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

To study the amplitude-time and amplitude-frequency characteristics of parametric vibration 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 induced 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 intensity. 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 andnonlinear index decreases with the drag coefficient. It plays a good role in learning parametric vibration properties and preventing and curing natural disasters.