Nonplanar post-buckling analysis of simply supported pipes conveying fluid with an axially sliding downstream end

Tianli JIANG, Huliang DAI, Kun ZHOU, Lin WANG

doi:10.1007/s10483-020-2557-9

Applied Mathematics and Mechanics >

2020 , Vol. 41 >Issue 1: 15 - 32

DOI: https://doi.org/10.1007/s10483-020-2557-9

Articles

Nonplanar post-buckling analysis of simply supported pipes conveying fluid with an axially sliding downstream end

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1. Department of Mechanics, Huazhong University of Science and Technology, Wuhan 430074, China;
2. Hubei Key Laboratory for Engineering Structural Analysis and Safety Assessment, Wuhan 430074, China

Received date: 2019-05-15

Revised date: 2019-07-24

Online published: 2019-12-14

Supported by

Project supported by the National Natural Science Foundation of China (Nos. 11622216, 11602090, and 11672115), the Natural Science Foundation of Hubei Province (No. 2017CFB429), and the fundamental Research Funds for the Central Universities of China (No. 2017KFYXJJ135)

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Abstract

In this study, the nonplanar post-buckling behavior of a simply supported fluid-conveying pipe with an axially sliding downstream end is investigated within the framework of a three-dimensional (3D) theoretical model. The complete nonlinear governing equations are discretized via Galerkin's method and then numerically solved by the use of a fourth-order Runge-Kutta integration algorithm. Different initial conditions are chosen for calculations to show the nonplanar buckling characteristics of the pipe in two perpendicular lateral directions. A detailed parametric analysis is performed in order to study the influence of several key system parameters such as the mass ratio, the flow velocity, and the gravity parameter on the post-buckling behavior of the pipe. Typical results are presented in the form of bifurcation diagrams when the flow velocity is selected as the variable parameter. It is found that the pipe will stay at its original straight equilibrium position until the critical flow velocity is reached. Just beyond the critical flow velocity, the pipe would lose stability by static divergence via a pitchfork bifurcation, and two possible nonzero equilibrium positions are generated. It is shown that the buckling and post-buckling behaviors of the pipe cannot be influenced by the mass ratio parameter. Unlike a pipe with two immovable ends, however, the pinned-pinned pipe with an axially sliding downstream end shows some different features regarding post-buckling behaviors. The most important feature is that the buckling amplitude of the pipe with an axially sliding downstream end would increase first and then decrease with the increase in the flow velocity. In addition, the buckled shapes of the pipe varying with the flow velocity are displayed in order to further show the new post-buckling features of the pipe with an axially sliding downstream end.

Key words： fluid-conveying pipe; axially sliding downstream end; nonplanar; postbuckling behavior

Cite this article

Tianli JIANG, Huliang DAI, Kun ZHOU, Lin WANG . Nonplanar post-buckling analysis of simply supported pipes conveying fluid with an axially sliding downstream end[J]. Applied Mathematics and Mechanics, 2020 , 41(1) : 15 -32 . DOI: 10.1007/s10483-020-2557-9

References

[1] ARIARATNAM, S. T. and NAMACHCHIVAYA, N. S. Dynamic stability of pipes conveying fluid with stochastic flow velocity. Studies in Applied Mechanics, Elsevier, New York, 1-17(1986)
[2] ZHOU, X. W., DAI, H. L., and WANG, L. Dynamics of axially functionally graded cantilevered pipes conveying fluid. Composite Structures, 190, 112-118(2018)
[3] TANG, Y. and YANG, T. Post-buckling behavior and nonlinear vibration analysis of a fluidconveying pipe composed of functionally graded material. Composite Structures, 185, 393-400(2018)
[4] LIANG, F. and WEN, B. Forced vibrations with internal resonance of a pipe conveying fluid under external periodic excitation. Acta Mechanica Solida Sinica, 24(6), 477-483(2011)
[5] ZHANG, Y. L. and CHEN, L. Q. External and internal resonances of the pipe conveying fluid in the supercritical regime. Journal of Sound and Vibration, 332(9), 2318-2337(2013)
[6] KUIPER, G. L., METRIKINE, A. V., and BATTJES, J. A. A new time-domain drag description and its influence on the dynamic behaviour of a cantilever pipe conveying fluid. Journal of Fluids and Structures, 23(3), 429-445(2007)
[7] ZHAO, Q. and SUN, Z. In-plane forced vibration of curved pipe conveying fluid by Green function method. Applied Mathematics and Mechanics (English Edition), 38(10), 1397-1414(2017) https://doi.org/10.1007/s10483-017-2246-6
[8] LIANG, F., YANG, X. D., QIAN, Y. J., and ZHANG, W. Forced response analysis of pipes conveying fluid by nonlinear normal modes method and iterative approach. Journal of Computational and Nonlinear Dynamics, 13(1), 014502(2017)
[9] PAÏDOUSSIS, M. P. and ISSID, N. Dynamic stability of pipes conveying fluid. Journal of Sound and Vibration, 33(3), 267-294(1974)
[10] VASSILEV, V. M. and DJONDJOROV, P. A. Dynamic stability of viscoelastic pipes on elastic foundations of variable modulus. Journal of Sound and Vibration, 297(1/2), 414-419(2006)
[11] HUANG, Y. M., GE, S., WU, W., and HE, J. A direct method of natural frequency analysis on pipeline conveying fluid with both ends supported. Nuclear Engineering and Design, 253, 12-22(2012)
[12] PANDA, L. N. and KAR, R. C. Nonlinear dynamics of a pipe conveying pulsating fluid with combination, principal parametric and internal resonances. Journal of Sound and Vibration, 309(3), 375-406(2008)
[13] STANGL, M., GERSTMAYR, J., and IRSCHIK, H. An alternative approach for the analysis of nonlinear vibrations of pipes conveying fluid. Journal of Sound and Vibration, 310(3), 493-511(2008)
[14] JIN, J. D. and SONG, Z. Y. Parametric resonances of supported pipes conveying pulsating fluid. Journal of Fluids and Structures, 20(6), 763-783(2005)
[15] GINSBERG, J. H. The dynamic stability of a pipe conveying a pulsatile flow. International Journal of Engineering Science, 11(9), 1013-1024(1973)
[16] ARIARATNAM, S. T. and NAMACHCHIVAYA, N. S. Dynamic stability of pipes conveying pulsating fluid. Journal of Sound and Vibration, 107(2), 215-230(1986)
[17] ZHANG, Y. F., YAO, M. H., ZHANG, W., and WEN, B. C. Dynamical modeling and multi-pulse chaotic dynamics of cantilevered pipe conveying pulsating fluid in parametric resonance. Aerospace Science and Technology, 68, 441-453(2017)
[18] ZHANG, T., OUYANG, H., ZHANG, Y. O., and LV, B. L. Nonlinear dynamics of straight fluidconveying pipes with general boundary conditions and additional springs and masses. Applied Mathematical Modelling, 40(17), 7880-7900(2016)
[19] MODARRES-SADEGHI, Y., SEMLER, C., WADHAM-GAGNON, M., and PAÏDOUSSIS, M. P. Dynamics of cantilevered pipes conveying fluid, part 3:three-dimensional dynamics in the presence of an end-mass. Journal of Fluids and Structures, 23(4), 589-603(2007)
[20] GHAYESH, M. H., PAÏDOUSSIS, M. P., and MODARRES-SADEGHI, Y. Three-dimensional dynamics of a fluid-conveying cantilevered pipe fitted with an additional spring-support and an end-mass. Journal of Sound and Vibration, 330(12), 2869-2899(2011)
[21] WANG, L., LIU, Z. Y., ABDELKEFI, A., WANG, Y. K., and DAI, H. L. Nonlinear dynamics of cantilevered pipes conveying fluid:towards a further understanding of the effect of loose constraints. International Journal of Non-Linear Mechanics, 95, 19-29(2017)
[22] PENG, G., XIONG, Y., GAO, Y., LIU, L., WANG, M., and ZHANG, Z. Non-linear dynamics of a simply supported fluid-conveying pipe subjected to motion-limiting constraints:two-dimensional analysis. Journal of Sound and Vibration, 435, 192-204(2018)
[23] NI, Q., WANG, Y., TANG, M., LUO, Y., YAN, H., and WANG, L. Nonlinear impacting oscillations of a fluid-conveying pipe subjected to distributed motion constraints. Nonlinear Dynamics, 81(1), 893-906(2015)
[24] GAN, C., JING, S., YANG, S., and LEI, H. Effects of supported angle on stability and dynamical bifurcations of cantilevered pipe conveying fluid. Applied Mathematics and Mechanics (English Edition), 36(6), 729-746(2015) https://doi.org/10.1007/s10483-015-1946-6
[25] DZHUPANOV, V. A. and LILKOVA-MARKOVA, S. V. Dynamic stability of a fluid-coveying cantilevered pipe on an additional combined support. International Applied Mechanics, 39(2), 185-191(2003)
[26] LIANG, F., YANG, X. D., ZHANG, W., and QIAN, Y. J. Coupled bi-flexural-torsional vibration of fluid-conveying pipes spinning about an eccentric axis. International Journal of Structural Stability and Dynamics, 19(2), 1950003(2019)
[27] LIANG, F., YANG, X. D., ZHANG, W., and QIAN, Y. J. Nonlinear free vibration of spinning viscoelastic pipes conveying fluid. International Journal of Applied Mechanics, 10(7), 1850076(2018)
[28] LIANG, F., YANG, X. D., QIAN, Y. J., and ZHANG, W. Transverse free vibration and stability analysis of spinning pipes conveying fluid. International Journal of Mechanical Sciences, 137, 195-204(2018)
[29] LIANG, F., YANG, X. D., ZHANG, W., and QIAN, Y. J. Dynamical modeling and free vibration analysis of spinning pipes conveying fluid with axial deployment. Journal of Sound and Vibration, 417, 65-79(2018)
[30] HOLMES, P. Pipes supported at both ends cannot flutter. Journal of Applied Mechanics, 45(3), 619-622(1978)
[31] NAGULESWARAN, S. and WILLIAMS, C. J. H. Lateral vibration of a pipe conveying a fluid. Journal of Mechanical Engineering Science, 10(3), 228-238(1968)
[32] MODARRES-SADEGHI, Y. and PAÏDOUSSIS, M. P. Nonlinear dynamics of extensible fluidconveying pipes, supported at both ends. Journal of Fluids and Structures, 25(3), 535-543(2009)
[33] WANG, L., JIANG, T. L., and DAI, H. L. Three-dimensional dynamics of supported pipes conveying fluid. Acta Mechanica Sinica, 33(6), 1065-1074(2017)
[34] PENG, G., XIONG, Y., LIU, L., GAO, Y., WANG, M., and ZHANG, Z. 3-D non-linear dynamics of inclined pipe conveying fluid, supported at both ends. Journal of Sound and Vibration, 449, 405-426(2019)
[35] PAÏDOUSSIS, M. P. and ISSID, N. T. Experiments on parametric resonance of pipes containing pulsatile flow. Journal of Applied Mechanics, 43(2), 198-202(1976)
[36] JENDRZEJCZYK, J. A. and CHEN, S. S. Experiments on tubes conveying fluid. Thin-Walled Structures, 3(2), 109-134(1985)
[37] BINULAL, B. R., RAJAN, A., UNNIKRISHNAN, M., and KOCHUPILLAI, J. Experimental determination of time lag due to phase shift on a flexible pipe conveying fluid. Measurement, 83, 86-95(2016)
[38] YOSHIZAWA, M., NAO, H., HASEGAWA, E., and TSUJIOKA, Y. Buckling and postbuckling behavior of a flexible pipe conveying fluid. Bulletin of JSME, 28(240), 1218-1225(1985)
[39] YOSHIZAWA, M., NAO, H., HASEGAWA, E., and TSUJIOKA, Y. Lateral vibration of a flexible pipe conveying fluid with pulsating flow. Bulletin of JSME, 29(253), 2243-2250(1986)
[40] PAÏDOUSSIS, M. P. Fluid-Structure Interactions:Slender Structures and Axial Flow, Vol. 1, Academic Press, New York (1998)
[41] SNOWDON, J. C. Vibration and Shock in Damped Mechanical Systems, Wiley, New York (1968)
[42] WADHAM-GAGNON, M., PAÏDOUSSIS, M. P., and SEMLER, C. Dynamics of cantilevered pipes conveying fluid, part 1:nonlinear equations of three-dimensional motion. Journal of Fluids and Structures, 23(4), 545-567(2007)
[43] SEMLER, C., LI G. X., and PAÏDOUSSIS, M. P. The non-linear equations of motion of pipes conveying fluid. Journal of Sound and Vibration, 169(5), 577-599(1994)
[44] DODDS, H. L. and RUNYAN, H. L. Effect of High-Velocity Fluid Flow on the Bending Vibrations and Static Divergence of a Simply Supported Pipe, NASA Technical Note D-2870, NASA (1965)
[45] PAÏDOUSSIS, M. P. and SEMLER, C. Nonlinear and chaotic oscillations of a constrained cantilevered pipe conveying fluid:a full nonlinear analysis. Nonlinear Dynamics, 4(6), 655-670(1993)

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