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Free vibrations of cylindrical panel supported by discrete system of stingers

Sil'chenko L.G.

#### Abstract:

Two approaches are established within discrete-continual approach to analysis of deformation of ribbed plates. One method is based on a concept of singularly heterogeneous body. This method allows us to reduce the problems under consideration to the problem of solution of differential equations with coefficients dependent on functions and their derivatives. The basis of another approach makes the method of `gluing’. Among different versions of this method, the version most generally used is one that decomposes an elastic system under analysis into the smaller elements. This method allows us to reduce the problems to that of solution of differential-difference equations. Our goal is to study the small free elastic oscillations of rectangular in plane cylindrical panels, which have unidirectional sets of stringer arranged along curvilinear edges and isotropic panelling. Making general assumptions on the panel geometry, we state a corresponding differential-difference eigenvalue problem. This problem can be reduced exactly to a discrete (difference) eigenvalue problem in the case of a semi-simple support at the panel rectangular edges, which are perpendicular to the set of stringers. We illustrate the exact solution of this problem by examples.

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