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TECHNICAL PAPERS

Nonlinear Vibrations and Multiple Resonances of Fluid-Filled, Circular Shells, Part 1: Equations of Motion and Numerical Results

[+] Author and Article Information
M. Amabili

Dipartimento di Ingegneria Industriale, Università di Parma, Parma, I-43100 Italy

F. Pellicano

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

A. F. Vakakis

Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801

J. Vib. Acoust 122(4), 346-354 (May 01, 2000) (9 pages) doi:10.1115/1.1288593 History: Received March 01, 1999; Revised May 01, 2000
Copyright © 2000 by ASME
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References

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.
Chen,  J. C., and Babcock,  C. D., 1975, “Nonlinear Vibration of Cylindrical Shells,” AIAA J., 13, pp. 868–876.
Evensen, D. A., 1967, “Nonlinear Flexural Vibrations of Thin-Walled Circular Cylinders,” NASA TN D-4090.
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.
Ginsberg,  J. H., 1973, “Large Amplitude Forced Vibrations of Simply Supported Thin Cylindrical Shells,” J. Appl. Mech., 40, pp. 471–477.
Ganapathi,  M., and Varadan,  T. K., 1996, “Large Amplitude Vibrations of Circular Cylindrical Shells,” J. Sound Vib., 192, pp. 1–14.
Gonçalves,  P. B., and Batista,  R. C., 1988, “Non-Linear Vibration Analysis of Fluid-Filled Cylindrical Shells,” J. Sound Vib., 127, pp. 133–143.
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.
Amabili,  M., Pellicano,  F., and Païdoussis,  M. P., 1999, “Non-linear Dynamics and Stability of Circular Cylindrical Shells Containing Flowing Fluid. Part II: Large Amplitude Vibrations Without Flow,” J. Sound Vib., 228, pp. 1103–1124.
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., (to be published).
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., (to be published).
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Figures

Grahic Jump Location
Response-frequency curves and backbone curves for the driven mode without companion mode participation, case of Chen and Babcock 2. – present results; [[long_dash_short_dash]] Amabili et al. 1; [[dashed_line]] Chen and Babcock 2; ⋅-⋅-○-⋅ backbone of Ganapathi and Varadan 6.
Grahic Jump Location
Response-frequency curve with companion mode participation, case of Chen and Babcock 2. (a) Maximum of A1,n(t)/h; (b) maximum of B1,n(t)/h; (c) maximum of A1,0(t)/h; (d) maximum of A3,0(t)/h. – stable solutions; [[dashed_line]] unstable solutions; integer numbers identify the different branches of the solution.
Grahic Jump Location
Response-frequency curve with companion mode participation, case of 1:1:1:2 internal resonances and f1=0.01. (a) Maximum of A1,n(t)/h; (b) particular of Part (a); (c) maximum of B1,n(t)/h; (d) maximum of A1,0(t)/h; (e) maximum of A3,0(t)/h. – stable solutions; [[dashed_line]] unstable solutions; integer numbers identify the different branches of the solution.
Grahic Jump Location
Time response for f1=0.01 and ω/ω1,n=1; case of 1:1:1:2 internal resonances. (a) A1,n(t)/h; (b) B1,n(t)/h; (c) A1,0(t)/h; (d) A3,0(t)/h.
Grahic Jump Location
Response amplitude with companion mode participation versus the excitation amplitude. Case of 1:1:1:2 internal resonances with excitation frequency ω=ω1n. (a) Maximum of A1,n(t)/h; (b) particular of Part (a); (c) maximum of B1,n(t)/h; (d) maximum of A1,0(t)/h; (e) maximum of A3,0(t)/h. – stable solutions, by Auto ; [[dashed_line]] unstable solutions, by Auto ; • direct integration; integer numbers identify the different branches of the solution.

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