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

ZHANG Kaikai; TAN Xia; DING Hu; CHEN Liqun

doi:10.21656/1000-0887.390121

Volume 39 Issue 11

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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

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

doi: 10.21656/1000-0887.390121

¹Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University,Shanghai 200072, P.R.China;²Department of Mechanics, Shanghai University, Shanghai 200444, P.R.China

Funds: The National Natural Science Foundation of China(11772181)

Received Date: 2018-04-16
Rev Recd Date: 2018-09-14
Publish Date: 2018-11-01

Abstract

Abstract

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.
- fluid-conveying pipe,
- internal resonance,
- multiscale method,
- parametric vibration,
- supercritical

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References(16)

References

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