Stability of Nonlinear Two-Frequency Oscillation of Cylindrical Shells
Publication: Journal of Engineering Mechanics
Volume 123, Issue 10
Abstract
The moment scheme of the finite element method and the method of generalized coordinates are used to construct a multi-degree-of-freedom nonlinear model of a cylindrical shell subjected to two-frequency excitations. This model consists of a system of nonlinear differential equations. The incremental method is then used to find the solution of the equation in the frequency domain, while the Poincaré map, spectral analysis, and Floquet's theory are applied to the stability of the solution at every step of the incremental method. Solutions and discussions are presented to substantiate the suggested algorithm. It is shown that similar results are obtained by using the Poincaré map with numerical integration and Floquet's theory with Fourier's expansion. However, Floquet's theory is a lot less time-consuming and it pinpoints more accurately the moment of loss of stability.
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References
1.
Bolotin, V. V. (1956). Dynamic stability of elastic systems. Gosudarstvennoe isdatelstvo technico-theoretical literature, Moscow, Russia.
2.
Dekhtyariuk, Y. S., and Lumelskii, Y. D. (1984). “Numerical construction of nonlinear dynamic models of shallow shells and plates.”Strength of Mat. and the Theory of Structures, 45, 5–9 (in Russian).
3.
Eneremadu, K. O. (1991). “Steady state oscillations of plates and shells subjected to two-frequency excitations,” PhD thesis, Kiev Inst. of Civ. Engrg., Kiev, Ukraine (in Russian).
4.
Haken, H. (1983). Advanced synergetics: Instability hierarchies of self-organising systems and devices. Springer-Verlag, Berlin, Germany.
5.
Kurdiumov, A. A.(1961). “Towards the theory of a physical and geometrical nonlinear problem of deformation and stability of plates and shells.”Rep., Leningrad's shipbuilding institute, St. Petersburg, Russia, 34, 55–62.
6.
Mook, D. T., Plaut, R. H., and Haquang, N.(1986). “The influence of an internal resonance on nonlinear structural vibrations under combination resonance conditions.”J. Sound and Vibration, 104, 229–241.
7.
Nayfeh, A. H.(1984). “Combination tones in the response of single degree-of-freedom systems with quadratic and cubic nonlinearities.”J. Sound and Vibration, 92, 379–386.
8.
Nayfeh, A. H. (1993). Method of normal forms. Wiley Interscience, New York, N.Y.
9.
Sakharov, A. S., Kislooky, V. N., and Kirichevsky, V. V. (1987) “Method of finite elements in the mechanics of hard bodies.” Visha shkola, Kiev, Ukraine (in Russian)
10.
Van Dooren, R.(1971). “Combination tones of summed type in a nonlinear damped vibratory system with two degrees of freedom.”Int. J. Nonlinear Mech., 6, 237–254.
11.
Yamamoto, T., and Hayashi, S. (1964). “Combination tones of differential type in nonlinear vibratory systems.”Bull. JSME, 7, 690– 698.
12.
Yamamoto, T., and Nakao, Y.(1964). “Combination tones of summed type in nonlinear vibratory systems.”Bull. JSME, 6, 682–689.
13.
Yamamoto, T., Yasuda, K., and Nakamura, T.(1974). “Subcombination tones in nonlinear vibratory systems.”Bull. JSME, 17, 1426–1437.
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Copyright © 1997 American Society of Civil Engineers.
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Published online: Oct 1, 1997
Published in print: Oct 1997
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