0
TECHNICAL PAPERS

Nonlinear Stability of Circular Cylindrical Shells in Annular and Unbounded Axial Flow

[+] Author and Article Information
M. Amabili

Dipartimento di Ingegneria Industriale, Università di Parma, Parco Area delle Scienze 181/Z, Parma I-43100, Italy Mem. ASMEe-mail: marco@me.unipr.it

F. Pellicano

Dipartimento di Scienze dell’Ingegneria, Università di Modena e Reggio Emilia, Via Campi 213B, Modena I-41100, Italy

M. A. Païdoussis

Department of Mechanical Engineering, McGill University, 817 Sherbrooke Street, W. Montreal, Quebec H3A 2K6, Canada Fellow ASME

J. Appl. Mech 68(6), 827-834 (May 10, 2001) (8 pages) doi:10.1115/1.1406957 History: Received January 20, 2000; Revised May 10, 2001
Copyright © 2001 by ASME
Your Session has timed out. Please sign back in to continue.

References

Horn,  W., Barr,  G., Carter,  L., and Stearman,  R., 1974, “Recent Contributions to Experiments on Cylindrical Shell Panel Flutter,” AIAA J., 12, pp. 1481–1490.
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, pp. 201–235.
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, pp. 193–205.
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, pp. 389–396.
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, pp. 105–125.
Horáček,  J., 1993, “Approximate Theory of Annular Flow-Induced Instabilities of Cylindrical Shells,” J. Fluids Struct., 7, pp. 123–135.
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, pp. 349–364.
Librescu,  L., 1965, “Aeroelastic Stability of Orthotropic Heterogeneous Thin Panels in the Vicinity of the Flutter Critical Boundary. Part I: Simply Supported Panels,” J. Mec., 4, pp. 51–76.
Librescu,  L., 1967, “Aeroelastic Stability of Orthotropic Heterogeneous Thin Panels in the Vicinity of the Flutter Critical Boundary. Part II,” J. Mec., 6, pp. 133–152.
Olson,  M. D., and Fung,  Y. C., 1967, “Comparing Theory and Experiment for the Supersonic Flutter of Circular Cylindrical Shells,” AIAA J., 5, pp. 1849–1856.
Evensen,  D. A., and Olson,  M. D., 1968, “Circumferentially Travelling Wave Flutter of a Circular Cylindrical Shell,” AIAA J., 6, pp. 1522–1527.
Amabili,  M., Pellicano,  F., and Païdoussis,  M. P., 1998, “Nonlinear Vibrations of Simply Supported, Circular Cylindrical Shells, Coupled to Quiescent Fluid,” J. Fluids Struct., 12, pp. 883–918.
Amabili,  M., Pellicano,  F., and Païdoussis,  M. P., 1999, “Non-Linear Dynamics and Stability of Circular Cylindrical Shells Containing Flowing Fluid. Part I: Stability,” J. Sound Vib., 225, pp. 655–699.
Lakis,  A. A., and Laveau,  A., 1991, “Non-Linear Dynamic Analysis of Anisotropic Cylindrical Shells Containing a Flowing Fluid,” Int. J. Solids Struct., 28, pp. 1079–1094.
Païdoussis,  M. P., and Denise,  J.-P., 1972, “Flutter of Thin Cylindrical Shells Conveying Fluid,” J. Sound Vib., 20, pp. 9–26.
Dowell,  E. H., and Widnall,  S. E., 1966, “Generalized Aerodynamic Forces on an Oscillating Cylindrical Shell,” Q. Appl. Math., 24, pp. 1–17.
Dowell,  E. H., and Ventres,  C. S., 1968, “Modal Equations for the Nonlinear Flexural Vibrations of a Cylindrical Shell,” Int. J. Solids Struct., 4, pp. 975–991.
Amabili,  M., Pellicano,  F., and Païdoussis,  M. P., 2000, “Non-Linear Dynamics and Stability of Circular Cylindrical Shells Containing Flowing Fluid, Part III: Truncation Effect Without Flow and Experiments,” J. Sound Vib., 237, pp. 617–640.
Doedel, E. J., Champneys, A. R., Fairgrieve, T. F., Kuznetsov, Y. A., Sandstede, B., and Wang, X., 1998, AUTO 97: Continuation and Bifurcation Software for Ordinary Differential Equations (with HomCont), Concordia University, Montreal, Canada.
Amabili,  M., Pellicano,  F., and Païdoussis,  M. P., 2000, “Non-Linear Dynamics and Stability of Circular Cylindrical Shells Containing Flowing Fluid, Part IV: Large-Amplitude Vibrations With Flow,” J. Sound Vib., 237, pp. 641–666.
Weaver,  D. S., and Unny,  T. E., 1973, “On the Dynamic Stability of Fluid-Conveying Pipes,” ASME J. Appl. Mech., 40, pp. 48–52.

Figures

Grahic Jump Location
Frequency obtained from the linearized equations without viscous damping (ζ=0) versus the flow velocity: –, fluid model with separation of variables; [[dashed_line]], fluid model with Fourier transform method
Grahic Jump Location
Amplitude of nonoscillatory solutions versus the flow velocity (rubber shell); in-antiphase modes. –, stable branches; [[dashed_line]], unstable branches. (a) Amplitude of the first longitudinal mode A1,n/h; (b) amplitude of the second longitudinal mode A2,n/h; (c) amplitude of the first axisymmetric mode A1,0/h; (d) amplitude of the third axisymmetric mode A3,0/h; (e) amplitude of the fifth axisymmetric mode A5,0/h.
Grahic Jump Location
Amplitude of nonoscillatory solutions versus the flow velocity (rubber shell); modes orthogonal in θ. –, stable branches; [[dashed_line]], unstable branches. (a) Amplitude of the first longitudinal mode A1,n/h; (b) amplitude of the second longitudinal mode A2,n/h.
Grahic Jump Location
Basin of attraction of undisturbed and bifurcated solutions; minimum amplitude necessary for divergence is indicated with a thick solid line. (a) Shell with antiphase modes, static displacement with first axial-mode shape; (b) shell with antiphase modes, static displacement with second axial-mode shape; (c) shell with seven degrees-of-freedom at first-axial-mode, resonant modal excitation.
Grahic Jump Location
Post-divergence shape of the rubber shell for mode (n=3,m=1). (a) Computed shape for flow velocity 30 m/s; (b) experimental shape, from Ref. 7.
Grahic Jump Location
Amplitude of nonoscillatory solutions versus the nondimensional external axial flow velocity; in-antiphase modes. ——, stable branches; [[dashed_line]], unstable branches. (a) Amplitude of the first longitudinal mode A1,n/h; (b) amplitude of the second longitudinal mode A2,n/h.
Grahic Jump Location
Amplitude of nonoscillatory solutions versus the non-dimensional external axial flow velocity; modes orthogonal in θ. –, stable branches; [[dashed_line]], unstable branches. (a) Amplitude of the first longitudinal mode A1,n/h; (b) amplitude of the second longitudinal mode B2,n/h.
Grahic Jump Location
Behavior of the system starting from a point where the system is subjected to coupled-mode divergence at V=6, and then slowly decreasing the nondimensional flow velocity V. Generalized coordinates: (a) A1,n and B1,n versus V; (b) A2,n and B2,n versus V.

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In