Evaluation of the influence of shear stiffness of the core on the natural frequencies and deflections of sandwich plate

In calculations of sandwich structures real core of complex structure, in particular, honeycomb, corrugated, folded, etc., are replaced by a conventional homogeneous layer with reduced elasticity characteristics, the most important of which are shear rigidity. It is technically very difficult to obtain the values of these rigidities by testing the core directly under conditions of relative shear of the bearing layers. Therefore, the problem of identifying the shear rigidities of the core based on the results of indirect measurements, for example, natural frequencies or displacements during transverse bending of the structure, arises. The identification procedure includes an analysis of the influence of the sought parameters on the values measured in the tests. The article investigates the effect of the shear rigidity of an isotropic core on the deflections and natural frequencies of a three-layer rectangular plate. For calculations, the theory of E.I. Grigolyuk — P.P. Chulkov, constructed on the basis of the hypothesis of a broken normal, is used. The complete system of differential equations of the problem, having the eighth order, is presented in the form of three equations for the deflection and shear angles in the core. For the case of hinged fixing of the plate along the contour, analytical expressions for deflections and natural frequencies are obtained, clearly determining their dependence on the shear rigidity of the core. The obtained formulas allow us to establish the value of the core rigidity based on the known data of the corresponding tests.
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