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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
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References

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.
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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.
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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.
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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.

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