Abstract
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.
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This work is supported by the National Natural Science Foundation of China (NSFC: 60976094, 61076108 and 60676043).
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Wang, K., Liao, X. & Zhang, Z. 2-Dimensional vibration model of MEMS cantilever beams with step-up anchors. Microsyst Technol 22, 893–901 (2016). https://doi.org/10.1007/s00542-015-2559-7
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DOI: https://doi.org/10.1007/s00542-015-2559-7