Nonlinearity and periodic solution of a standard-beam balance oscillation system

doi:10.1088/1674-1056/21/6/064601

Abstract We present the motion equation of the standard-beam balance oscillation system, whose beam and suspensions, compared with the compound pendulum, are connected flexibly and vertically. The nonlinearity and the periodic solution of the equation are discussed by the phase-plane analysis. We find that this kind of oscillation can be equivalent to a standard-beam compound pendulum without suspensions; however, the equivalent mass centre of the standard beam is extended. The derived periodic solution shows that the oscillation period is tightly related to the initial pivot energy and several systemic parameters: beam length, masses of the beam, and suspensions, and the beam mass centre. A numerical example is calculated.

Keywords: balance oscillation nonlinearity limit cycle phase plane

Received: 15 June 2011
Revised: 13 August 2011
Accepted manuscript online:

PACS:	46.25.Cc	(Theoretical studies)
	46.40.Ff	(Resonance, damping, and dynamic stability)
	46.05.+b	(General theory of continuum mechanics of solids)
	46.40.-f	(Vibrations and mechanical waves)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 51077120) and the National Department Public Benefit Research Foundation (Grant No. 201010010).

Corresponding Authors: Li Shi-Song
E-mail: leeshisong@sina.com

Cite this article:

Li Shi-Song(李世松), Lan Jiang(兰江), Han Bing(韩冰), Tan Hong(谭红), and Li Zheng-Kun(李正坤) Nonlinearity and periodic solution of a standard-beam balance oscillation system 2012 Chin. Phys. B 21 064601

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