2-Dimensional vibration model of MEMS cantilever beams with step-up anchors

This paper presents a 2-Dimensional mathematical model which only considers the length and thickness of the cantilever beams and omits the width to analyze the vibrational behavior of the step-up supported cantilever beams. This model accounts for the step-up boundary condition by replacing it with a simply-supported boundary condition in conjunction with equivalent torsional stiffness, which is more accurate boundary condition compared with a clamped boundary condition. In this paper, the mathematical model is compared with the finite element simulation, and the effect of the thickness t _m of the support beam and the Young’s modulus E on the resonant frequencies is analyzed. The comparison shows that the differences between the model prediction and simulated results are <2 % for the case of the t _m  = 2 μm and E = 79.42 GPa at the length of 50–380 μm. In addition, with decreasing the E or t _m , the resonant frequency of the cantilever beam will decrease. Furthermore, the measurement of the resonant frequencies demonstrates the validity of this model, with small errors.