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IssuesArchive of Issues2016-5pp.588-595

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T.I. Belyankova and V.V. Kalinchuk, "Dynamic Equations of a Prestressed Magnetoelectroelastic Medium," Mech. Solids. 51 (5), 588-595 (2016)
Year 2016 Volume 51 Number 5 Pages 588-595
DOI 10.3103/S0025654416050125
Title Dynamic Equations of a Prestressed Magnetoelectroelastic Medium
Author(s) T.I. Belyankova (South Scientific Center, Russian Academy of Sciences, ul. Chekhova 41, Rostov-on-Don, 344006 Russia; South Federal University, pr. Stachki 200/1, Rostov-on-Don, 344090 Russia)
V.V. Kalinchuk (South Scientific Center, Russian Academy of Sciences, ul. Chekhova 41, Rostov-on-Don, 344006 Russia; South Federal University, pr. Stachki 200/1, Rostov-on-Don, 344090 Russia, vkalin415@mail.ru)
Abstract The constitutive relations of nonlinear mechanics of a magnetoelectroelastic medium subjected to initial mechanical stresses are linearized in the framework of material (Lagrangian) coordinates. The final expressions are constructed independently of the choice of curvilinear coordinates and are represented in a form convenient for theoretical and applied studies. The constitutive relations for the motion of a prestressed magnetoelectroelastic medium are given in rectangular Cartesian coordinates. The influence of the initial mechanical stresses on piezomagnetoelectric materials of the class 6 mm is studied.
Keywords electromagnetic medium, magnetoelectroelasticity, linearization, preliminary stress, initial strain
References
1.  G. Maugin, Continuum Mechanics of Electromagnetic Solids (North Holland, 1988; Mir, Moscow, 1991).
2.  V. V. Kalinchuk, T. I. Belyankova, and O. V. Evdokimova, "Constitutive Relations of Dynamics of Prestressed Piezoactive Medium in the Absence of External Electric Fields," Vestnik Yuzhn. Nauchn. Tsentra RAN 2 (1), 16-23 (2006).
3.  O. V. Evdokimova, T. I. Belyankova, and V. V. Kalinchuk, "Equations of Dynamics of Prestressed Piezoactive Medium in the Presence of External Electrostatic Field," Vestnik Yuzhn. Nauchn. Tsentra RAN 3 (4), 19-25 (2007).
4.  V. V. Kalinchuk, T. I. Belyankova, and D. N. Sheidakov, "Equations of Dynamics of Prestressed Magnetoelastic Medium," Vestnik Yuzhn. Nauchn. Tsentra RAN 9 (Jubilee number), 20-28 (2013).
5.  V. V. Kalinchuk, T. I. Belyankova, M. O. Levi, and K. L. Agayan, "Some Specific Characteristics of Dynamics of Weakly Homogeneous Magnetoelastic Half-Space," Vestnik Yuzhn. Nauchn. Tsentra RAN 9 (4), 13-17 (2013).
6.  V. I. Alshits, A. N. Darinskii, and J. Lothe, "On the Existence of Surface Waves in Half-Infinite Anisotropic Elastic Media with Piezoelectric and Piezomagnetic Properties," Wave Motion 16, 265-283 (1992).
7.  C. W. Nan, "Magnetoelectric Effect in Composites of Piezoelectric and Piezomagnetic Phases," Phys. Rev. 50, 6082-6089 (1994).
8.  J. Y. Li and L. D. Martin, "Anisotropic Coupled-Field Inclusion and Inhomogeneity Problems," Phil. Mag. A 77 (5), 1341-1350 (1998).
9.  Z. Chen, S. Yu, L. Meng, and Y. Lin, "Effective Properties of Layered Magneto-Electro-Elastic Composites," Compos. Struct. 57, 177-182 (2002).
10.  S. Srinivas, J. Y. Li, Y. C. Zhou, and A. K. Soh, "The Effective Magnetoelectroelastic Moduli of Matrix-Based Multiferroic Composites," J. Appl. Phys. 99 (4), 1-7 (2006).
11.  V. I. Alshits, H. O. K. Kirchner, and T. C. T. Ting, "Angularly Inhomogeneous Piezoelectric Piezomagnetic Magnetoelectric Anisotropic Media," Phil. Mag. Lett. 71 (5), 285-288 (1995).
12.  A. I. Lurie, Nonlinear Theory of Elasticity (Nauka, Moscow, 1980) [in Russian].
13.  V. V. Kalinchuk and T. I. Belyankova, Dynamics of the Surface of Inhomogeneous Media (Fizmatlit, Moscow, 2009) [in Russian].
Received 25 April 2016
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