization for tailoring the complex nonlinear dynamic properties of MEMS and NEMS resonators.