Abstract
A variant of vibration theory for three-layered shells of revolution under axisymmetric loads is elaborated by applying independent kinematic and static hypotheses to each layer, with account of transverse normal and shear strains in the core. Based on the Reissner variational principle for dynamic processes, equations of nonlinear vibrations and natural boundary conditions are obtained. The numerical method proposed for solving initial boundary-value problems is based on the use of integrodifferential approach for constructing finite-difference schemes with respect to spatial and time coordinates. Numerical solutions are obtained for dynamic deformations of open three-layered spherical and ellipsoidal shells, over a wide range of geometric and physical parameters of the core, for different types of boundary conditions. A comparative analysis is given for the results of investigating the dynamic behavior of three-layered shells of revolution by the equations proposed and the shell equations of Timoshenko and Kirhhoff-Love type, with the use of unified hypotheses across the heterogeneous structure of shells.
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REFERENCES
E. I. Grigolyuk and G. M. Kulikov, “General direction of development of the theory of multilayered shells,” Mech. Compos. Mater., 24, No. 2, 231–241 (1988).
V. V. Bolotin and Yu. N. Novichkov, Mechanics of Multilayer Structures [in Russian], Moscow (1980).
A. O. Rasskazov, I. I. Sokolovskaya, and N. A. Shul'ga, Theory and Calculation of Layered Orthotropic Plates and Shells [in Russian], Vishcha Shkola, Kiev (1986).
V. V. Novozhilov, Fundamentals of the Nonlinear Theory of Elasticity [in Russian], Gostekhizdat, Moscow–Leningrad (1948).
I. K. Naval, V. I. Patsyuk, and V. K. Rimskii, Nonstationary Waves in Deformable Media [in Russian], Shtiintsa, Kishinev (1986).
A. A. Samarskii, Theory of Finite-Difference Schemes [in Russian], Nauka, Moscow (1977).
N. A. Shulga, V. F. Meish, and Yu. A. Khamrenko, “Nonstationary vibrations of three-layered cylindrical shells under axisymmetric loading,” Int. Appl. Mech., 35, No. 8, 754–757 (1999).
P. Z. Lugovoi, V. F. Meish, and E. A. Shtantsel, “On consideration of geometrical nonlinearity in dynamic problems of the theory of discretely supported cylindrical shells under nonstationary loading,” Int. Appl. Mech., 36, No. 4, 532–537 (2000).
N. A. Abrosimov, V. G. Bazhenov, and V. P. Stolov, “Numerical investigation of dynamic deformation of multilayer composite cylindrical shells with thin rigid layers,” in: Applied Problems of Strength and Plasticity. Algorithmization and Automatization of the Solution of Elasticity and Plasticity Problems. Collection of Works [in Russian], Gorki Univ. (1988), pp. 48–53.
P. Z. Lugovoi, “Dynamics of thin-walled structures under nonstationary loads,” Int. Appl. Mech., 37, No. 5, 625–655 (2001).
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Shul'ga, N.A., Meish, V.F. Forced Vibration of Three-Layered Spherical and Ellipsoidal Shells under Axisymmetric Loads. Mechanics of Composite Materials 39, 439–446 (2003). https://doi.org/10.1023/B:MOCM.0000003294.75072.58
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DOI: https://doi.org/10.1023/B:MOCM.0000003294.75072.58