| 1. | The normal form calculation of the inner resonances systems
内共振系统的范式计算 |
| 2. | On internal resonance of nonlinear vibration of axially moving beams
轴向运动梁非线性振动内共振研究 |
| 3. | Singular analysis of bifurcation of nonlinear normal modes for a class of systems with dual internal resonances
双重内共振系统非线性模态分岔的奇异性分析 |
| 4. | The 1 : 1 internal resonance of the stay cable coupling the in - plane and out - of - plane modes is analyzed
本文对斜拉索的1 ： 1面内、外模态耦合内共振进行了研究。 |
| 5. | 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。 |
| 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 coupling nonlinear vibration equations involving both the first in - plane and the first out - of - plane modes is generated by using the galerkin method . according to the derived equations , the internal resonance subjected to the in - plane excitation is analyzed by the multiple scale method . the results reveal that the internal resonance of the stay cables posses the characteristics of multiple values and divergence
通过galerkin方法，得到了一个反映面内一阶及面外一阶模态的耦合非线性动力系统，用多尺度法对面内激励下的内共振进行了分析，以实际桥梁拉索为例，得出了拉索模态耦合非线性振动具有多值、分叉等特点，并分析了拉索阻尼对模态耦合内共振的影响。 |
| 8. | 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。 |
