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Chin. Phys. B, 2012, Vol. 21(11): 110401    DOI: 10.1088/1674-1056/21/11/110401
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Dynamic stability of parametrically-excited linear resonant beams under periodic axial force

Li Jing (李晶)a b c d , Fan Shang-Chun (樊尚春)a b c , Li Yan (李艳)a b c , Guo Zhan-She (郭占社 )a b c
a School of Instrument Science & Opto-electronics Engineering, Beihang University, Beijing 100191, China;
b Key Laboratory of Precision Opto-mechatronics Techonology, Ministry of Education Beijing 100191, China;
c Key Laboratory of Inertial Science and Technology for National Defence, Beijing 100191, China;
d School of Information and Communication Engineering, North University of China, Taiyuan 030051, China
Abstract  The parametric dynamic stability of resonant beams with various parameters under periodic axial force is studied. It is assumed that the theoretical formulations are based on Euler-Bernoulli beam theory. The governing equations of motion are derived by using Rayleigh-Ritz method and transformed into Mathieu equations, which is formed to determine the stability criterion and stability regions for parametrically-excited linear resonant beams. An improved stability criterion is obtained using periodic Lyapunov functions. The boundary points on the stable regions are determined by using small parameter perturbation method. Numerical results and discussion are presented to highlight the effects of beam length, axial force and damped coefficient on the stability criterion and stability regions. While some stability rules are easy to anticipate, we draw some conclusions: with the increase of damped coefficient, stable regions arise; with the decrease of beam length, the conditions of the damped coefficient arise instead. These conclusions can provide a reference for the robust design of the parametrically-excited linear resonant sensors.
Keywords:  resonant beams      dynamic stability      parametrically excitation      periodic axial force  
Received:  07 March 2012      Revised:  07 July 2012      Accepted manuscript online: 
PACS:  04.40.Dg (Relativistic stars: structure, stability, and oscillations)  
  02.30.Hq (Ordinary differential equations)  
  05.10.-a (Computational methods in statistical physics and nonlinear dynamics)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 60927005), the 2012 Innovation Foundation of BUAA for PhD Graduates, and the Fundamental Research Funds for the Central Universities, China (Grant No. YWF-10-01-A17).
Corresponding Authors:  Li Yan     E-mail:  yanli.83@163.com

Cite this article: 

Li Jing (李晶), Fan Shang-Chun (樊尚春), Li Yan (李艳), Guo Zhan-She (郭占社 ) Dynamic stability of parametrically-excited linear resonant beams under periodic axial force 2012 Chin. Phys. B 21 110401

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