Synchronisation and general dynamic symmetry of a vibrating system with two exciters rotating in opposite directions

doi:10.1088/1674-1056/19/3/030301

Abstract We derive the non-dimensional coupling equation of two exciters, including inertia coupling, stiffness coupling and load coupling. The concept of general dynamic symmetry is proposed to physically explain the synchronisation of the two exciters, which stems from the load coupling that produces the torque of general dynamic symmetry to force the phase difference between the two exciters close to the angle of general dynamic symmetry. The condition of implementing synchronisation is that the torque of general dynamic symmetry is greater than the asymmetric torque of the two motors. A general Lyapunov function is constructed to derive the stability condition of synchronisation that the non-dimensional inertia coupling matrix is positive definite and all its elements are positive. Numeric results show that the structure of the vibrating system can guarantee the stability of synchronisation of the two exciters, and that the greater the distances between the installation positions of the two exciters and the mass centre of the vibrating system are, the stronger the ability of general dynamic symmetry is.

Keywords: synchronisation vibrating system symmetry stability

Received: 20 November 2008
Revised: 15 October 2009
Accepted manuscript online:

PACS:	45.20.da	(Forces and torques)
	45.80.+r	(Control of mechanical systems)
	45.20.dc	(Rotational dynamics)
	02.30.Yy	(Control theory)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos.~50535010 and 10702014), the Project of Liaoning Province Science (Grant No. 2008S095) and the National High Technology Research and Development Program of China (Grant No.~2007AA04Z442).

Cite this article:

Zhao Chun-Yu(赵春雨), Zhang Yi-Min(张义民), and Wen Bang-Chun(闻邦椿) Synchronisation and general dynamic symmetry of a vibrating system with two exciters rotating in opposite directions 2010 Chin. Phys. B 19 030301

[1]	Senator M 2006 J. Sound Vib . 291 566
[2]	Zhang Z, Fu Z Q and Yan G 2009 Chin. Phys. B 18 2209
[3]	Huygens C 1673 Horologium Oscilatorium (Paris, France)
[4]	van der Pol B 1920 Radio Rev. 1 701
[5]	Rayleigh J 1945 Theory of Sound (New York: Dover)
[6]	Kuramoto Y and Nishikawa I 1987 J. Stat. Phys. 49 569
[7]	Strogate S H 2000 Physica D 143 1
[8]	Ren Q and Zhao J 2007 Phys. Rev. E 76 016207
[9]	Hong H, Chate H, Park H and Tang L H 2007 Phys. Rev. Lett. 99 184101
[10]	Wang X, Lai Y and Lai C 2007 Phys. Rev. E 75 056205
[11]	Wang J W, Chen A M, Zhang J J, Yuan Z J and Zhou T S 2009 Chin. Phys. B 18 1294
[12]	Feng X Q and Shen K 2005 Chin. Phys. 14 1526
[13]	Nijmeijer A 2001 Physica D 154 219
[14]	Blekhman I I 1988 Synchronisation in Science and Technology (New York: ASME Press)
[15]	Blekhman I I 1971 Synchronisation of Dynamical Systems (Moscow: Nauka) (in Russian)
[16]	Wen B C, Zhao C Y, Su H P and Xong W L 2002 Vibrated Synchronisation andControlled Synchronisation (Beijing: Science Press) (inChinese)
[17]	Xu X J, Qin M C and Mei F X 2005 Chin. Phys. 14 1287
[18]	Li Y C, Jing H X, Xia L L, Wang J and Hou Q B 2007 Chin. Phys. 16 2154
[19]	Xia L L, Li Y C, Hou Q B and Wang J 2006 Chin. Phys. 15 903
[20]	Li A M, Jiang J H and Li Z P 2003 Chin. Phys. 12 467
[21]	Wang P, Fang J H, Ding N and Zhang P Y 2006 Chin. Phys. 15 1403
[22]	Zhao C Y, Zhu H T, Wang R Z and Wen B C 2009 Shock and Vib . 16 505
[23]	Zhang X H and Zhang Q L 2007 Control Theory of Nonlinear Differential Algebraic System and Its Applications (Beijing: Science Press) (in Chinese)

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Synchronisation and general dynamic symmetry of a vibrating system with two exciters rotating in opposite directions

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