激振摆参数振动中非稳定区运动特性的探讨

A study on characteristics of the excited parametric vibration in unstable region

为了研究激振摆参数振动中非稳定区的幅时特性和幅频特性,采用matelab软件求解激振摆非线性动力学方程。数值解结果表明,小振幅的激励可诱导大的响应——运动失稳、共振发生。激振摆共振条件是激振频率为固有频率的两倍,是否发生共振以及共振的强度与激振信号的初相位无关,初相位的不同仅导致共振的初始时刻不同。激振信号的振幅、激振摆的阻力系数和固有频率对共振的幅时特性都有影响,加大激振振幅和固有频率都可增加共振强度,而阻力系数增加则抑制共振强度,当阻力系数超过临界值时共振被完全抑制。非稳定区的临界频宽与固有频率无关,但与激振信号的振幅和阻力系数有关,它随激振振幅线性增加,但随阻力系数非线性指数减小。研究结果对于了解参数振动的特性以及防治参数共振的危害具有一定的参考作用。

To study the amplitude-time and amplitude-frequency characteristics of parametric vibra- tion in the unstable region, the nonlinear dynamic equations are solved using mate-lab software. The results of the numerical solution showed that the larger response which is the resonance can be in- duced by the smaller excitation. The resonance condition is that exciting frequency is twice as large as inherent frequency. Both the occurrence and the strength of the resonance is independent on the initial phase of the exciting signal. The initial phase only impact on the initial time of resonance. All of the drag coefficient, the exciting amplitude and inherent frequency influenced the amplitude-time characteristic of the resonance. The strength of the resonance can increase with the increase of the exciting amplitude and inherent frequency. The increase of drag coefficient suppresses resonance in- tensity. The resonance is completely suppressed when the drag coefficient exceeds the critical value. Frequency bandwidth of the unstable range is independent from inherent frequency, but it is related to the exciting amplitude and drag coefficient. It is linear increasing with exciting amplitude and nonlinear index decreases with the drag coefficient. It plays a good role in learning parametric vibra- tion properties and preventing and curing natural disasters.