Computationally efficient approaches to characterize the dynamic response of microstructures under mechanical shock

We present computationally efficient models and approaches to simulate the response of microstructures under mechanical shock. These approaches include a Galerkin-based reduced-order model and a hybrid approach utilizing the response of structures to static loads combined with the dynamic shock spectrum of a spring-mass-damper system. To demonstrate the accuracy and efficiency of these approaches, we apply them on cantilever and clamped-clamped microbeams, and compare their predictions with analytical and finite-element (FE) results. We conclude that the hybrid approach is computationally efficient and accurate for microstructures behaving linearly in both quasi-static and dynamic loading conditions. The hybrid approach enables using simple analytical expressions that can be easily utilized by microelectromechanical system designers to judge the reliability of their devices. We show that reduced-order models are capable of capturing accurately the dynamic behavior of microstructures under shock pulses of various amplitudes (low-g and high-g), damping conditions, structural boundaries, and can capture linear and nonlinear behavior. Our results indicate that modeling the shock force as a quasi-static force for microstructures with low-natural frequencies may lead to erroneous results. High-g loading cases are investigated. Significant increase in the computational cost of simulations is reported when using traditional FE models because of the activation of higher order modes. The developed reduced-order model employing at least six modes is shown to be efficient in such cases. Design parameters are investigated to determine their effect on the shock resistance of microstructures. It is concluded that increasing air damping and tensile residual stresses improves the shock resistance of microstructures. A case study for the response of an optical fiber switch to shock is presented.