Free vibrations of layered anisotropic thick-walled cylindrical shells

The article presents an approach to the calculation of free oscillations of thick-walled elastic layered anisotropic cylindrical shells. Anisotropy is due to the use of material whose elastic characteristics are in one plane parallel to the middle surface of the shell. This type of anisotropy arises due to the non-coincidence of the main directions of elasticity of the orthotropic fibrous composite with the axes of the cylindrical coordinate system. Calculations describing the free oscillations of thick-walled cylindrical anisotropic shells are implemented by deriving a system of six differential equations of motion in partial derivatives of the spatial linear theory of elasticity. For this purpose, the authors modified the Hu-Washizu variational principle accordingly, which allows writing not only the equations of motion, but also the boundary conditions corresponding to them. When using the Bubnov-Galyorkin analytical method, an infinite one-dimensional system of differential equations of the normal Cauchy form is obtained, which allows finding the frequencies of free oscillations of thick-walled layered anisotropic cylindrical shells. The unknowns in the system of equations of motion describing the parameters of the stress-strain state of the shells are selected in the radial direction. To implement a one-dimensional solving system of differential equations of cylindrical shells, the numerical method of discrete orthogonalization was used, which was adapted accordingly by the authors. On this basis, an algorithm was written and a software complex was created for personal computers, which allows solving problems related to setting parameters of free oscillations of thick-walled layered anisotropic composite cylindrical shells. The solutions of problems on the influence on the frequencies of free oscillations of an anisotropic thick-walled cylindrical shell are presented, taking into account: the angle of rotation of the main directions of elasticity of an orthotropic fibrous composite; increasing the number of cross-stacked layers; changes in the geometric parameters of the structure; four types of boundary conditions.