Determination of the Inhomogeneous Preliminary Stress–Strain State in a Piezoelectric Disk
- Authors: Vatulyan A.O.1,2, Dudarev V.V.1,2, Mnukhin R.M.1
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Affiliations:
- Southern Federal University
- Southern Mathematical Institute, Vladikavkaz Science Center
- Issue: Vol 59, No 3 (2018)
- Pages: 542-550
- Section: Article
- URL: https://journals.rcsi.science/0021-8944/article/view/161146
- DOI: https://doi.org/10.1134/S0021894418030197
- ID: 161146
Cite item
Abstract
The problem of steady radial vibrations of a thin electroelastic hollow disk in the presence of a preliminary inhomogeneous plane stress–strain state is solved. Vibrations are induced by applying a potential difference across the electrodes placed on the end surfaces of the disk. Equations of the vibrations and boundary conditions are formulated. The preliminary stress state corresponding to the solution of the Lam´e problem was investigated. The direct problem of determining the displacement function is solved numerically by the shooting method. The inverse problem of determining a pre-stress parameter from the change in the natural frequency of the disk is formulated and solved. The accuracy of determining the prestressed state for initial data specified with an error is analyzed.
About the authors
A. O. Vatulyan
Southern Federal University; Southern Mathematical Institute, Vladikavkaz Science Center
Author for correspondence.
Email: vatulyan@math.rsu.ru
Russian Federation, Rostov-on-Don, 344090; Vladikavkaz, 362027
V. V. Dudarev
Southern Federal University; Southern Mathematical Institute, Vladikavkaz Science Center
Email: vatulyan@math.rsu.ru
Russian Federation, Rostov-on-Don, 344090; Vladikavkaz, 362027
R. M. Mnukhin
Southern Federal University
Email: vatulyan@math.rsu.ru
Russian Federation, Rostov-on-Don, 344090