激振摆参数振动的实验研究

Experimental research of double frequency resonance phenomenon subjected to vertical excitation

研究了一种激振摆参数振动的实验.当激振频率为激振摆固有频率2倍时激振摆会产生共振.实验探讨了激振摆从微阻尼振动到共振的幅时特性和幅频特性.对于小振幅纵向激振,当激振频率接近激振摆固有频率2倍时,激振摆的摆幅对激振频率很敏感,在减小频宽数使激振摆振动接近共振的过程中,激振摆的摆幅数随时间数会震荡变化(类似"拍"现象),"拍"的周期数和峰谷差数都随频宽数减小而增加;"拍"现象消失后继续减小频宽数,摆幅数随时间数将持续指数增大,运动失稳;在频宽数为零时,摆幅数随时间数增加最剧烈,即共振发生.通过激振摆理论模型对实验结果进行了动力学分析,非线性动力学方程的数值解结果与实验结果吻合较好.该实验研究对于解决与共振相关的问题有潜在的应用价值.

An experimental study of an excited parametric vibration is reported,the resonance condition is that external frequency is twice as large as inherent frequency, and the direction of driving force is vertical to movement direction. The amplitude-frequency characteristic of the resonance and the critical state are discussed. When both intensity of vertical excitation and frequency width number are small, the law of vibration is sensitive to frequency width number . While frequency width number is reduced, amplitude number will oscillate with time. That is ＂beat＂ phenomenon. Both period number and peak-valley difference number increase with the decrease of frequency width number. After ＂beat＂ disappears, the amplitude number continues increasing exponentially with time number. When frequency width number equals to zero, the amplitude number increases sharply with the period number, the vibra- tion is unstable and then resonance occurs. Based on the pendulum model ,the numerical solutions of dynamic equa- tion are in well agreement with the experimental results. The experimental study for solving problems such as pre- vention of natural disasters associated with resonance has potential applications.