Abstract:
The problem of steady radial vibrations of a thin electroelastic hollow disk in a preliminary inhomogeneous plane stress-strain state is solved. Vibrations are caused by a potential difference at the electrodes placed on the end surfaces of the disk. Equations of vibrations and boundary conditions are formulated. The preliminary stress state corresponding to the solution of the Lame problem was investigated. The direct problem of determining the displacement function is solved numerically by the shooting method. The inverse problem of determining the prestress parameter from the change in the natural frequency of the disk is formulated and solved. The accuracy of determining the prestressed state for initial put data specified with an error is analyzed.
Citation:
A. O. Vatulyan, V. V. Dudarev, R. M. Mnukhin, “Determination of the inhomogeneous preliminary stress-strain state in a piezoelectric disk”, Prikl. Mekh. Tekh. Fiz., 59:3 (2018), 181–190; J. Appl. Mech. Tech. Phys., 59:3 (2018), 542–550
\Bibitem{VatDudMnu18}
\by A.~O.~Vatulyan, V.~V.~Dudarev, R.~M.~Mnukhin
\paper Determination of the inhomogeneous preliminary stress-strain state in a piezoelectric disk
\jour Prikl. Mekh. Tekh. Fiz.
\yr 2018
\vol 59
\issue 3
\pages 181--190
\mathnet{http://mi.mathnet.ru/pmtf586}
\crossref{https://doi.org/10.15372/PMTF20180319}
\elib{https://elibrary.ru/item.asp?id=35076584}
\transl
\jour J. Appl. Mech. Tech. Phys.
\yr 2018
\vol 59
\issue 3
\pages 542--550
\crossref{https://doi.org/10.1134/S0021894418030197}
Linking options:
https://www.mathnet.ru/eng/pmtf586
https://www.mathnet.ru/eng/pmtf/v59/i3/p181
This publication is cited in the following 5 articles:
A. A. Pan'kov, “Effect of Increasing Piezomodules of the Initially Compressed Flexible Bimorph”, Opt. Spectrosc., 132:1 (2024), 9
Vyacheslav Berkovich, Victor Poltinnikov, Lecture Notes in Networks and Systems, 575, XV International Scientific Conference “INTERAGROMASH 2022”, 2023, 786
Vladimir V. Dudarev, M. Letunov, “Electroelastic waveguide: Analysis of the effect of prestresses”, Mechanics Research Communications, 115 (2021), 103735
Iryna Lebedyeva, Oleksandr Boryseiko, Valeriy Yashchuk, “Influence of spatial static and dynamic inhomogeneities on the distribution of electroelastic fields and electronic processes in piezoceramic composites”, Molecular Crystals and Liquid Crystals, 719:1 (2021), 11
Vladimir V. Dudarev, Alexander O. Vatulyan, Roman M. Mnukhin, Rostislav D. Nedin, “Concerning an approach to identifying the Lamé parameters of an elastic functionally graded cylinder”, Math Methods in App Sciences, 43:11 (2020), 6861
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