Abstract
Forced vibrations of cylindrical shells described by a system of three ordinary differential equations are studied. There are two internal resonances. Standing and traveling waves in the shells are described by a system of six modulation equations derived using the multiple-scales method. These waves are analyzed for stability
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
K. V. Avramov, “Bifurcation analysis of a vibropercussion system by the method of amplitude surfaces,” Int. Appl. Mech., 38, No. 9, 1151–1156 (2002).
K. V. Avramov, “Bifurcations at combination resonance and quasiperiodic vibrations of flexible beams,” Int. Appl. Mech., 39, No. 8, 976–982 (2003).
A. S. Belomyttsev and V. N. Karaban, “An algorithm of solving a nonlinear boundary-value problem for ordinary differential equations in the multiplicity domain,” Zh. Vych. Mat. Mat. Fiz., 26, No. 7, 1099–1102 (1986).
A. S. Vol’mir, Nonlinear Dynamics of Plates and Shells [in Russian], Nauka, Moscow (1972).
R. F. Ganiev and P. S. Koval’chuk, Dynamics of Systems of Rigid and Elastic Bodies [in Russian], Mashinostroenie, Moscow (1980).
V. D. Kubenko, P. S. Koval’chuk, and T. S. Krasnopol’skaya, Nonlinear Interaction of Flexural Vibration Modes of Cylindrical Shells [in Russian], Naukova Dumka, Kiev (1984).
V. D. Kubenko, P. S. Koval’chuk, and N. P. Podchasov, Nonlinear Vibrations of Cylindrical Shells [in Russian], Vyshcha Shkola, Kiev (1989).
A. H. Nayfeh, Perturbation Methods, Wiley, New York (1973).
Y. C. Fung and E. E. Sechler (eds.), Thin-Shell Structures: Theory, Experiment, and Design, Prentice-Hall, Englewood Cliffs, NJ (1974).
V. D. Kubenko and P. S. Koval’chuk, “Nonlinear problems of the vibration of thin shells (review),” Int. Appl. Mech., 34, No. 8, 703–728 (1998).
A. W. Leissa, Vibrations of Shells, NASA SP-288 (1973).
F. Moussaoui and R. Benamar, “Non-linear vibrations of shell-type structures: a review with bibliography,” J. Sound Vibr., 255, No. 1, 161–184 (2002).
F. Pellicano, M. Amabili, and M. P. Paidoussis, “Effect of the geometry on the non-linear vibration of circular cylindrical shells,” Int. J. Non-Linear Mech., 37, 1181–1198 (2002).
K. V. Avramov and Yu. V. Mikhlin, “Damping of free elastic vibrations in linear systems,” Int. Appl. Mech., 41, No. 2, 203–209 (2005).
P. S. Koval’chuk, “Nonlinear vibrations of a cylindrical shell containing a flowing fluid,” Int. Appl. Mech., 41, No. 4, 405–412 (2005).
P. S. Koval’chuk and L. A. Kruk, “The problem of forced nonlinear vibrations of cylindrical shells completely filled with liquid,” Int. Appl. Mech., 41, No. 2, 154–160 (2005).
Yu. V. Mikhlin and S. N. Reshetnikova, “Dynamic analysis of a two-mass system with essentially nonlinear vibration damping,” Int. Appl. Mech., 41, No. 1, 77–84 (2005).
Author information
Authors and Affiliations
Additional information
__________
Translated from Prikladnaya Mekhanika, Vol. 42, No. 2, pp. 51–58, February 2006.
Rights and permissions
About this article
Cite this article
Avramov, K.V. Nonlinear forced vibrations of a cylindrical shell with two internal resonances. Int Appl Mech 42, 169–175 (2006). https://doi.org/10.1007/s10778-006-0072-5
Received:
Issue Date:
DOI: https://doi.org/10.1007/s10778-006-0072-5