A method for determining the nature of vibrations and stress–strain state of ribbed orthotropic conical shells with asymmetric layers interacting with masses under dynamic loads is developed using the theory of shells and the Tymoshenko hypotheses. The equations of vibrations of a shell formulated for the displacements of points of the midsurface are obtained using the Hamilton principle. To solve the system of equations of motion of the shell, trigonometric series in spatial coordinates and an explicit finite-difference scheme with respect to time are used. The accuracy of calculations by the finite-difference method depending on the number of time steps is estimated for a layered cylindrical shell as an example. The stress–strain state of a conical orthotropic shell with symmetric and asymmetric layers, longitudinal ribs, and masses under a short-term axisymmetric external load distributed over a portion of the shell and moving from the minor base to the major base is analyzed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
S. A. Ambartsumyan, Theory of Anisotropic Shells [in Russian], Gos. Izd. Fiz.-Mat. Lit., Moscow (1961).
K. G. Golovko, P. Z. Lugovoi, and V. F. Meish, Dynamics of Inhomogeneous Shells under Nonstationary Loads [in Russian], Izd.-Poligr. Tsentr “Kievskii Universitet,” Kyiv (2012).
N. N. Kalitkin, Numerical Methods [in Russian], Nauka, Moscow (1978).
P. Z. Lugovoi, V. F. Meish, and E. A. Shtantsel’, Nonstationary Dynamics of Inhomogeneous Shell Structures [in Russian], Izd.-Poligr. Tsentr “Kievskii Universitet,” Kyiv (2005).
P. Z. Lugovoy, Yu. V. Skosarenko, and S. P. Orlenko, “Application of the spline-collocation method for solving problems of the statics and dynamics of structurally inhomogeneous cylindrical shells,” Dop. NAN Ukrainy, No. 8, 25–33 (2019).
Yu. A. Meish, “Analysis of the forced axisymmetric vibrations of three-layer conical shells under a nonstationary load,” Syst. Tekhn., Mat. Probl. Tekhn. Mekh., 32, No. 3, 154–160 (2004).
I. Ya. Amiro and V. A. Zarutskii, Theory of Ribbed Shells, Vol. 2 of the five-volume series Methods of Shell Design [in Russian], Naukova Dumka, Kyiv (1980).
S. P. Orlenko, “Effect of asymmetry of cylindrical three-layer shells with light core on their stress–strain state under non-stationary loads,” Probl. Obch. Mekh. Mitz. Konstr., No. 31, 42–52 (2020).
S. P. Orlenko, “Numerical simulation of the dynamics of a three-layer spherical shell with a discrete inhomogeneous filler,” Dop. NAN Ukrainy, No. 8, 35–42 (2020).
S. P. Timoshenko, D. H. Young, and W. Weaver, Vibration Problems in Engineering, Wiley, New York (1974).
V. G. Piskunov and A. O. Rasskazov, “Development of the theory of layered plates and shells,” in: Vol. 3 of the six-volume series A. N. Guz (ed.), Advances in Mechanics [in Russian], A.S.K., Kyiv (2007), pp. 141–175.
I. I. Anik’ev, M. I. Mikhailova, and E. A. Sushchenko, “Dynamic loading of cylindrical and spherical bodies interacting with a shock wave,” Int. Appl. Mech., 40, No. 12, 1405–1410 (2004).
J. R. Banerjee, C. W. Cheung, R. Morishima, M. Perera, J. Njuguna, “Free vibration of a three-layered sandwich beam using the dynamic stiffness method and experiment,” Int. J. Solids Struct., 44, No. 22, 7543–7563 (2007).
E. Carrera, “On the use of the Murakami’s zig-zag function in the modeling of layered plates and shells,” Comp. Struct., 82, No. 7–8, 541–554 (2004).
I. Kreja, “A literature review on computational models for laminated composite and sandwich panels,” Cent. Eur. J. Eng., Publ. Online, 1, No. 1, 59–80 (2011).
P. Z. Lugovyi, V. V. Gaidaichuk, Yu. V. Skosarenko, and K. E. Kotenko, “Stress–strain state of three-layer cylindrical shells with reinforced light core under nonstationary loading,” Int. Appl. Mech., 57, No. 4, 395–404 (2021).
P. Z. Lugovyi, V. F. Meish, Yu. A. Meish, and S. P. Orlenko, “Dynamic design of compound shell structures of revolution under nonstationary loads,” Int. Appl. Mech., 56, No. 1, 22–32 (2020).
P. Z. Lugovoi, V. F. Meish, and S. P. Orlenko, “Numerical simulation of the dynamics of spherical sandwich shells reinforced with discrete ribs under a shock wave,” Int. Appl. Mech., 56, No. 5, 590–598 (2020).
P. Z. Lugovoi, V. N. Sirenko, Yu. V. Skosarenko, and T. Ya. Batutina, “Mathematical modeling of cylindrical adapter dynamics under the action of local momentary loads,” Sci. Innov., 12, No. 3, 35–42 (2016).
P. Z. Lugovoi, Yu. V. Skosarenko, S. P. Orlenko, and A. P. Shugailo, “Application of the spline-collocation method to solve problems of statics and dynamics for multilayer cylindrical shells with design and manufacturing features,” Int. Appl. Mech., 55, No. 5, 524–533 (2019).
V. F. Meish, Yu. A. Meish, and N. V. Arnauta, “Numerical analysis of nonstationary vibrations if discretely reinforced multilayer shells of different geometry,” Int. Appl. Mech., 55, No. 4, 426–433 (2019).
V. F. Meish, Yu. A. Meish, and A. V. Pavlyuk, “Dynamics of a three-layer elliptic cylindrical shell reinforced with discrete rings,” Int. Appl. Mech., 54, No. 2, 172–179 (2018).
N. J. Pagano and S. J. Hatfield, “Elastic behavior of multilayered bidirectional composites,” AIAA J., 10, 931–933 (1972).
M. S. Qatu, Vibration of Laminated Shells and Plates, Academic Press, New York (2004).
M. S. Qatu, E. Asadi, and W. Wang, “Review of recent literature on static analyses of composite shells: 2000–2100,” Open J. Comp. Mat., 2, No. 3, 61–86 (2012).
N. A. Shul’ga, V. F. Meish, Yu. A. Khamrenko, “Nonstationary oscillations of three-layer cylindrical shells under axisymmetric loading,” Int. Appl. Mech., 35, No. 8, 751–758 (1999).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Prykladna Mekhanika, Vol. 58, No. 3, pp. 40–49, May–June 2022.
* This study was sponsored by the budget program “Support for Priority Areas of Scientific Research” (KPKVK 6541230).
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Lugovyi, P.Z., Skosarenko, Y.V. Vibrations of a Layered Conical Shell Under Nonstationary Load*. Int Appl Mech 58, 280–288 (2022). https://doi.org/10.1007/s10778-022-01153-2
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10778-022-01153-2