Nonlinear Vibrations and Multiple Resonances of Fluid-Filled, Circular Shells, Part 1: Equations of Motion and Numerical Results-Reference-Cited by-同舟云学术

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

Published:2000-05-01 Issue:4 Volume:122 Page:346-354
ISSN:1048-9002
Container-title:Journal of Vibration and Acoustics
language:en
Short-container-title:

Author:

Amabili M.¹,Pellicano F.²,Vakakis A. F.³

Affiliation:

1. Dipartimento di Ingegneria Industriale, Universita` di Parma, Parma, I-43100 Italy

2. Dipartimento di Scienze dell’Ingegneria, Universita` di Modena e Reggio Emilia, Modena, I-41100 Italy

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

Abstract

The response-frequency relationship in the vicinity of a resonant frequency, the occurrence of travelling wave response and the presence of internal resonances are investigated for simply supported, circular cylindrical shells. Donnell’s nonlinear shallow-shell theory is used. The boundary conditions on radial displacement and the continuity of circumferential displacement are exactly satisfied. The problem is reduced to a system of four ordinary differential equations by means of the Galerkin method. The radial deflection of the shell is expanded by using a basis of four linear modes. The effect of internal fluid is also investigated. The equations of motion are studied by using a code based on the Collocation Method. The present model is validated by comparison of some results with others available. A water-filled shell presenting the phenomenon of 1:1:1:2 internal resonances is investigated for the first time; it shows intricate and interesting dynamics. [S0739-3717(00)01204-6]

Publisher

ASME International

Subject

General Engineering

Link

http://asmedigitalcollection.asme.org/vibrationacoustics/article-pdf/122/4/346/5825633/346_1.pdf

Reference20 articles.

1. Amabili, M., Pellicano, F., and Pai¨doussis, M. P., 1998, “Nonlinear Vibrations of Simply Supported, Circular Cylindrical Shells, Coupled to Quiescent Fluid,” J. Fluids Struct., 12, pp. 883–918.

2. Chen, J. C., and Babcock, C. D., 1975, “Nonlinear Vibration of Cylindrical Shells,” AIAA J., 13, pp. 868–876.

3. Evensen, D. A., 1967, “Nonlinear Flexural Vibrations of Thin-Walled Circular Cylinders,” NASA TN D-4090.

4. 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.

5. Ginsberg, J. H. , 1973, “Large Amplitude Forced Vibrations of Simply Supported Thin Cylindrical Shells,” J. Appl. Mech., 40, pp. 471–477.

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