Short Notes

On a model of oscillations of a thin flat plate with a variety of mounts on opposite sides

U. A. Iskakova

Institute of Mathematics and Mathematical Modelling, Almaty, Kazakhstan

Abstract: We consider a model case of stationary vibrations of a thin flat plate, one side of which is embedded, the opposite side is free, and the sides are freely leaned. In mathematical modeling there is a local boundary value problem for the biharmonic equation in a rectangular domain. Boundary conditions are given on all boundary of the domain. We show that the considered problem is self-adjoint. Herewith the problem is ill-posed. We show that the stability of solution to the problem is disturbed. Necessary and sufficient conditions of existence of the problem solution are found. Spaces of the ill-posedness of the considered problem are constructed.

Keywords: oscillations; thin flat plate; biharmonic equation; boundary value problem; ill-posed problem.

UDC: 517.956.29

MSC: 35J40, 35P20

Received: 28.02.2016

Language: English

DOI: 10.14529/mmp160210

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