Volume 9, no. 2Pages 110 - 116
On a Model of Oscillations of a Thin Flat Plate with a Variety of Mounts on Opposite SidesU.A. Iskakova
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. Full text
- oscillations; thin flat plate; biharmonic equation; boundary value problem; ill-posed problem.
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