小参数法在悬垂索共振中的应用

发布时间：2018-07-03 02:29

本文选题：悬垂索 + 主共振　；参考：《应用力学学报》2017年02期

【摘要】：当面外横向振动和面内横向振动频率的比接近1:2时,悬索会出现面内和面外耦合共振现象。为了研究悬索这种复杂独特的非线性特性,利用多尺度法对谐波激励的悬索动力学方程进行求解,得到对应于不同阶小量的偏微分方程组,其中二阶小量偏微分方程中的久期项不为0;采用提出的小参数法可以得到由久期项引起的悬索振动形态,解决久期项频率与系统频率相同但不能直接求解的问题;为了证明小参数法的准确性,采用Galerkin方法离散悬垂索的运动方程,然后利用多尺度法求解离散的运动方程,得到采用基函数描述的由久期项引起的连续系统的振动形态,与小参数法结论一致。
[Abstract]:When the frequency ratio of external transverse vibration and in-plane transverse vibration is close to 1:2, the in-plane and out-of-plane coupling resonance will occur in the suspension cable. In order to study the complex and unique nonlinear characteristics of the suspension cable, the dynamic equations of the suspension cable excited by harmonics are solved by using the multi-scale method, and the partial differential equations corresponding to different order small quantities are obtained. The duration term in the second order partial differential equation is not zero, the vibration form of suspension cable caused by the duration term can be obtained by using the proposed small parameter method, and the problem that the frequency of duration term is the same as that of the system can not be solved directly. In order to prove the accuracy of the small parameter method, the Galerkin method is used to discretize the equations of motion of the suspended cables, and then the discrete equations of motion are solved by using the multi-scale method, and the vibration shape of the continuous system caused by the duration term described by the basis function is obtained. It is consistent with the conclusion of small parameter method.
【作者单位】：重庆交通大学力学系;重庆大学力学系;
【基金】：国家自然科学基金(51308570;51277186) 重庆市教委科学技术研究项目(KJ1400302) 博士点联合基金(20125522120003)
【分类号】：O32

【相似文献】