Abstract
Main correlations in the theory of bending of thin electromagnetoelastic plates are obtained, in which complex potentials are used. Exact analytical solutions are obtained for the problems of bending an elliptical plate and an infinite plate with an elliptical hole. It is established that no electric or magnetic inductions arise in the case of a simply connected finite plate under mechanical influences and no mechanical stresses arise under the action of inductions, despite the fact that the piezoelectric effect occurs due to deformations, displacements, and field potentials. The piezoelectric effect in the case of an infinite simply connected plate is always observed and has a significant effect on the values of bending moments. The influence of the physical and mechanical properties of materials and the geometric characteristics of holes on the values of bending moments in the case of a plate with an elliptical hole is studied.
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REFERENCES
M. I. Bichurin, V. M. Petrov, D. A. Filippov, et al., Magnetoelectric Composites (Jenny Stanford Publishing, 2019).
A. P. Pyatakov, “Magnetoelectric Materials and Their Practical Application," Bul. Ros. Magnit. Obshchestva (MAGO) 5 (2), 1–3 (2006).
A. C. Eringen, “Theory of Electromagnetic Elastic Plates," Intern. J. Engng Sci. 27 (4), 363–375 (1989).
L. Librescu, D. Hasanyan, and D. R. Ambur, “Electromagnetically Conducting Elastic Plates in a Magnetic Field: Modeling and Dynamic Implications," Intern. J. Non-Linear Mech. 39 (5), 723–739 (2004).
C. Gales and N. Baroiu, “On the Bending of Plates in the Electromagnetic Theory of Microstretch Elastity," Z. angew. Math. Mech. 94 (1/2), 55–71 (2014).
S. A. Kaloerov and A. V. Petrenko, “Two-Dimensional Problem of Electromagnetoelasticity for Multiply Connected Media,"Matematychni Metody ta Fizyko-Mekhanichni Polya 51 (2), 208–221 (2008) [J. Math. Sci. 162, 254–273 (2009)].
S. A. Kaloerov, “Complex Potentials of the Theory of Bending of Thin Electromagnetoelastic Plates," Vestn. Don. Nats. Univ. Ser. A. Estestv. Nauki, No. 3/4, 37–57 (2019).
S. A. Kaloerov, “Boundary Value Problems of the Applied Theory of Bending of Thin Electromagnetoelastic Plates," Vestn. Don. Nats. Univ. Ser. A. Yestesv. Nauki, No. 1, 42–58 (2019).
G. R. Kirchhoff, “Uber das gleichgewichi und die bewegung einer elastishem scheibe," J. reine angew. Math. 40, 51–88 (1850).
S. G. Lekhnitskii, Theory of Elasticity of an Anisotropic Elastic Body (Holden-Day, 1963).
J. C. Maxwell, “A Treatise on Electricity and Magnetism" Vol. 2 (Clarendon Press, Oxford, 1873).
I. E. Tamm, Fundamentals of the Theory of Electricity (Nauka, Moscow, 1976) [in Russian].
W.-Y. Tian and U. Gabbert, “Multiple Crack Interaction Problem in Magnetoelectroelastic Solids," Europ. J. Mech. Pt A 23, 599–614 (2004).
P. F. Hou, G.-H. Teng, and H.-R. Chen, “Three-Dimensional Greens Function for a Point Heat Source in Two-Phase Transversely Isotropic Magneto-Electro-Thermo-Elastic Material," Mech. Materials 41, 329–338 (2009).
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2021, Vol. 63, No. 2, pp. 151-165. https://doi.org/10.15372/PMTF20220214.
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Kaloerov, S.A., Seroshtanov, A.V. BENDING OF THIN ELECTROMAGNETOELASTIC PLATES. J Appl Mech Tech Phy 63, 308–320 (2022). https://doi.org/10.1134/S0021894422020146
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DOI: https://doi.org/10.1134/S0021894422020146