This paper is concerned with non-linear coupling of in-plane rigid-body and flexural motion in capacitive MEMS ring sensors due to shock excitation. A Lagrangian approach is used to derive the equations of motion for the system, including non-linear electrostatic forces. The shock acceleration is modelled as a half-sine wave input and acts on the rigid-body motion only. The mechanism of modal coupling is derived theoretically, and numerical simulations are performed to quantify the coupling. Different electrode configurations are considered by including electrostatic plates both inside and outside the ring, and insights into modal coupling are gained.

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