Shear stiffness determination of the three-layer rod based on the deflections or natural frequencies known values

In mathematical simulation of the three-layer structures, real fillers of complex structure (honeycomb, corrugated, folded, etc.) are replaced by a conventional homogeneous layer with the given elastic characteristics. Shear stiffness is one of the most important characteristics of a filler. It is rather difficult to obtain its value directly by testing the filler. The problem is set to identify shear stiffness of the three-layer rod filler based on the known values ??of natural frequencies or displacement under the transverse bending. In computation of the three-layer rods, the paper uses the E.I. Grigolyuk - P.P. Chulkov theory constructed on the basis of the broken normal hypothesis. It considers results of applying this approximate theory to computation of the rod natural frequencies and vibration modes. To assess the approximate theory accuracy, the paper compares computation results with solutions to the plane dynamic problem of the elasticity theory by the finite element method. It shows that for the lowest vibration modes with wavelengths significantly exceeding the cross-section height, the broken normal hypothesis provides results practically matching solutions of the elasticity theory. The paper analyzes the filler stiffness effect on the values ??of the natural vibration frequencies and displacement under the three-point bending of a rod. Formulas are obtained making it possible to establish the filler shear stiffness values based on the known data of the corresponding tests.
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