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

MAO Xiao-ye; DING Hu; CHEN Li-qun

doi:10.3879/j.issn.1000-0887.2016.04.002

Volume 37 Issue 4

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MAO Xiao-ye, DING Hu, CHEN Li-qun. Forced Vibration Responses of Supercritical Fluid-Conveying Pipes in 3∶1 Internal Resonance[J]. Applied Mathematics and Mechanics, 2016, 37(4): 345-351. doi: 10.3879/j.issn.1000-0887.2016.04.002

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

doi: 10.3879/j.issn.1000-0887.2016.04.002

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（Key Program）(11232009);The National Natural Science Foundation of China(11372171；11422214)

Received Date: 2016-01-15
Rev Recd Date: 2016-03-03
Publish Date: 2016-04-15

Abstract

Abstract

The multi-scale method was used to investigate the vibration responses of supercritical fluid-conveying pipes in the 3∶1 internal resonance condition. In view of the buckling pipe shape under the supercritical flow velocity, 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.
- pipe conveying fluid,
- internal resonance,
- supercritical,
- multi-scale method,
- nonlinear vibration

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References

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