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Normal modes of plane interval-reinforced rectangular panels

Rybakov L.S., Sil'chenko L.G.

#### Abstract:

There are now two defined directions of investigation in the discrete-continuous approach to analysis of the deformation of ribbed plates and shells. One of them (see [1-6] and others) is based on the concept of the singularly inhomogeneous body, which makes it possible to reduce the problems of interest to solution of differential equations with coefficients that depend on а и function and its derivatives. The other trend is based on “gluing.” Perhaps the most promising of its several versions is one that provides for breakup of the elastic system to be analyzed into minimal elements (see [7-10] and others) and permits reduction of the problems of interest to solution of differential-difference equations. The object of the present paper, which comes under the second of the above two directions of exploration, is to study small elastic natural vibrations of plane rectangular panels with unidirectional stringer complements and orthotropic (constructively orthotropic) plates (skin). Below, under rather general assumptions regarding the geometric and elastic properties of the panel, we state the corresponding differential-difference eigenvalue problem. For a system resting free on the edges perpendicular to the stringers, the latter can be reduced exactly to a discrete (difference) eigenvalue problem, the exact numerical solution of which is illustrated in two examples, including one problem of partial optimization of panel structure.

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