Determination of the Inhomogeneous Preliminary Stress–Strain State in a Piezoelectric Disk


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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.

作者简介

A. Vatulyan

Southern Federal University; Southern Mathematical Institute, Vladikavkaz Science Center

编辑信件的主要联系方式.
Email: vatulyan@math.rsu.ru
俄罗斯联邦, Rostov-on-Don, 344090; Vladikavkaz, 362027

V. Dudarev

Southern Federal University; Southern Mathematical Institute, Vladikavkaz Science Center

Email: vatulyan@math.rsu.ru
俄罗斯联邦, Rostov-on-Don, 344090; Vladikavkaz, 362027

R. Mnukhin

Southern Federal University

Email: vatulyan@math.rsu.ru
俄罗斯联邦, Rostov-on-Don, 344090

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