Theoretical approaches to studying the free vibrations of imperfect (with small geometrical imperfections) orthotropic cylindrical shells filled with a fluid are proposed. A geometrically nonlinear problem is solved. The emphasis is on the interaction and energy exchange between the “conjugate” flexural modes in the dynamic radial deflection. The effect of initial deflections on the interaction of the initial deflection modes is analyzed
Similar content being viewed by others
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 Shells [in Russian], Nauka, Moscow (1972).
A. S. Vol’mir, Shells in Fluid Flow: Problems of Hydroelasticity [in Russian], Nauka, Moscow (1979).
R. F. Ganiev and P. S. Koval’chuk, Dynamics of Systems of Rigid and Elastic Bodies [in Russian], Mashinostroenie, Moscow (1980).
V. D. Kubenko (ed.), Dynamics of Structural Members, Vol. 9 of the 12-volume series Mechanics of Composite Materials [in Russian], ASK, Kyiv (1999).
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, Kyiv (1984).
V. D. Kubenko, P. S. Koval’chuk, and N. P. Podchasov, Nonlinear Vibrations of Cylindrical Shells [in Russian], Vyshcha Shkola, Kyiv (1989).
A. Yu. Manevich, “Interaction of coupled modes accompanying non-linear flexural vibrations of a circular ring,” J. Appl. Math. Mech., 58, No. 6, 1061–1068 (1994).
Yu. A. Mitropolsky, Averaging Method in Nonlinear Mechanics [in Russian], Naukova Dumka, Kyiv (1971).
M. Amabili, “Theory and experiments for large amplitude vibrations of empty and fluid-filled circular cylindrical shell with imperfections,” J. Sound Vibr., 262, 921–975 (2003).
M. Amabili and M. P. Pa¿doussis, “Review of studies on geometrically nonlinear vibrations and dynamics of circular cylindrical shells and panels with and without fluid-structure interaction,” Appl. Mech. Rev., 56, No. 4, 349–381 (2003).
M. Amabili, F. Pellicano, and A. F. Vakakis, “Nonlinear vibrations and multiple resonances of fluid-filled circular shells. P.1: Equations of motion and numerical results,” J. Vibr. Acoust., 122, 346–354 (2000).
V. D. Kubenko and P. S. Koval’chuk, “The stability and nonlinear vibrations of closed cylindrical shells interacting with fluid flow (review),” Int. Appl. Mech., 51, No. 1, 18–77 (2015).
V. D. Kubenko and P. S. Koval’chuk, “Experimental studies of the vibrations and dynamic stability of laminated composite shells,” Int. Appl. Mech., 45, No. 9, 514–534 (2010).
V. D. Kubenko and P. S. Koval’chuk, “Modeling the nonlinear interaction of standing and traveling bending waves in fluid-filled cylindrical shells subject to internal resonances,” Int. Appl. Mech., 50, No. 4, 353–364 (2014).
V. D. Kubenko, P. S. Kova’lchuk, and L. A. Kruk, “Nonlinear interaction of bending deformation of free oscillating cylindrical shells,” J. Sound Vibr., No. 265, 245–268 (2003).
V. D. Kubenko, P. S. Koval’chuk, and L. A. Kruk, “On free nonlinear vibrations of fluid-filled cylindrical shells with multiple natural frequencies,” Int. Appl. Mech., 41, No. 10, 1193–1203 (2005).
V. D. Kubenko, P. S. Koval’chuk, and L. A. Kruk, “Nonlinear vibrations of cylindrical shells filled with a fluid and subjected to longitudinal and transverse periodic excitation,” Int. Appl. Mech., 46, No. 2, 186–194 (2010).
F. Pellicano and M. Amabili, “Stability and vibration of empty and fluid-filled circular cylindrical shells under static and periodic axial loads,” Int. J. Solids Struct., 40, 3229–3251 (2003).
F. Pellicano, M. Amabili, and A. F. Vakakis, “Nonlinear vibrations and multiple resonances of fluid-filled circular cylindrical shells. P. 2: Perturbation analysis. Equations of motion and numerical results,” J. Vibr. Acoust., 122, 346–354 (2000).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Prikladnaya Mekhanika, Vol. 53, No. 2, pp. 3–12, March–April, 2017.
Rights and permissions
About this article
Cite this article
Kubenko, V.D., Koval’chuk, P.S. Nonlinear Vibrations of Fluid-Filled Cylindrical Shells with Initial Imperfections. Int Appl Mech 53, 121–129 (2017). https://doi.org/10.1007/s10778-017-0797-3
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10778-017-0797-3