Large Amplitude Vibrations Of Noncircular Cylindrical Shells
The aim of this paper is to review the literature on the large amplitude vibration of circumferentially closed shells and to study the nonlinear forced response characteristics of noncircular cylindrical shells. The study is carried out using semi-analytical method with the meridional approximation of the displacement field as the superposition of the linear free vibration modal functions and the three noded quadratic finite element approximation in the circumferential direction. The Sander ' s type strain-displacement relations are used. The governing equations are solved using Newmark ' s time integration approach coupled with the Newton-Raphson iterative technique. The forced response curves in the frequency domain are obtained from the steady state dynamic response of the shells. Some of the interesting characteristics pertaining to the noncircular shells are highlighted.
Keywordsemi-analytical noncircular large amplitude forced response shell
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- 1.D. A. Evensen, 1974. Nonlinear vibrations of circular cylindrical shells, Thin-Shell Structures: Theory, Experiment and Design, YC Fung and EE Sechler (eds), Prentice Hall, Englewood Cliffs, NY, 133 – 155.Google Scholar
- 4.E. Reissner, 1955. Nonlinear effects in vibrations of cylindrical shells, Ramo Wooldridge Corporation Report AM 5–6. Google Scholar
- 9.D. A. Evensen, 1966. Nonlinear flexural vibrations of thin circular rings, ASME Journal of Applied Mechanics, 33, 553 – 560.Google Scholar
- 10.D. A. Evensen, E. Fulton, 1967. Some studies on the nonlinear dynamic response of shell-type structures, Proceedings of the International Conference on Dynamic Stability of Structures, Evanston, IL, Oct 18 – 20 1965, Pergamon Press, 237 – 254.Google Scholar
- 11.D. A. Evensen, 1964. Non-linear flexural vibrations of thin circular rings, PhD Thesis, California Institute of Technology, Pasadena, CA.Google Scholar
- 12.D. A. Evensen, 1965. A theoretical and experimental study of nonlinear flexural vibrations of thin circular rings, NASA TR R-227, Washington, DC, Government Printing Office.Google Scholar
- 13.D. A. Evensen, 1967. Nonlinear flexural vibrations of thin-walled circular cylinders, NASA TN D-4090.Google Scholar
- 15.Y. Matsuzaki, S. Kobayashi, 1970. A theoretical and experimental study of the nonlinear flexural vibration of thin circular cylindrical shells with clamped ends, Trans. of the Japan Society for Aeronautical and Space Sciences, 12, 55 – 62.Google Scholar
- 16.Y. Matsuzaki, S. Kobayashi, 1969. An analytical study of the nonlinear flexural vibration of thin circular cylindrical shells (in Japanese), Journal of the Japan Society for Aeronautical and Space Sciences, 17, 308 – 315.Google Scholar
- 22.H. V. Ramani, 1985. An analytical investigation of large amplitude free flexural vibration of thin circular cylindrical shells, M. S. Thesis, Department of Aerospace Engineering, IIT Madras, India.Google Scholar
- 35.K. A. V. Pandalai, M. Sathyamoorthy, 1970. Non-linear flexural vibrations of orthotropic oval cylindrical shells, Studies in Structural Mechanics (K. A. V. Pandalai, editor), 47–74.Google Scholar
- 36.B. P. Patel, M. Ganapathi, D. P. Makhecha, S. S. Gupta, 2002. On the nonlinear free flexural vibrations problem for thin elastic rings, Journal of The Aeronautical Society of India, 54, 298 – 309.Google Scholar