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Sensors 2013, 13(12), 15880-15897; doi:10.3390/s131215880

Dynamic Characteristics of Micro-Beams Considering the Effect of Flexible Supports

*  and
State Key Laboratory of Mechanical System and Vibration, School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
* Author to whom correspondence should be addressed.
Received: 9 September 2013 / Revised: 4 November 2013 / Accepted: 8 November 2013 / Published: 25 November 2013
(This article belongs to the Special Issue Modeling, Testing and Reliability Issues in MEMS Engineering 2013)
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Normally, the boundaries are assumed to allow small deflections and moments for MEMS beams with flexible supports. The non-ideal boundary conditions have a significant effect on the qualitative dynamical behavior. In this paper, by employing the principle of energy equivalence, rigorous theoretical solutions of the tangential and rotational equivalent stiffness are derived based on the Boussinesq’s and Cerruti’s displacement equations. The non-dimensional differential partial equation of the motion, as well as coupled boundary conditions, are solved analytically using the method of multiple time scales. The closed-form solution provides a direct insight into the relationship between the boundary conditions and vibration characteristics of the dynamic system, in which resonance frequencies increase with the nonlinear mechanical spring effect but decrease with the effect of flexible supports. The obtained results of frequencies and mode shapes are compared with the cases of ideal boundary conditions, and the differences between them are contrasted on frequency response curves. The influences of the support material property on the equivalent stiffness and resonance frequency shift are also discussed. It is demonstrated that the proposed model with the flexible supports boundary conditions has significant effect on the rigorous quantitative dynamical analysis of the MEMS beams. Moreover, the proposed analytical solutions are in good agreement with those obtained from finite element analyses.
Keywords: equivalent stiffness; flexible supports; micro-beams; resonance frequency shift; dynamics equivalent stiffness; flexible supports; micro-beams; resonance frequency shift; dynamics
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Zhong, Z.-Y.; Zhang, W.-M.; Meng, G. Dynamic Characteristics of Micro-Beams Considering the Effect of Flexible Supports. Sensors 2013, 13, 15880-15897.

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