Abstract
A technique is proposed to study the multimode nonlinear vibrations of circular shells fully filled with a perfect incompressible liquid. This technique is used to study the basic laws of modal interaction at nonlinear, including sub-harmonic resonances
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
N. N. Bogolyubov and Yu. A. Mitropol'skii, Asymptotic Methods in the Theory of Nonlinear Vibrations [in Russian], Nauka, Moscow (1974).
A. S. Vol'mir, Nonlinear Dynamics of Plates and Shells [in Russian], Nauka, Moscow (1972).
A. S. Vol'mir, Shells in Fluid Flow. Hydroelastic Problems [in Russian], Nauka, Moscow (1979).
V. D. Kubenko (ed.), Dynamics of Structural Members, Vol. 9 of the 12-volume series Mechanics of Composites [in Russian], A.S.K., Kiev (1999).
A. N. Guz (ed.), S. Markus, L. Pust et al., Dynamics of Bodies Interacting with a Medium [in Russian], Naukova Dumka, Kiev (1991).
V. D. Kubenko, P. S. Koval'chuk, and T. S. Krasnopol'skaya, Nonlinear Modal Interaction of the Flexural Vibrations of Cylindrical Shells [in Russian], Naukova Dumka, Kiev (1984).
V. D. Kubenko, P. S. Koval'chuk, and N. P. Podchasov, Nonlinear Vibration of Cylindrical Shells [in Russian], Vyshcha Shkola, Kiev (1989).
V. D. Kubenko, V. D. Lakiza, V. S. Pavlovskii, and N. A. Pelykh, Dynamics of Elastic Gas–Liquid Systems under Vibratory Actions [in Russian], Naukova Dumka, Kiev (1988).
M. Amabili, F. Pellicano, and M. P. Páidoussis, “Nonlinear vibrations of simply supported circular cylindrical shells, coupled to quiescent fluid,” J. Fluids Struct., 12, 883–918 (1998).
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).
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 and P. S. Koval'chuk, “Problems of nonlinear multiple-mode vibrations of thin elastic shells of revolution,” in: M. P. Páidoussis, M. Amabily, and P. B. Gonsalves (eds.), Int. Mech. Eng. Congr. Expos. (Orlando, Florida), 238, New York (2000), pp. 147–153.
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).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Kubenko, V.D., Koval'chuk, P.S. & Kruk, L.A. On Multimode Nonlinear Vibrations of Filled Cylindrical Shells. International Applied Mechanics 39, 85–92 (2003). https://doi.org/10.1023/A:1023672201760
Issue Date:
DOI: https://doi.org/10.1023/A:1023672201760