On Regularization in Design for Reliability for Nonlinear Planar Beam-Type Resonators

Robustness is a highly desirable quality in microelectromechanical systems (MEMS). Sensors and resonators operating on nonlinear dynamic principles such as internal resonances are no exception to this, and in addition, when nonlinear dynamic phenomena are used to enhance device sensitivity, their requirements for robustness may even be greater. This work discusses two aspects as they relate to the robustness and performance of nonlinear resonators. In the first aspect, different resonator designs are compared to find which among them have a better capacity to deliver reliable and reproducible performance in face of variations from the nominal design due to manufacturing process uncertainties/tolerances. The second aspect attempts to identify the inherent topological features that, if present in a resonator, enhance its robustness. Thus, the first part of this work is concerned with uncertainty analysis of several candidate nonlinear resonators operating under the principle of 1:2 internal resonance and obtained via a hierarchical optimization method introduced by the authors. The second part discusses specific changes to the computational design process that can be made so as to enhance the robustness and reliability of the candidate resonators.