The forced vibrations of discretely reinforced multilayer cylindrical, spherical, and conical shells under nonstationary loading are studied. The dynamic behavior of the shells is studied using Timoshenko-type theory of shells and rods. Problem statements are presented and a numerical algorithm of solving problems of this class is elaborated. Numerical examples of dynamic behavior of the shells are presented, and the results obtained are analyzed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
I. Ya. Amiro, V. A. Zarutskii, and V. G. Palamarchuk, Dynamics of Ribbed Shells [in Russian], Naukova Dumka, Kyiv (1983).
K. G. Golovko, P. Z. Lugovoi, and V. F. Meish, Dynamics of Inhomogeneous Shells under Nonstationary Loads [in Russian], Kievskii Universitet, Kyiv (2012).
I. Ya. Amiro, V. A. Zarutskii, V. N. Revutskii, Yu. V. Skosarenko, A. I. Telalov, and S. Yu. Fialko, Vibrations of Ribbed Shells of Revolution [in Russian], Naukova Dumka, Kyiv (1988).
G. I. Marchuk, Methods of Computational Mathematics [in Russian], Nauka, Moscow (1977).
A. A. Samarskii, Theory of Difference Schemes [in Russian], Nauka, Moscow (1977).
H. Altenbach, “Theories for laminated and sandwich plates: A review,” Mech. of Comp. Mater., 34, No. 3, 243–252 (1998).
V. M. Efimtsov and L. A. Lazarev, “Forced vibrations of plates and cylindrical shells with regular orthogonal system of stiffeners,” J. Sound Vibr., 327, No. 1–2, 41–54 (2009).
P. Z. Lugovoi and V. F. Meish, “Dynamics of inhomogeneous shell systems under nonstationary loading (Survey),” Int. Appl. Mech., 53, No. 5, 481–537 (2017).
V. F. Meish and N. V. Maiborodina, “Stress state of discretely stiffened ellipsoidal shells under a nonstationary normal load,” Int. Appl. Mech., 54, No. 6, 675–686 (2018).
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).
A. K. Noor and W. S. Burton, “Assessment of computational models of multilayered composite shells,” Appl. Mech. Rev., 43, No. 4, 67–97 (1990).
N. J. Pagano, “Exact solutions for composite laminates in cylindrical bending,” J. Comp. Mater., 3, 389–411 (1969).
N. J. Pagano, “Free edge stress fields in composite laminates,” Int. J. Solids Struct., 14, 401–406 (1978).
M. S. Qatu, “Recent research advances in the dynamic behavior of shells. Part 1: Laminated composite shells,” Appl. Mech. Rev., 55, No. 4, 325–350 (2002).
M. S. Qatu, R. W. Sullivan, and W. Wang, “Recent research advances in the dynamic behavior of composite shells,” Compos. Struct., 93, No. 1, 14–31 (2010).
J. N. Reddy and C. F. Liu, “A higher-order shear deformation theory of laminated elastic shells,” Int. J. Eng. Sci., 23, 669–683 (1985).
J. N. Reddy, “On refined computational models of composite laminates,” Int. J. Numer. Meth. Eng., 27, 361–382 (1989).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Prikladnaya Mekhanika, Vol. 55, No. 4, pp. 113–122, July–August 2019.
Rights and permissions
About this article
Cite this article
Meish, V.F., Meish, Y.A. & Arnauta, N.V. Numerical Analysis of Nonstationary Vibrations of Discretely Reinforced Multilayer Shells of Different Geometry. Int Appl Mech 55, 426–433 (2019). https://doi.org/10.1007/s10778-019-00962-2
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10778-019-00962-2