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Research Papers

Specific Features of Dynamic Behavior of Stationary and Rotating Single/Coaxial Cylindrical Shells Interacting With the Axial and Rotational Fluid Flows

[+] Author and Article Information
Sergey A. Bochkarev

Institute of Continuous Media Mechanics RAS,
Acad. Korolev Str 1,
Perm 614013, Russia
e-mail: bochkarev@icmm.ru

Valery P. Matveenko

Institute of Continuous Media Mechanics RAS,
Acad. Korolev Str 1,
Perm 614013, Russia

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received May 22, 2013; final manuscript received October 13, 2014; published online November 14, 2014. Assoc. Editor: Massimo Ruzzene.

J. Vib. Acoust 137(2), 021001 (Apr 01, 2015) (10 pages) Paper No: VIB-13-1176; doi: 10.1115/1.4028829 History: Received May 22, 2013; Revised October 13, 2014; Online November 14, 2014

The paper is concerned with the finite element analysis of hydroelastic stability of stationary or rotating elastic single and coaxial cylindrical shells subjected to compressible fluid flows having axial and tangential velocity components. The behavior of the flowing and rotating fluid is described in the framework of the potential theory. Consideration of elastic shells is based on the classical shell model. The results of the numerical analysis of shell stability for various boundary conditions, geometrical dimensions and different sizes of the annular gap between the outer and inner shells are discussed. It has been found that single and coaxial shells interacting with the combined fluid flows show qualitative differences in the dynamic behavior.

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References

Païdoussis, M. P., 2004, Fluid-Structure Interactions: Slender Structures and Axial Flow, Vol. 2, Elsevier Academic, London, UK.
Gosselin, F., and Païdoussis, M. P., 2007, “Stability of a Rotating Cylindrical Shell Containing Axial Viscous Flow,” 18ème Congrès Français de Mécanique (CFM’07), Grenoble, France, Aug 27–31, Paper No. CFM2007-1578.
Ilgamov, M. A., 1969, Oscillations of Elastic Shells Containing Liquid and Gas, Nauka, Moscow, Russia (in Russian).
Selmane, A., and Lakis, A. A., 1997, “Vibration Analysis of Anisotropic Open Cylindrical Shells Subjected to a Flowing Fluid,” J. Fluid Struct., 11(1), pp. 111–134. [CrossRef]
Zhang, Y. L., Gorman, D. G., and Reese, J. M., 2001, “A Finite Element Method for Modelling the Vibration of Initially Tensioned Thin-Walled Orthotropic Cylindrical Tubes Conveying Fluid,” J. Sound Vib., 245(1), pp. 93–112. [CrossRef]
Lakis, A. A., Van Dyke, P., and Ouriche, H., 1992, “Dynamic Analysis of Anisotropic Fluid-Filled Conical Shells,” J. Fluid Struct., 6(2), pp. 135–162. [CrossRef]
Kerboua, Y., Lakis, A. A., and Hmila, M., 2010, “Vibration Analysis of Truncated Conical Shells Subjected to Flowing Fluid,” Appl. Math. Model., 34(3), pp. 791–809. [CrossRef]
Zhang, Y. L., Gorman, D. G., and Reese, J. M., 2003, “Vibration of Prestressed Thin Cylindrical Shells Conveying Fluid,” Thin Walled Struct., 41(12), pp. 1103–1127. [CrossRef]
Kochupillai, J., Ganesan, N., and Padmanabhan, C., 2002, “A Semi-Analytical Coupled Finite Element Formulation for Shells Conveying Fluids,” Comput. Struct., 80(3–4), pp. 271–286. [CrossRef]
Kochupillai, J., Ganesan, N., and Padmanabhan, C., 2002, “A Semi-Analytical Coupled Finite Element Formulation for Composite Shells Conveying Fluids,” J. Sound Vib., 258(2), pp. 287–307. [CrossRef]
Kumar, D. S., and Ganesan, N., 2008, “Dynamic Analysis of Conical Shells Conveying Fluid,” J. Sound Vib., 310(1–2), pp. 38–57. [CrossRef]
Bochkarev, S. A., and Matveenko, V. P., 2011, “Natural Vibrations and Stability of Shells of Revolution Interacting With An Internal Fluid Flow,” J. Sound Vib., 330(13), pp. 3084–3101. [CrossRef]
Uğurlu, B., and Ergin, A., 2006, “A Hydroelasticity Method for Vibrating Structures Containing and/or Submerged in Flowing Fluid,” J. Sound Vib., 290(3–5), pp. 572–596. [CrossRef]
Uğurlu, B., and Ergin, A., 2008, “A Hydroelastic Investigation of Circular Cylindrical Shells-Containing Flowing Fluid With Different End Conditions,” J. Sound Vib., 318(4–5), pp. 1291–1312. [CrossRef]
Firouz-Abadi, R. D., Noorian, M. A., and Haddadpour, H., 2010, “A Fluid-Structure Interaction Model for Stability Analysis of Shells Conveying Fluid,” J. Fluids Struct., 26(5), pp. 747–763. [CrossRef]
Païdoussis, M. P., Chan, S. P., and Misra, A. K., 1984, “Dynamics and Stability of Coaxial Cylindrical Shells Containing Flowing Fluid,” J. Sound Vib., 97(2), pp. 201–235. [CrossRef]
El Chebair, A., Païdoussis, M. P., and Misra, A. K., 1989, “Experimental Study of Annular-Flow-Induced Instabilities of Cylindrical Shells,” J. Fluids Struct., 3(4), pp. 349–364. [CrossRef]
Païdoussis, M. P., Misra, A. K., and Chan, S. P., 1985, “Dynamics and Stability of Coaxial Cylindrical Shells Conveying Viscous Fluid,” ASME J. Appl. Mech., 52(2), pp. 389–396. [CrossRef]
Amabili, M., and Garziera, R., 2002, “Vibrations of Circular Cylindrical Shells With Nonuniform Constraints, Elastic Bed and Added Mass; Part II: Shells Containing or Immersed in Axial Flow,” J. Fluids Struct., 16(1), pp. 31–51. [CrossRef]
Païdoussis, M. P., Nguyen, V. B., and Misra, A. K., 1991, “A Theoretical Study of the Stability of Cantilevered Coaxial Cylindrical Shells Conveying Fluid,” J. Fluids Struct., 5(2), pp. 127–164. [CrossRef]
Païdoussis, M. P., Misra, A. K., and Nguyen, V. B., 1992, “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(2), pp. 193–205. [CrossRef]
Nguyen, V. B., Païdoussis, M. P., and Misra, A. K., 1994, “A CFD-Based Model for the Study of the Stability of Cantilevered Coaxial Cylindrical Shells Conveying Viscous Fluid,” J. Sound Vib., 176(1), pp. 105–125. [CrossRef]
Nguyen, V. B., Païdoussis, M. P., and Misra, A. K., 1993, “An Experimental Study of the Stability of Cantilevered Coaxial Cylindrical Shells Conveying Fluid,” J. Fluids Struct., 7(8), pp. 913–930. [CrossRef]
Bochkarev, S. A., and Matveenko, V. P., 2010, “The Dynamic Behaviour of Elastic Coaxial Cylindrical Shells Conveying Fluid,” J. Appl. Math. Mech., 74(4), pp. 467–474. [CrossRef]
Bochkarev, S. A., and Matveenko, V. P., 2010, “Stability Analysis of Loaded Coaxial Cylindrical Shells With Internal Fluid Flow,” Mech. Sol., 45(6), pp. 789–802. [CrossRef]
Chen, Y., Zhao, H. B., Shen, Z. P., Grieger, I., and Kröplin, B.-H., 1993, “Vibrations of High Speed Rotating Shells With Calculations for Cylindrical Shells,” J. Sound Vib., 160(1), pp. 137–160. [CrossRef]
Sivadas, K. R., and Ganesan, N., 1994, “Effect of Rotation on Vibration of Moderarately Thick Circular Cylindrical Shells,” ASME J. Vib. Acoust., 116(1), pp. 198–202. [CrossRef]
Guo, D., Zheng, Z., and Chu, F., 2002, “Vibration Analysis of Spinning Cylindrical Shells by Finite Element Method,” Int. J. Solids Struct., 39(3), pp. 725–739. [CrossRef]
Dey, S., and Karmakar, A., 2012, “Natural Frequencies of Delaminated Composite Rotating Conical Shells—A Finite Element Approach,” Finite Elem. Anal. Des., 56, pp. 41–51. [CrossRef]
Hua, L., Lam, K. Y., and Ng, T. Y., 2005, Rotating Shell Dynamics, Elsevier Academic, London, UK.
Lai, Y.-C., and Chow, C.-Y., 1973, “Stability of a Rotating Thin Elastic Tube Containing a Fluid Flow,” Z. Angew Math. Mech., 53(8), pp. 511–517. [CrossRef]
Vorob'ev, Y. S., and Detistov, S. I., 1985, “Effect of a Gas Flow on Vibrations of Rotating Cylindrical Shells,” Int. Appl. Mech., 21(7), pp. 657–660. [CrossRef]
Chen, T. L. C., and Bert, C. W., 1977, “Wave Propagation in Isotropic- or Composite-Material Piping Conveying Swirling Liquid,” Nucl. Eng. Des., 42(2), pp. 247–255. [CrossRef]
Chen, T. L. C., and Bert, C. W., 1977, “Dynamic Stability of Isotropic or Composite Material Cylindrical Shells Containing Swirling Fluid Flow,” ASME J. Appl. Mech., 44(1), pp. 112–116. [CrossRef]
Bochkarev, S. A., and Matveenko, V. P., 2011, “Natural Vibrations and Stability of a Stationary or Rotating Circular Cylindrical Shell Containing a Rotating Fluid,” Comput. Struct., 89(7–8), pp. 571–580. [CrossRef]
Cortelezzi, L., Pong, A., and Païdoussis, M. P., 2004, “Flutter of Rotating Shells With a Co-Rotating Axial Flow,” ASME J. Appl. Mech., 71(1), pp. 143–145. [CrossRef]
Bochkarev, S. A., and Matveenko, V. P., 2013, “Numerical Analysis of Stability of a Stationary or Rotating Circular Cylindrical Shell Containing Axially Flowing and Rotating Fluid,” Int. J. Mech. Sci., 68, pp. 258–269. [CrossRef]
Srinivasan, A. V., 1971, “Flutter Analysis of Rotating Cylindrical Shells Immersed in a Circular Helical Flowfield of Air,” AIAA J., 9(3), pp. 394–400. [CrossRef]
David, T. S., and Srinivasan, A. V., 1974, “Flutter of Coaxial Cylindrical Shells in a Incompressible Axisymmetric Flow,” AIAA J., 12(12), pp. 1631–1635. [CrossRef]
Bochkarev, S. A., and Matveenko, V. P., 2013, “Stability of a Cylindrical Shell Subject to an Annular Flow of Rotating Fluid,” J. Sound Vib., 332(18), pp. 4210–4222. [CrossRef]
Dowell, E. H., Srinivasan, A. V., McLean, J. D., and Ambrose, J., 1974, “Aeroelastic Stability of Cylindrical Shells Subjected to a Rotating Flow,” AIAA J., 12(12), pp. 1644–1651. [CrossRef]
McLean, J. D., and Dowell, E. H., 1975, “Swirling Flows Between Coaxial Cylinders With Injection by Radial Jets,” AIAA J., 13(11), pp. 1435–1440. [CrossRef]
Amabili, M., Pellicano, F., and Païdoussis, M. P., 2001, “Nonlinear Stability of Circular Cylindrical Shells in Annular and Unbounded Axial Flow,” ASME J. Appl. Mech., 68(6), pp. 827–834. [CrossRef]
Paak, M., Païdoussis, M. P., and Misra, A. K., 2013, “Nonlinear Dynamics and Stability of Cantilevered Circular Cylindrical Shells Conveying Fluid,” J. Sound Vib., 332(14), pp. 3474–3498. [CrossRef]
Chen, C., and Dai, L., 2009, “Nonlinear Vibration and Stability of a Rotary Truncated Conical Shell With Intercoupling of High- and Low-Order Modals,” Comm. Nonlinear Sci. Numer. Simul., 14(1), pp. 254–269. [CrossRef]
Liu, Y., and Chu, F., 2012, “Nonlinear Vibrations of Rotating Thin Circular Cylindrical Shell,” Nonlinear Dyn., 67(2), pp. 1467–1479. [CrossRef]
Alfutov, N. A., Zinov'ev, P. A., and Popov, B. G., 1984, Analysis of Multilayer Plates and Shells of Composite Materials, Izdatel'stvo Mashinosiroenie, Moscow, Russia (in Russian).
Matveenko, V. P., 1980, “On an Algorithm of Solving the Problem on Natural Vibrations of Elastic Bodies by the Finite Element Method,” Boundary-Value Problems of the Elasticity and Viscoelasticity Theory, Ural Science Center, USSR Akad. Sci., Sverdlovsk, Russia, pp. 20–24 (in Russian).
Troyanovskii, I. Ye., Shardakov, I. N., and Shevelev, N. A., 1991, “The Problem of the Eigenvalues and Modes of Rotating Deformable Structures,” J. Appl. Math. Mech., 55(5), pp. 733–740. [CrossRef]

Figures

Grahic Jump Location
Fig. 2

Variation of the forward (solid lines) and backward (dashed lines) modes of low-frequency vibrations λ1 (Hz) with the angular velocity Ωs (rev/s) of an empty shell with free end-clamped end boundary conditions at m = 1 for two harmonics: lines correspond to the results of calculations; symbols denote the results obtained in Guo et al. [28]

Grahic Jump Location
Fig. 1

Computational scheme

Grahic Jump Location
Fig. 4

The real λ1 and imaginary λ2 parts of eigenvalues (Hz) versus the angular velocity (rad/s) of the internal Ωfi and annular Ωfo flows for stationary shells simply supported at both ends: (a) configuration 1; (b) configuration 3; forward waves—solid lines; backward waves—dashed lines; imaginary parts—dashed-dotted lines

Grahic Jump Location
Fig. 3

Variation of the real parts Ξo1 of dimensionless eigenvalues with dimensionless axial velocity of the annular flow Λo for clamped coaxial shells; k = 1/10, j = 3; lines—the results of our calculations; symbols—the results of Païdoussis et al. [16]; antisymmetric modes—solid lines and open symbols; symmetric modes—dashed lines and closed symbols

Grahic Jump Location
Fig. 5

The real λ1 and imaginary λ2 parts of eigenvalues (Hz) versus the angular velocity of the rotating shell and corotating fluid Ω (rad/s) for shells simply supported at both ends: (a) configuration 1, Ω=Ωsi=Ωfi; (b) configuration 3, Ω=Ωso=Ωfo≠0,Ωfi=0; forward waves—solid lines; backward waves—dashed lines; imaginary parts—dashed-dotted lines

Grahic Jump Location
Fig. 6

Stability diagram for shells with different boundary conditions under the combined action of the axial flow Ui (m/s) and rotational flow with the angular velocity Ωfi (rad/s): configuration 2; j = 4; (a) L/R = 4; (b) L/R = 10; SS—simply supported shells; CC—clamped shells; CF—cantilevered shells

Grahic Jump Location
Fig. 7

Stability diagram for coaxial shells with different boundary conditions under the combined action of the axial flow Uo (m/s) and rotational flow with the angular velocity Ωfo (rad/s): configuration 3; j = 3; (a) k = 1/2; (b) k = 1/10; SS—simply supported shells; CC—clamped shells; CF—cantilevered shells

Grahic Jump Location
Fig. 8

Stability diagram of the system under the combined action of the axial flow Ui (m/s) and simultaneous rotation of the shell and the fluid Ω=Ωsi=Ωfi (rad/s) for shells with various boundary conditions: configuration 2; j = 4; (a) L/R = 4; (b) L/R = 10; SS—simply supported shells; CC—clamped shells; CF—cantilevered shells

Grahic Jump Location
Fig. 9

Stability diagram for coaxial shells with various boundary conditions under the combined action of the axial flow Uo (m/s) and simultaneous rotation of the shell and the fluid with the angular velocity Ω=Ωso=Ωfo≠0,Ωfi=0 (rad/s): configuration 3; j = 3; (a) k = 1/2; (b) k = 1/10; SS—simply supported shells; CC—clamped shells; CF—cantilevered shells

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