Abstract
The forced nonlinear vibrations of a thin cylindrical shell completely filled with a liquid are studied. A refined mathematical model is used. The model takes into account the nonlinear terms up to the fifth power of the generalized displacement of the shell. The Bogolyubov’Mitropolsky averaging method is used to plot amplitude’frequency response curves for steady-state vibrations. The steady-state vibrations at the frequency of principal harmonic resonance are analyzed for stability
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REFERENCES
N. N. Bogolyubov and Y. A. Mitropolsky, Asymptotic Methods in the Theory of Nonlinear Oscillations, Gordon and Breach, New York (1962).
A. S. Vol’mir, Nonlinear Dynamics of Plates and Shell [in Russian], Nauka, Moscow (1972).
A. S. Vol’mir, Shells in Liquid’Gas Flow: Hydroelastic Problems [in Russian], Nauka, Moscow (1979).
V. D. Kubenko, P. S. Koval’chuk, and N. P. Podchasov, Nonlinear Vibrations of Cylindrical Shells [in Russian], Vyshcha Shkola, Kiev (1989).
V. D. Kubenko, V. D. Lakiza, V. S. Pavlovskii, and N. A. Pelykh, Dynamic Behavior of Elastic Gas’Liquid Systems under Vibratory Actions [in Russian], Naukova Dumka, Kiev (1988).
M. Amabili, F. Pellicano, and A. F. Vakakis, “Nonlinear vibrations and multiple resonances of fluid-filled, circular shells. Part 1: Equations of motion and numerical results,” J. Vibr. Acoust., 122, 346’354 (2000).
P. S. Koval’chuk and L. A. Kruk, “Nonlinear energy interchange between the natural modes of freely vibrating circular cylindrical shells filled with liquid,” Int. Appl. Mech., 36, No.1, 103’110 (2000).
P. S. Koval’chuk and L. A. Kruk, “Forced nonlinear vibrations of cylindrical shells filled with a liquid, ” Int. Appl. Mech., 38, No.11, 1388’1393 (2002).
P. S. Koval’chuk and L. A. Kruk, “Chaotic modes of forced nonlinear vibrations of fluid-filled cylindrical shells,” Int. Appl. Mech., 39, No.12, 1452’1457 (2003).
P. S. Koval’chuk, N. P. Podchasov, and V. V. Kholopova, “Periodic modes in the forced nonlinear vibrations of filled cylindrical shells with an initial deflection,” Int. Appl. Mech., 38, No.6, 716’722 (2002).
V. D. Kubenko and P. S. Koval’chuk, “Nonlinear problems of the dynamics of elastic shells partially filled with a liquid,” Int. Appl. Mech., 36, No.4, 421’448 (2000).
V. D. Kubenko, P. S. Koval’chuk, and L. A. Kruk, “On multimode nonlinear vibrations of filled cylindrical shells,” Int. Appl. Mech., 39, No.1, 85’920 (2003).
V. D. Kubenko, P. S. Koval’chuk, and L. A. Kruk, “Nonlinear interaction of bending deformations of free-oscillating cylindrical shells,” J. Sound Vibr., 265, No.2, 245’268 (2003).
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Translated from Prikladnaya Mekhanika, Vol. 41, No. 2, pp. 52–59, February 2005.
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Koval’chuk, P.S., Kruk, L.A. The Problem of Forced Nonlinear Vibrations of Cylindrical Shells Completely Filled with Liquid. Int Appl Mech 41, 154–160 (2005). https://doi.org/10.1007/s10778-005-0071-y
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DOI: https://doi.org/10.1007/s10778-005-0071-y