VARIATIONAL PRINCIPLE FOR DETERMINING THE PARAMETERS OF FREE VIBRATIONS OF A THICK-WALLED ELASTIC ANISOTROPIC CYLINDRICAL SHELL

Abstract

In this work, based on the modified Hu-Washizu variational principle, a three-dimensional system of homogeneous differential equations of motion in partial derivatives of the linear theory of elasticity of an anisotropic body in a cylindrical coordinate system is obtained. To reduce it to one-dimensional, the Bubnov-Galerkin method was used. The unknown of system of equations along the generatrix and in the circumferential directions were approximated by this method. To solve the one-dimensional problem in the direction normal to the middle surface of the shell was used the method of discrete orthogonalization.

The frequencies of free vibrations of an anisotropic thick-walled composite cylindrical shell are investigated. The analysis of the change in the frequencies of free vibrations of the shell is carried out depending on the change in the angle of rotation of the main directions of elasticity of unidirectional fibrous material and the thickness of the cylinder.