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Mechanics of Composite Materials
Published in: Mechanics of Composite Materials 3/2016

13-07-2016

Asymptotic Solutions of Boundary Value Problems of Electroelasticity for Transversely Isotropic Toroidal Shells Made of Piezoceramic Materials

Authors: L. A. Aghalovyan, R. S. Gevorkyan

Published in: Mechanics of Composite Materials | Issue 3/2016

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Abstract

By asymptotic integration of the equations and relations of a three-dimensional problem of electroelasticity theory for transversely isotropic ceramics, boundary-value problems for a thin toroidal shell are solved in the cases where the conditions of the first, second, or mixed dynamic boundary-value problems of elasticity theory are given on its surface. Recurrent formulas for calculating components of the displacement vector and stress tensor and the electric field potential in thickness-polarized ceramics are deduced. The resonance frequencies are also found.
next article Optimization of a Hybrid-Fiber-Reinforced High-Strength Concrete

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Literature
1.
V. N. Bulgakov, Statics of Toroidal Shells [in Russian], Akad. Nauk. USSR, Kiev (1962).
2.
A. L. Gol’denveizer, Theory of Thin Elastic Shells [in Russian], Nauka, Moscow (1976).
3.
L. A. Aghalovyan and R. S. Gevorkyan, “Dynamic problems of thermoelasticity for anisotropic inhomogeneous toroidal shells,” in: Problems of Dynamics of Interaction of Deformable Media, Yerevan (2008), pp. 27-35.
4.
M. G. Asratyan and R. S. Gevorkyan, “Mixed boundary-value problems of thermoelasticity for in-plane anisotropic inhomogeneous toroidal shells,” Prikl. Matem. Mekh., 74, Iss. 3, 433-440 (2010).
5.
L. A. Aghalovyan and R. S. Ghevorkyan, Nonclassical Boundary-Value Problems of Anisotropic Layered Beams, Plates, and Shells, Gitutyun, Yerevan (2005).
6.
V. T. Grinchenko, A. F. Ulitko, and N. A. Shul’ga, Electroelasticity [in Russian], Naukova Dumka, Kiev (1989).
7.
V. Z. Parton and B. A. Kudryavtsev, Electromagnetoelasticity of Piezoelectric and Electroconductive Bodies [in Russian], Naukova Dumka, Kiev (1988).
8.
L. Aghalovyan, Asymptotic Theory of Anisotropic Plates and Shells, World Scientific Publ., Singapore (2015).CrossRef
9.
L. A. Aghalovyan and M. L. Aghalovyan, “To the determination of frequencies and modes of free vibrations of orthotropic strips,” Dokl. Armen. Nat. Akad. Nauk., 103, No. 4, 296-301 (2003).
Metadata
Title
Asymptotic Solutions of Boundary Value Problems of Electroelasticity for Transversely Isotropic Toroidal Shells Made of Piezoceramic Materials
Authors
L. A. Aghalovyan
R. S. Gevorkyan
Publication date
13-07-2016
Publisher
Springer US
Published in
Mechanics of Composite Materials / Issue 3/2016
Print ISSN: 0191-5665
Electronic ISSN: 1573-8922
DOI
https://doi.org/10.1007/s11029-016-9581-4

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