Identification of the patterns of influence the number of reinforcing elements and the inhomogeneity parameter of the shell material on frequencies of a reinforced inhomogeneous orthotropic spherical shell with a medium

Abstract

Spherical shells are used in many areas of the national economy. Spherical domes are widely used in the construction of various structures (technoparks, testing laboratories, entertainment complexes, reservoirs, etc.). They are also used in aircraft, ship structures, radar antennas and other structures. It is known that coatings have sufficient strength and durability even with a small thickness. However, to increase the working life of coatings, to ensure their long-term operation, as well as to increase their hardness, it is necessary to strengthen them on the surface or inside with rods. Sometimes it is possible to reduce the weight of the structure and save material consumption by strengthening it with. One of the advantages of these structures is that they give the maximum useful volume, being both load-bearing and enclosing structures. Checking the shells for stability is a priority task, since it is known that the shells, even with an insignificant thickness, have great strength and therefore their insufficient stability can be a criterion determining the bearing capacity. This article is devoted to identifying the regularities of the influence of the number of reinforcing elements and the inhomogeneity parameter of the shell material on the frequencies supported by an inhomogeneous orthotropic spherical shell with a medium. To solve the problem under consideration, the Hamilton-Ostrogradsky variation principle is applied. The frequency equation is constructed and implemented numerically. Such studies have not been considered for a reinforced spherical shell with a no uniform filler in thickness