| 1. | Parametric resonances of a pipe conveying fluid and their numerical simulations
输流管的参数共振及共振响应的数值模拟与分析 |
| 2. | Optimal control of parametric resonances of a clamped - clamped pipe conveying pulsating fluid
两端固定输流管道在脉动内流作用下参数共振的最优控制 |
| 3. | When the axial speed varies harmonically about a constant mean one , the method of multiple scales is applied to the axially moving beam to determine the instability boundary due to parametric resonance
当轴向运动速度在其常平均值附近作简谐波动时，应用多尺度法给出轴向变速运动梁参数共振时的不稳定条件。 |
| 4. | We got the averaged equations of the system in three resonant cases . those are principal parametric resonance and 1 : 1 internal resonance , principal parametric resonance and 1 : 2 internal resonance and principal parametric resonance and 1 : 3 internal resonance
这三种共振情形分别是1 ： 1内共振和主参数共振； 1 ： 2内共振和主参数共振； 1 ： 3内共振和主参数共振。 |
| 5. | A comprehensive introduction to the theory of dynamic stability is given . the concept of parametric resonance is introduced . the system differential equations ( mathieu - hill equations ) for dynamic stability analysis is derived
对动力稳定理论作了全面的介绍，引入了参数共振的概念，并推导了动力稳定问题的微分方程? ? mathieu - hill方程，对floquet理论作了简单介绍。 |
| 6. | For the nonlinear planar cantilever , the two resonant cases are considered . one of the two cases is primary resonance - principal parametric resonance and 1 : 3 internal resonance . the other is 1 / 2 subharmonic resonance - principal parametric resonance and 1 : 3 internal resonance
对于平面运动悬臂梁研究了二种共振情况，一是主共振-主参数共振和1 ： 3内共振的情形，另一是1 2亚谐共振-主参数共振和1 ： 3内共振的情形。 |
| 7. | The second case is 1 / 2 subharmonic resonance - principal parametric resonance and 1 : 1 internal resonance . the final case is primary resonance for the second mode - principal parametric resonance and 1 : 2 internal resonance . the adjoint operator method and the theory of normal form are used to investigated the normal forms in the four dimensional nonlinear systems with cubic nonlinearities
第一种共振情况是主共振-主参数共振和1 ： 1内共振的情形；第二种共振情况是1 2亚谐共振-主参数共振和1 ： 1内共振的情形；第三种共振情况是第二模态主共振-主参数共振和1 ： 2内共振的情形。 |
