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Article

Stability and Bifurcation Analysis of a Pipe Conveying Pulsating Fluid with Combination Parametric and Internal Resonances

by
Liangqiang Zhou
1,*,
Fangqi Chen
1,* and
Yushu Chen
2
1
Department of Mathematics Nanjing University of Aeronautics and Astronautics, Nanjing 210016, PR China
2
Department of Mechanics Tianjin University, Tianjin, 300072, PR China
*
Authors to whom correspondence should be addressed.
Math. Comput. Appl. 2015, 20(3), 200-216; https://doi.org/10.3390/mca20010216
Published: 1 December 2015
Versions Notes

Abstract

The stability and bifurcations of a hinged-hinged pipe conveying pulsating fluid with combination parametric and internal resonances are studied with both analytical and numerical methods. The system has geometric cubic nonlinearity. Three types of critical points for the bifurcation response equations are considered. These points are characterized by a double zero and two negative eigenvalues, double zero and a pair of purely imaginary eigenvalues, and two pairs of purely imaginary eigenvalues, respectively. With the aid of normal form theory, the expressions for the critical bifurcation lines leading to incipient and secondary bifurcations are obtained. Possible bifurcations leading to 2-D tori are also investigated. Numerical simulations confirm the analytical results.
Keywords: pipe with pulsating fluid; nonlinear vibration; perturbation methods; parametric resonances; stability; bifurcation pipe with pulsating fluid; nonlinear vibration; perturbation methods; parametric resonances; stability; bifurcation

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MDPI and ACS Style

Zhou, L.; Chen, F.; Chen, Y. Stability and Bifurcation Analysis of a Pipe Conveying Pulsating Fluid with Combination Parametric and Internal Resonances. Math. Comput. Appl. 2015, 20, 200-216. https://doi.org/10.3390/mca20010216

AMA Style

Zhou L, Chen F, Chen Y. Stability and Bifurcation Analysis of a Pipe Conveying Pulsating Fluid with Combination Parametric and Internal Resonances. Mathematical and Computational Applications. 2015; 20(3):200-216. https://doi.org/10.3390/mca20010216

Chicago/Turabian Style

Zhou, Liangqiang, Fangqi Chen, and Yushu Chen. 2015. "Stability and Bifurcation Analysis of a Pipe Conveying Pulsating Fluid with Combination Parametric and Internal Resonances" Mathematical and Computational Applications 20, no. 3: 200-216. https://doi.org/10.3390/mca20010216

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