Abstract
Considering initial axial loads, dynamics and stability of an inner functionally graded cylindrical shell conveying swirling fluid (i.e., water) in the annulus between the flexible inner shell and the identical rigid outer shell are investigated by the traveling wave approach. Shell motions are described by Donnell’s thin shell equations. The fluid forces associated with shell motions are treated in the frame of the potential flow theory. The theoretical analysis is conducted by the zero-level contour method. The critical velocities of losing stability are determined. The influences of angular flow on the critical axial velocity and axial flow on the critical annular velocity are studied. Moreover, effects of the magnitude and the direction of initial axial loads on the critical velocities are fully discussed.
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Tijsseling, A.S., et al.: Fluid-structure interaction in liquid-filled pipe systems: a review. J. Fluids Struct. 10, 109–146 (1996)
Weaver, S.S., et al.: Flow-inducted vibrations in power and process plant components-progress and prospects. J. Press. Vessel. 122, 339–348 (2000)
Païdoussis, M.P., Chan, S.P., Misra, A.K.: Dynamics and stability of coaxial cylindrical shells containing flowing fluid. J. Sound. Vib. 97, 201–235 (1984)
Païdoussis, M.P., Misra, A.K., Chan, S.P.: Dynamics and stability of coaxial cylindrical shells conveying viscous fluid. J. Appl. Mech. 52, 389–396 (1985)
Païdoussis, M.P., Misra, A.K., Nguyen, V.B.: Internal- and annular-flow-induced instabilities of a clamped-clamped or cantilevered cylindrical shell in a coaxial conduit: the effects of system parameters. J. Sound. Vib. 159, 193–205 (1992)
Chebair, E.I.: A., Misra, A.K., Païdoussis, M.P.: Theoretical study of the the effect of unsteady viscous forces on inner- and annular-flow-induced instabilities of cylindrical shells. J Sound. Vib. 138, 457–478 (1990)
Experimental study of annular-flow-induced instabilities of cylindrical shells: EI Chebair, A., Païdoussis, M.P., Misra, A.K. J. Fluids Struct. 3, 349–364 (1989)
Amabili, M., Pellicano, F., Païdoussis, M.P.: Nonlinear dynamics and stability of circular cylindrical shells containing flowing fluid. Part 1. Stability. J Sound. Vib. 225, 655–699 (1999)
Karagiozis, K.N., Païdoussis, M.P., Amabili, M., Misra, A.K.: Nonlinear stability of cylindrical shells subjected to axial flow: theory and experiments. J. Sound. Vib. 309, 637–676 (2007)
Ghayesh, M.H., Païdoussis, M.P., Amabili, M.: Nonlinear dynamics of cantilevered extensible pipes conveying fluid. J. Sound. Vib. 332, 6405–6418 (2013)
Horáĉek, J., Zolotarev, I.: Influence of fixing the edges of a cylindrical shell with conveying fluid on its dynamic characteristics. Int. Appl. Mech. 20, 756–765 (1984)
Horáĉek, J.: Approximate theory of annular flow-induced instability of cylindrical shells. J. Fluids Struct. 7, 123–135 (1993)
Srinivasan, A.V.: Flutter analysis of rotating cylindrical shells immersed in helical circular flowfield of air. AIAA J. 9, 394–400 (1971)
Dowell, E.H., Srinivasan, A.V., Mclean, J.D., Ambrose, J.: Aeroelastic stability of cylindrical shells subjected to a rotating flow. AIAA J. 12, 1644–1651 (1974)
Bochkarev, S.A., Matveenko, V.P.: The dynamic behaviour of elastic coaxial cylindrical shells conveying fluid. J. Appl. Math. Mech. 74, 467–474 (2010)
Bochkarev, S.A., Matveenko, V.P.: Stability analysis of loaded coaxial cylindrical shells with internal fluid flow. Mech. Solids. 45, 789–802 (2010)
Bochkarev, S.A., Lekomtsev, S.V., Matveenko, V.P.: Parametric investigation of the stability of coaxial cylindrical shells containing flowing fluid. Eur. J. Mech. A Solids. 47, 174–181 (2014)
Bochkarev, S.A., Matveenko, V.P.: Stability of a cylindrical shell subjected to an annular flow of rotating fluid. J. Sound Vib. 332, 4210–4222 (2013)
Bochkarev, S.A., Matveenko, V.P.: Stability analysis of cylindrical shells containing a fluid with axial and circumferential components. J. Appl. Mech. Tech. Phys. 53, 768–776 (2012)
Bochkarev, S.A., Matveenko, V.P.: Natural vibrations and stability of a stationary or rotating circular cylindrical shell containing a rotating fluid. Comput. Struct. 89, 571–580 (2011)
Bochkarev, S.A., Matveenko, V.P.: Numerical analysis of stability of a stationary or rotating circular cylindrical shell containing axially flowing and rotating fluid. Int. J. Mech. Sci. 68, 258–269 (2013)
Bochkarev, S.A., Matveenko, V.P.: Specific features of dynamic behavior of stationary and rotating single/coaxial cylindrical shells interacting with the axial and rotational fluid flows. J. Vib. Acoust. 137, 21001 (2015)
Bochkarev, S.A., Matveenko, V.P.: Stability of rotating coaxial cylindrical shells interacting with the flowing and rotating fluid. Int. J. Struct. Stab. Dyn. 15, 1450071 (2015)
Chen, T.L.C., Bert, C.W.: Dynamic stability of isotropic or composite-material cylindrical shell carrying a rotation flow by using travelling wave forms. J. Appl. Mech. 44, 112–116 (1977)
Dao, H.B., Dao, V.D., Vu, H.N., Nguyen, T.P.: Nonlinear static and dynamic buckling analysis of imperfect eccentrically stiffened functionally graded circular cylindrical thin shells under axial compression. Int. J. Mech. Sci. 74, 190–200 (2013)
Chen, W.Q., Bian, Z.G., Ding, H.J.: Three-dimensional vibration analysis of fluid-filled orthotropic FGM cylindrical shells. Int. J. Mech. Sci. 46, 159–171 (2004)
Iqbal, Z., Naeem, M.N., Sultana, N., Arshad, S.H., Shah, A.G.: Vibration characteristics of FGM circular cylindrical shells filled with fluid using wave propagation approach. Appl. Math. Mech. 30, 1393–1404 (2009)
Shah, A.G., Mahmood, T., Naeem, M.N., Arshad, S.H.: Vibrational study of fluid-filled functionally graded cylindrical shells resting on elastic foundations. ISRN Mech. Eng. 2011, 1–13 (2011)
Silva, F.M.A., Montes, R.O.P., Goncalves, P.B., Del Prado, Z.J.G.N.: Nonlinear vibrations of fluid-filled functionally graded cylindrical shell considering a time-dependent lateral load and static preload. J. Mech. Eng. Sci. 230, 102–119 (2016)
Sheng, G.G., Wang, X.: Thermomechanical vibration analysis of functionally graded cylindrical shells with flowing fluid. Eur. J. Mech. A-Solids. 27, 1075–1087 (2008)
Sheng, G.G., Wang, X.: Dynamic characteristics of fluid-conveying functionally graded cylindrical shells under mechanical and thermal loads. Compos. Struct. 93, 162–170 (2010)
Shen, H.J., Païdoussis, M.P., Wen, J.H., et al.: The beam-mode stability of periodic functionally-graded-material shells conveying fluid. J. Sound. Vib. 333, 2735–2749 (2014)
Shen, H.J., Wen, J.H., Yu, D.L., et al.: Stability of fluid-conveying periodic shells on an elastic foundation with external loads. J. Fluids Struct. 46, 134–148 (2014)
Amabili, M.: Nonlinear Vibration and Stability of Shells and Plates. Cambridge University Press, Cambridge (2008)
Shun, S.P., Cao, D.Q., Chu, S.M.: Free vibration analysis of thin rotating cylindrical shells using wave propagating approach. Arch. Appl. Mech. 83, 521–531 (2013)
Timoshenko, S.P., Gere, J.M.: Theory of Elastic Stability. McGraw-Hill, New York (1961)
Acknowledgments
The authors wish to thank Prof. Shen H.-S. of Shanghai Jiao Tong University for considerable support. The work is supported by grants from National Basic Research Program of China. The authors are grateful for the financial support.
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Ning, WB., Zhang, JG. & Chen, WD. Dynamics and stability of a functionally graded cylindrical thin shell containing swirling annular fluid flow including initial axial loads. Acta Mech 227, 2157–2170 (2016). https://doi.org/10.1007/s00707-016-1627-0
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DOI: https://doi.org/10.1007/s00707-016-1627-0