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.
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)
