Dynamic characteristics of resonant gyroscopes study based on the Mathieu equation approximate solution

doi:10.1088/1674-1056/21/5/050401

Abstract Dynamic characteristics of the resonant gyroscope are studied based on the Mathieu equation approximate solution in this paper. The Mathieu equation is used to analyze the parametric resonant characteristics and the approximate output of the resonant gyroscope. The method of small parameter perturbation is used to analyze the approximate solution of the Mathieu equation. The theoretical analysis and the numerical simulations show that the approximate solution of the Mathieu equation is close to the dynamic output characteristics of the resonant gyroscope. The experimental analysis shows that the theoretical curve and the experimental data processing results coincide perfectly, which means that the approximate solution of the Mathieu equation can present the dynamic output characteristic of the resonant gyroscope. The theoretical approach and the experimental results of the Mathieu equation approximate solution are obtained, which provides a reference for the robust design of the resonant gyroscope.

Keywords: resonant gyroscopes dynamic characteristics Mathieu equation approximate solution

Received: 10 June 2011
Revised: 27 April 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 Innovation Foundation of BUAA for Ph. D. Graduates, China, and the Fundamental Research Funds for the Central Universities, China (Grant No. YWF-10-01-A17).

Cite this article:

Fan Shang-Chun(樊尚春), Li Yan(李艳), Guo Zhan-She(郭占社), Li Jing(李晶), and Zhuang Hai-Han(庄海涵) Dynamic characteristics of resonant gyroscopes study based on the Mathieu equation approximate solution 2012 Chin. Phys. B 21 050401

[1]	Seshia A A 2002 Integrated Micromechanical Resonant Sensors for Inertial Measurement Systems (Ph. D. dissertation) (Berkeley:University of California at Berkeley)
[2]	Acar C and Shkel A M 2004 Journal of Micromechanics and Microengineering 14 15
[3]	Yang J B, Jiang L J and Chen D C 2004 Journal of Sound and Vibration 274 863
[4]	Mohite S, Patil N and Pratap R 2006 Journal of Physics 34 757
[5]	Mahmoodi S N, Jalili N and Khadem S E 2008 Journal of Sound Vibration 311 1409
[6]	Seshia A A, Howe R T and Montague S 2002 Proceeding of the 15th IEEE Int. Conf. MEMS, January 20--24, 2002 Las Vegas, USA, p. 722
[7]	Moussa H and Bourquin R 2006 IEEE Sensors Journal 6 310
[8]	Jeong C, Seok S, Lee B, Kim H and Chun K 2004 J. Micromech. Microeng. 14 1530
[9]	Gallacher B J, Burdess J S and Harish K M 2006 J. Micromech. Microeng. 16 320
[10]	Park S, Tan C W, Kim H and Hong S K 2009 Sensors 9 5952
[11]	Sammarco P, Tran H H, Gottlieb O and Mei C C 1997 J. Fluid Mech. 15 327
[12]	Vittori G 1998 J. Hydraul. Eng. 4 124
[13]	Poulin F J, Flierl G R and Pedlosky J 2003 J. Fluid Mech. 481 329
[14]	Pedlosky J and Thomson J 2003 J. Fluid Mech. 490 189
[15]	McLachlan N W 1964 Theory and Application of Mathieu Function (New York:Dover Publicatons Inc) pp. 90--95
[16]	Liu S S and Liu S D 2002 Special Function (Weather Publicatons Inc) pp. 737--739 (in Chinese)
[17]	Harris C and Crede C 1976 Shock and Vibration Handbook (2nd Edn.) (New York:Mc-Graw Hill) pp. 1--13
[18]	Wang Y Z and Zhou Y Z 2011 Chin. Phys. B 20 040501
[19]	Francis J P and Glenn R F 2008 Proc. R. Soc. A 464 1885
[20]	Coisson R, Vernizzi G and Xiao K Y 2009 Proceeding of the International Workshop on Open-source Software for Scientific Computation (OSSC), September 18--20, 2009 Guiyang, China, p. 3
[21]	Rand R H, Sah S M and Suchorsky M K 2010 Commun. Nonlinear Sci. Numer. Simulat. 15 3254
[22]	http://www.taihangybc.com

[1]	Chaos generation by a hybrid integrated chaotic semiconductor laser Ming-Jiang Zhang(张明江), Ya-Nan Niu(牛亚楠), Tong Zhao(赵彤), Jian-Zhong Zhang(张建忠), Yi Liu(刘毅), Yu-Hang Xu(徐雨航), Jie Meng(孟洁), Yun-Cai Wang(王云才), An-Bang Wang(王安帮). Chin. Phys. B, 2018, 27(5): 050502.
[2]	Application of asymptotic iteration method to a deformed well problem Hakan Ciftci, H F Kisoglu. Chin. Phys. B, 2016, 25(3): 030201.
[3]	The dynamic characteristics of a valve-less micropump Jiang Dan(蒋丹) and Li Song-Jing(李松晶) . Chin. Phys. B, 2012, 21(7): 074701.
[4]	Approximate solution of the magneto-hydrodynamic flow over a nonlinear stretching sheet Eerdunbuhe(额尔敦布和) and Temuerchaolu(特木尔朝鲁) . Chin. Phys. B, 2012, 21(3): 035201.
[5]	Approximate solutions of nonlinear PDEs by the invariant expansion Wu Jiang-Long (吴江龙), Lou Sen-Yue (楼森岳). Chin. Phys. B, 2012, 21(12): 120204.
[6]	Asymptotic solution for the Eiño time delay sea–air oscillator model Mo Jia-Qi(莫嘉琪), Lin Wan-Tao(林万涛), and Lin Yi-Hua(林一骅). Chin. Phys. B, 2011, 20(7): 070205.
[7]	Homotopic mapping solving method of the reduces equation for Kelvin waves Mo Jia-Qi(莫嘉琪), Lin Yi-Hua(林一骅), and Lin Wan-Tao(林万涛). Chin. Phys. B, 2010, 19(3): 030202.
[8]	Approximate solution for the Klein－Gordon－Schr?dinger equation by the homotopy analysis method Wang Jia(王佳), Li Biao(李彪), and Ye Wang-Chuan(叶望川). Chin. Phys. B, 2010, 19(3): 030401.
[9]	Three types of generalized Kadomtsev－Petviashvili equations arising from baroclinic potential vorticity equation Zhang Huan-Ping(张焕萍), Li Biao(李彪), Chen Yong (陈勇), and Huang Fei(黄菲). Chin. Phys. B, 2010, 19(2): 020201.
[10]	A new method to obtain approximate symmetry of nonlinear evolution equation from perturbations Zhang Zhi-Yong(张智勇), Yong Xue-Lin(雍雪林), and Chen Yu-Fu(陈玉福). Chin. Phys. B, 2009, 18(7): 2629-2633.
[11]	Study on an extended Boussinesq equation Chen Chun-Li(陈春丽), Zhang Jin E(张近), and Li Yi-Shen(李翊神). Chin. Phys. B, 2007, 16(8): 2167-2179.
[12]	The sea--air oscillator model of decadal variations in subtropical cells and equatorial Pacific SST Mo Jia-Qi(莫嘉琪), Lin Wan-Tao(林万涛), and Lin Yi-Hua(林一骅). Chin. Phys. B, 2007, 16(7): 1908-1911.
[13]	Variational iteration method for solving perturbed mechanism of western boundary undercurrents in the Pacific Mo Jia-Qi(莫嘉琪), Lin Wan-Tao(林万涛), and Wang Hui(王辉) . Chin. Phys. B, 2007, 16(4): 951-954.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Dynamic characteristics of resonant gyroscopes study based on the Mathieu equation approximate solution

Cite this article:

Online attention