ENSURING RELIABLE PARAMETERS OF FREE THROATING OF REINFORCED CONCRETE CYLINDRICAL SHELLS REINFORCED WITH ANISOTROPIC COMPOSITE

Abstract

In the article, using a three-dimensional system of partial differential equations of motion of the linear theory of elasticity of an anisotropic body in a cylindrical coordinate system, a study of the frequencies of free oscillations of a cylindrical reinforced concrete shell of a tunnel structure is carried out. This system is derived using the modified Hu – Wasidzu variational principle. To reduce the three-dimensional system of differential equations to a one-dimensional one, the procedure of the Bubnov – Galerkin analytical method is used. After its use, an infinite system of ordinary differential equations is obtained that describe the free oscillations of anisotropic layered cylindrical shells in the normal Cauchy form. The solution of the obtained one-dimensional system of differential equations is carried out using the numerical method of discrete orthogonalization, which was accordingly adapted to solve the problem. A study of the frequencies of free oscillations of a reinforced concrete cylindrical circular shell of a tunnel structure is carried out. To ensure reliable parameters of free oscillations, an option of strengthening the outer surface of the shell with a fibrous composite material was considered. Calculations were made and the results of establishing the frequencies of free vibrations of such a structure were analyzed depending on the angle of laying of the fibrous material.