Dynamic Analysis of a Beam-Type Resonator With Off-Axis Attached Mass
In this paper, the model of a micro-machined beam-type resonator is presented. The resonator is a micro-bridge which is modeled using Euler-Bernoulli beam theory. A comb-drive electrostatic actuator is attached to the micro-bridge for the excitation/detection of vibrations. In the models presented in the literature, it is assumed that the center of mass of the comb-drive is located on the neutral axis of the beam. In this paper, it is demonstrated that this assumption can not be applied for asymmetric-shaped comb-drives. Furthermore, the governing equations of motion are derived by relaxing the above assumption. It has been shown that the off-axis center of mass of the comb-drive generates an amplitude-dependent transverse force in the beam, which is essentially a nonlinear effect. The governing equations of motion are solved using a hybrid analytical-numerical approach. The end application of the structure under investigation is in resonant sensing and energy harvesting applications.