Modelling and dynamic analysis of a MEMS ring resonator supported by circular curved shaped inner beams

Abstract

Microelectromechanical systems (MEMS) based ring shaped resonators usually have a ring supported by spoke shaped springs. In this paper, we developed a general analytical model that can determine the natural frequency of any MEMS ring resonator considering effective mass and stiffness of spokes in both radial and tangential displacements. Our model is also able to determine the stiffness of the circular curved beam with arbitrary central angle. The well-known energy based Castigliano’s method was used to calculate the stiffness of a circular curved beam considering both flexural and axial rigidities. The stiffness of a circular curved beam with different central angles was determined and compared with the literature and finite element method (FEM). The results show that for the case of a central angle of the curved beam larger than 60 degrees, the deviation between the FEM and analytical approach is less than 1%. The potential energy and kinetic energy of the outside ring and spokes were determined based on the displacement function. The natural frequency of a ring resonator with different number of circular curved beams in the form of petals in modes n = 2 and n = 3 were determined and the results were compared with a numerical approach using FEM. The deviations between the analytical approach and numerical method are less than 4%.