A Galerkin Numerical Method for the Pipe Conveying Supercritical Fluid Under Forced Vibration

HUANG Hui-chun; ZHANG Yan-lei; CHEN Li-qun

doi:10.3879/j.issn.1000-0887.2014.10.004

Volume 35 Issue 10

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HUANG Hui-chun, ZHANG Yan-lei, CHEN Li-qun. A Galerkin Numerical Method for the Pipe Conveying Supercritical Fluid Under Forced Vibration[J]. Applied Mathematics and Mechanics, 2014, 35(10): 1100-1106. doi: 10.3879/j.issn.1000-0887.2014.10.004

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A Galerkin Numerical Method for the Pipe Conveying Supercritical Fluid Under Forced Vibration

doi: 10.3879/j.issn.1000-0887.2014.10.004

¹College of Engineering, Shanghai Second Polytechnic University, Shanghai 201209, P.R.China;²Department of Mechanics, Shanghai University, Shanghai 200072, P.R.China

Funds: The National Natural Science Foundation of China(11302122)

Received Date: 2014-04-22
Rev Recd Date: 2014-09-10
Publish Date: 2014-10-15

Abstract

Abstract

For the pipe conveying fluid, as the flow rate increased over a critical value, the equilibrium configuration was found to get unstable and bifurcate into curved equilibrium patterns. The nonlinear dynamic model for the simply-supported pipe was built and converted to variable-coefficient partial differential control equations through coordinate transformation. The 4-term Galerkin truncation procedure was then applied and the control equations of motion were transformed to 2nd-order ordinary differential equations to be solved with numerical techniques. The natural frequencies of the simply-supported pipe conveying fluid were calculated, and the result comparison was made between the 2-term and 4-term Galerkin truncation methods to give that the latter had higher accuracy. For specific system parameters, the 2nd-order natural frequency was approximately two times of the 1st-order one within a certain range of flow velocity, and the 2-to-1 internal resonance occurred. Massive computation of the amplitude-frequency responses of the pipe conveying fluid before and after internal resonance was conducted with the Runge-Kutta numerical technique. The results show that, as the flow rate and tuning parameter vary, the softening, hardening and double jumping phenomena will be respectively identified by the amplitude-frequency responses of the pipe.
- supercritical fluid,
- Galerkin procedure,
- internal resonance,
- softening and hardening,
- double jumping

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References(20)

References

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