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Analytical expressions for the displacements of a surface of piezoelectric FGM-coated half-plane with a strip electrode

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Abstract

Electroelastic piezoelectric transversely isotropic half-plane with a homogeneous or a functionally graded coating is considered. Independent arbitrary variation of electroelastic properties in depth is assumed for a functionally graded coating. A strip electrode is attached to the surface of the coating. Electric potential difference is applied through an electrode which leads to electroelastic deformation of the coated half-plane. Integral transformation technique is used to reduce the problem to solution of a dual integral equation which is solved using the approximated analytical method. Asymptotically, exact analytical expressions for the displacements, electric potential and electric induction on the surface of the coating are obtained. Numerical results illustrate the difference between the distribution of displacements and electric potential on a surface for non-coated half-plane and half-plane with a homogeneous or a functionally graded coating. Influence of relative coating thickness on the results is analyzed. Differences between the results for functionally graded and homogeneous coatings are discussed.

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Funding

This work was supported by the Russian Science Foundation (RSF) through Grant No. 19-19-00444.

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Authors and Affiliations

  1. Don State Technical University, 1 Gagarina sqr., 344000, Rostov-on-Don, Russia

    Andrey S. Vasiliev, Sergei S. Volkov & Evgeniy A. Kislyakov

  2. K. G. Razumovsky Moscow State University of Technologies and Management (the First Cossack University), 73 Zemlyanoy Val, Moscow, 109004, Russia

    Vladimir A. Irkha

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  1. Andrey S. Vasiliev
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  2. Sergei S. Volkov
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  3. Evgeniy A. Kislyakov
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  4. Vladimir A. Irkha
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Correspondence to Andrey S. Vasiliev.

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Communicated by Marcus Aßmus, Victor A. Eremeyev and Andreas Öchsner.

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Vasiliev, A.S., Volkov, S.S., Kislyakov, E.A. et al. Analytical expressions for the displacements of a surface of piezoelectric FGM-coated half-plane with a strip electrode. Continuum Mech. Thermodyn. 33, 1555–1566 (2021). https://doi.org/10.1007/s00161-021-00991-8

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