Nonlinearity reduction in MEMS resonators based on design of H-shaped beams

Structural nonlinearity for conventional double-end fixed beam MEMS resonators considerably restricts their performance because of large displacement instabilities and excessive frequency noise. To solve this problem, a new resonator design based on H-shaped structural beams is proposed to alleviate the axial force caused by a large deflection of the beam structure. An analytical expression for the nonlinear stiffness of the proposed beam is derived using the Rayleigh–Ritz energy method. Nonlinear vibration equations of the resonant system are then formulated and solved analytically via the method of multiple scales. The results show that the H-shaped beam design can effectively reduce the nonlinearity without significantly decreasing the linear stiffness. The solution to the nonlinear stiffness of a given electrically excited resonant system is quantitatively verified by finite element analysis. The analytical solution to the nonlinear vibration of the system is verified by numerical simulation. The obtained dynamic results indicate that the H-shaped beam design can effectively improve the stability of the resonant frequency and it can also depress the cross-sensitivity of the resonator.