ZHANG Kaikai, TAN Xia, DING Hu, CHEN Liqun. Parametric Vibration Responses of Supercritical Fluid-Conveying Pipes in 3∶1 Internal Resonance[J]. Applied Mathematics and Mechanics, 2018, 39(11): 1227-1235. doi: 10.21656/1000-0887.390121
 Citation: ZHANG Kaikai, TAN Xia, DING Hu, CHEN Liqun. Parametric Vibration Responses of Supercritical Fluid-Conveying Pipes in 3∶1 Internal Resonance[J]. Applied Mathematics and Mechanics, 2018, 39(11): 1227-1235.

# Parametric Vibration Responses of Supercritical Fluid-Conveying Pipes in 3∶1 Internal Resonance

##### doi: 10.21656/1000-0887.390121
Funds:  The National Natural Science Foundation of China(11772181)
• Rev Recd Date: 2018-09-14
• Publish Date: 2018-11-01
• The parametric vibration responses were studied in the supercritical fluid-conveying pipes in the 3∶1 internal resonance condition. In the control equation, the non-normal static configuration of the pipe at the supercritical velocity was introduced, and the partial differential-integral control equation was obtained. The approximate analytic solution was deduced with the direct multiscale method, and the reliability of the approximate analytic results was verified with the Galerkin truncation method. Numerical examples show that, there exists energy transfer between different modes of the pipeline system in internal resonance. The influence of the parameter amplitude on the amplitude-frequency response was predicted based on approximate analytical results.
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