Parametric resonance of bi-directional axial loads shallow arch microresonators

Abstract

In this work, we investigate analytically and experimentally parametric resonances of an in-plane clamped-guided shallow arch microresonator. The arch is connected to a T-shaped moveable mass, which is sandwiched between two electrodes to electrostatically activate the device and to offer bi-directional axial loads option. The device is tested under primary and secondary parametric resonances. In addition, an analytical model is presented taking into account the initial rise of the microbeam and the sliding motion at the guided side. The static and free vibration problems are solved using the Differential Quadrature Method, and the dynamic response is simulated using an assumed mode Galerkin approximation. The theoretical results of the static and dynamic behavior of the device are compared to experimental data showing good agreement. Moreover, we demonstrate the use of parametric excitation to significantly amplify the axial motion. It is found that the second parametric resonance, corresponding to the fundamental mode of the arched microbeam, has a higher amplitude than the principal parametric case, due to the initial curvature of the beam. Thus, the proposed device can be a promising candidate for variety of sensing applications