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Dynamic Response Analysis of the Fractional-Order System of MEMS Viscometer

X.S. He1, Q.X. Liu1, X.C. Huang2, Y.M. Chen1,3
Department of Mechanics, Sun Yat-sen University, No. 135 Xingang Road 510275 Guangzhou, China
Department of Mechanical Engineering, Ganzhou Institute of Technology, No. 88 Loutiling Road341000, Ganzhou, Jiangxi Province, China
Corresponding author: Dr. Y.M. Chen, Email: chenymao@mail.sysu.edu.cn

Computer Modeling in Engineering & Sciences 2015, 108(3), 159-169. https://doi.org/10.3970/cmes.2015.108.159

Abstract

This paper presented dynamic response analysis for an MEMS viscometer. The responses are governed by a set of differential equations containing fractional derivatives. The memory-free Yuan-Agrawal’s approach was extended to solve fractional differential equations containing arbitrary fractional order derivative and then a simple yet efficient numerical scheme was constructed. Numerical examples show that the proposed method can provide very accurate results and computational efforts can be significantly saved. Moreover, the numerical scheme was extended to solve problems with a nonlinear spring. The influences of the nonlinear parameters on the dynamic responses were also efficiently analyzed. The dependence of the angular frequency on damping parameters was also revealed. The presented method can provide us a new perspective to measure the fluid viscosity.

Keywords

MEMS viscometer, Memory-free scheme, Fractional derivative.

Cite This Article

He, X., Liu, Q., Huang, X., Chen, Y. (2015). Dynamic Response Analysis of the Fractional-Order System of MEMS Viscometer. CMES-Computer Modeling in Engineering & Sciences, 108(3), 159–169.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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