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Figure 1. Response-frequency curves and backbone curves for the driven mode, for the shell studied by Chen and Babcock [51]. Present results (·-·-·--); Amabili et al. [91 (--);Chen and Babcock [SJ ( - - - ); backbone of Ganapathi and Varadan [?J (--·-0-·).
FROM:
Marco Amabili (1) and Francesco Pellicano (2)
(1) Dipartimento di lngegneria Industriale, Universita di Parma, Parma, Italy, I - 43100
(2) Dipartimento di Scienze dell'Ingegneria, Universita di Modena, Modena, Italy
“Low-dimensional model for nonlinear vibration of circular cylindrical shells”, (publisher and date not given in the pdf file. Most recent reference is dated 1998.)
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 ordinary differential equations by means of the Galerkin method. The mode shape is expanded by using four degrees of freedom. The effect of internal dense fluid is studied. The solution is obtained by the Method of Normal Forms. Comparison of a three and a four degree-of-freedom model is performed. A water-filled shell presenting the phenomenon of I:1:1:2 internal resonances is investigated; specific Normal Forms
are developed for this study.
References listed at the end of the paper:
[1] D. A. EVENSEN 1967 Nonlinear flexural vibrations of thin-walled circular cylinders. NASA TN D-4090.
[2] E. H. DOWELL and C. S. VENTRES 1968 International Journal of Solids and Structures 4, 975-991. Modal equations for the nonlinear flexural vibrations of a cylindrical shell.
[3] S. ATLURl 1972 International Journal of Solids and Structures 8, 549-569. A perturbation analysis of non- linear free flexural vibrations of a circular cylindrical shell.
[4] J. H. GINSBERG 1973 Journal of Applied Mechanics 40, 471-477. Large amplitude forced vibrations of simply supported thin cylindrical shells.
[5] J. C. CHEN and C. D. BABCOCK 1975 AIAA Journal 13, 868-876. Nonlinear vibration of cylindrical shells.
[6] P. B. GONCALVES and R. C. BATISTA 1988 Journal of Sound and Vibration 127, 133-143. Non-linear vibration analysis of fluid-filled cylindrical shells.
[7] M. GANAPATHI and T. K. VARADAN 1996 Journal of Sound and Vibration 192, 1-14. Large amplitude vibrations of circular cylindrical shells.
[8] A. SELMANE and A. A. LAKIS 1997 Journal of Sound and Vibration 202, 67-93. Non-linear dynamic analysis of orthotropic open cylindrical shells subjected to a flowing fluid.
[9] M. AMABILI, F. PELLICANO and M. P. PAIDOUSSIS 1998 (in press) Journal ofFluids and Structures 12(7). Nonlinear vibrations of simply supported, circular cylindrical shells, coupled to quiescent fluid.
[10] S. WOLFRAM 1996 The Mathematica Book, 3rd edition. Cambridge, UK: Cambridge University Press.
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