中文摘要：

首次研究了超临界流速输液管在3∶1内共振条件下的稳态幅频响应.考虑超临界速度引起的管道屈曲位形,建立描述连续体非线性振动的偏微分-积分方程.通过Galerkin截断方法,将连续体方程离散化.对于同时含有平方与立方非线性的多自由度系统,发展高阶多尺度法建立可解性条件.稳态幅频响应曲线揭示了内共振条件下,不同模态间能量的转移.最后,数值仿真结果验证了近似解析分析的有效性.

英文摘要：

The multi-scale method was used to investigate the vibration responses of supercritical fluidconveying pipes in the 3 ∶ 1 internal resonance condition. In viewof the buckling pipe shape under the supercritical flowvelocity,the partial differential-integral equation for the nonlinear vibration of continuous bodies was established and then discretized into a set of ordinary differential equations with the Galerkin truncation method. Both quadratic and cubic nonlinearities of the MDOF system were taken into consideration,and the high-order multi-scale method was applied to build the solvable conditions. 2 natural modes with 2 vibration shapes were introduced to express the approximate solution. The 3 ∶ 1 internal resonance causes the first 2 modes couple in the primary resonance,where the vibration response of the nonlinear system is soft. But in the secondary resonance the vibration response of the nonlinear system is hard.The quadratic nonlinearity makes the system response properties unpredictable. The analytical solutions are perfectly consistent with the numerical simulation results.