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

作　　者：李世松 兰江 韩冰 谭红 李正坤 

机构地区：[1]Department of Electrical Engineering,Tsinghua University [2]National Institute of Metrology(NIM)

出　　处：《Chinese Physics B》2012年第6期339-343,共5页中国物理B（英文版）

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

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.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 

分 类 号：O314[理学—一般力学与力学基础]