中国物理B ›› 2012, Vol. 21 ›› Issue (6): 64601-064601.doi: 10.1088/1674-1056/21/6/064601

• ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS • 上一篇    下一篇

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

李世松a b, 兰江a b, 韩冰b, 谭红b, 李正坤b   

  1. a. Department of Electrical Engineering, Tsinghua University, Beijing 100084, China;
    b. National Institute of Metrology (NIM), Beijing 100013, China
  • 收稿日期:2011-06-15 修回日期:2011-08-13 出版日期:2012-05-01 发布日期:2012-05-01
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No. 51077120) and the National Department Public Benefit Research Foundation (Grant No. 201010010).

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

Li Shi-Song(李世松)a)b)†, Lan Jiang(兰江)a)b), Han Bing(韩冰)b), Tan Hong(谭红)b), and Li Zheng-Kun(李正坤)b)   

  1. a. Department of Electrical Engineering, Tsinghua University, Beijing 100084, China;
    b. National Institute of Metrology (NIM), Beijing 100013, China
  • Received:2011-06-15 Revised:2011-08-13 Online:2012-05-01 Published:2012-05-01
  • Contact: Li Shi-Song E-mail:leeshisong@sina.com
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No. 51077120) and the National Department Public Benefit Research Foundation (Grant No. 201010010).

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摘要： 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.

关键词: balance oscillation, nonlinearity, limit cycle, phase plane

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.

Key words: balance oscillation, nonlinearity, limit cycle, phase plane

中图分类号:  (Theoretical studies)

  • 46.25.Cc
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)