Numerical and Asymptotic Modeling of Annular Plate Vibrations

Free axisymmetric flexural vibrations of an annular elastic thin plate are studied. Numerical solutions of eigenvalue problem for various boundary conditions are obtained. The plate can be used as a model of the supporting frame of a shell. In this connection the boundary conditions corresponding the attaching of the plate to a cylindrical shell are also considered. The plate is called narrow if the ratio of its width to the radius of the inner edge is small. For the vibrations analysis of a narrow plate new asymptotic methods are elaborated. Comparison asymptotic and numerical results shows, that the error of the approximate formulae quickly decreases with reduction of the plate width.