The effects of cubic stiffness on fatigue characterization resonator performance

Micromachined, kHz-frequency resonators are now routinely employed as testing structures to characterize the fatigue degradation properties of thin film materials such as polycrystalline silicon (polysilicon). In addition to stress-life (S–N) fatigue curves, important properties such as crack propagation rates may be inferred from proper resonant frequency measurements throughout a fatigue test. Consequently, any nonlinear dynamic behavior that would complicate the interpretation of resonant frequency changes should be avoided. In this paper, nonlinear frequency–response curves of a polysilicon fatigue structure are measured in a vacuum environment. Finite element models of the structure are used to identify the source of geometric nonlinearity leading to a Duffing-type cubic stiffness. Given the origin of the behavior, a parametric optimization strategy is performed to minimize the cubic stiffness. This study highlights the importance of considering the dynamic behavior when designing resonating structures, especially when they are used for mechanistic studies in various environments.