Abstract
The effect of a small added mass on the frequency and shape of free vibrations of a thin shell is studied using shallow shell theory. The proposed mathematical model assumes that mass asymmetry even in a linear formulation leads to coupled radial flexural vibrations. The interaction of shape-generating waves is studied using modal equations obtained by the Bubnov–Galerkin method. Splitting of the flexural frequency spectrum is found, which is caused not only by the added mass but also by the wave-formation parameters of the shell. The ranges of the relative lengths and shell thicknesses are determined in which the interaction of flexural and radial vibrations can be neglected.
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References
S. A. Tobjas, “A Theory of Imperfection for the Vibration of Elastic Bodies of Revolution,” Engineering 44 (70), 409–420 (1951).
M. Amabili, Nonlinear Vibrations and Stability of Shells and Plates (Cambridge Univ. Press, New York, 2008).
V. D. Kubenko, P. S. Koval’chuk, and T. S. Krasnopol’skaya, Nonlinear Interaction of Flexural Vibration Modes of Cylindrical Shells (Naukova Dumka, Kiev, 1984) [in Russian].
L. V. Andreev, A. I. Stankevich, A. L. Dyshko, and I. D. Pavlenko, Dynamics of Thin-Walled Structures with Added Masses (Mosk. Aviats. Inst., Moscow, 2012) [in Russian].
V. F. Sivak and V. V. Sivak, “Experimental Investigation into the Vibrations of Shells of Revolution with Added Masses,” Int. Appl. Mech. 38 (5), 623–627 (2002).
S. V. Seregin, “Influence of the Contact Area and the Linearly Distributed and Concentrated Mass with a Circular Cylindrical Shell on the Frequency and Mode of Free Vibrations,” Vestnik. Mosk. Gos. Stroit. Univ., No. 7, 64–74 (2014).
S. V. Seregin, “On the Effect of Splitting of the Flexural Frequency Spectrum of Thin Circular Cylindrical Shells Carrying an Added Mass,” Stroit. Mekh. Raschet Sooruzh., No. 6, 59–61 (2014).
S. V. Seregin and G. S. Leizerovich, “Free Vibrations of an Infinitely Long Circular Cylindrical Shell with Initial Irregularities and a Small Added Mass,” Uchen. Zap. Koms.-na-Amure Gos. Tekh. Univ. 1 (4), 36–43 (2014).
S. V. Seregin, “Numerical and Analytical Study of Free Vibrations of Circular Cylindrical Shells with Added Masses Linearly Distributed along the Generatrix,” Vychisl. Mekh. Sploshn. Sred 7 (4), 378–384 (2014).
A. S. Vol’mir, Nonlinear Dynamics of Plates and Shells (Nauka, Moscow, 1972) [in Russian].
S. V. Seregin and G. S. Leizerovich, “Influence of an Added Mass on the Dynamic Characteristics of a Thin Shell,” Probl. Mashinostr. Avtomatiz. No. 4, 83–89 (2015).
S. V. Seregin, Dynamics of Thin Cylindrical Shells with an Added Mass (Komsomolsk-on-Amur State Tech. Univ., Komsomolsk-on-Amur, 2016) [in Russian].
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 57, No. 5, pp. 90–96, September–October, 2016.
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Leizerovich, G.S., Seregin, S.V. Free vibrations of circular cylindrical shells with a small added concentrated mass. J Appl Mech Tech Phy 57, 841–846 (2016). https://doi.org/10.1134/S0021894416050102
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DOI: https://doi.org/10.1134/S0021894416050102