Shape optimization of the nonlinear resonant response in nano- and micromechanical structures

The optimization of nonlinear resonant responses in mechanical systems is a subject of increasing importance, particularly for the design of nano- and microelectromechanical systems (NEMS/MEMS). High-quality-factor NEMS/MEMS resonators often exhibit complex nonlinear dynamics, which can be strategically exploited for novel device concepts or, conversely, can interfere with the desired linear behavior of precision instruments such as gyroscopes. Thus, a design methodology is needed that can accurately and efficiently manipulate geometric nonlinearity for arbitrary geometries and control whether the nonlinear response exhibits hardening or softening behavior. In this work, we introduce a method to optimize the nonlinear resonant response of 3D structures via node-based shape optimization using 3D finite element models, providing high accuracy for arbitrary structures. By employing a gradient-based optimization approach, we achieve computational efficiency through analytical sensitivity calculations. The method is first validated against published experimental data using a clamped-clamped beam, which also serves as the first optimization test case. The method’s capabilities are then demonstrated on a cantilever and a MEMS gyroscope of industrial complexity, showcasing its ability to handle arbitrary geometries with multiple operational constraints.