Interconnection of maximum deflections and frequencies of free vibrations of composite two-layeroval plates on pliable connections

Abstract

The paper considers the relationship between the maximum deflections and the frequencies of natural oscillations of oval isotropic composite plates, as well as the dependence of the stiffness coefficient of the seam on the stiffness of the shift connections and the frequency of the natural oscillations of the plate. At the first stage, the system of differential equations of transverse bending of a plate under the action of a uniformly distributed load and the differential equation of free transverse oscillations of the plate is solved. The composite plate at this stage is represented in the form of a solid structure with cylindrical stiffness Ds, which is equivalent to the cylindrical rigidity of the composite plate on the pliable connections. After the transformations, the following regularity is obtained, connecting the maximal deflection of the plate with its frequency of transverse oscillations. Oval two-layer composite plates with a ratio of small to major axis from 1.0 to 0.2 with transverse connections and shift connections of variable stiffness were studied over the entire surface of the plate for rigid pinching and pivoting along the contour. The determination of oscillation frequencies and deflections was carried out by a numerical method. As a result of the research it was established that the oval composite plates, regardless of the support scheme and the stiffness of the shift connections, comply with the regularities (1) with an accuracy of 5%. Based on the results of the study, the graphs of the dependence of the maximum deflection and the natural oscillation frequency of the plate on the stiffness of the shift connections at hinged support and pinching along the contour are constructed. On the second stage of the research, based on A.P. Rzhanitsyn’s theory of compound rods, an analytical dependence of the stiffness of the seam on the rigidity of the shift connections was obtained. Based on the results of numerical studies, the dependence of the frequency of natural oscillations on the stiffness coefficient of the seam was obtained. The graphs of the dependence of the frequency of the natural oscillations of the composite plate and the stiffness coefficient of the seam upon the stiffness of the shift connections were constructed.