Modelling one-dimensional elastic diffusion processes in an orthotropic solid cylinder under unsteady volumetric perturbations

Abstract

A polar-symmetric elastic diffusion problem is considered for an orthotropic multicomponent homogeneous cylinder under uniformly distributed radial unsteady volumetric perturbations. Coupled elastic diffusion equations in a cylindrical coordinate system is used as a mathematical model. The model takes into account a relaxation of diffusion effects implying finite propagation speed of diffusion perturbations. The solution of the problem is obtained in the integral convolution form of Green's functions with functions specifying volumetric perturbations. The integral Laplace transform in time and the expansion into the Fourier series by the special Bessel functions are used to find the Green's functions. The theory of residues and tables of operational calculus are used for inverse Laplace transform. A calculus example based on a three-component material, in which two components are independent, is considered. The study of the mechanical and diffusion fields interaction in a solid orthotropic cylinder is carried out.

Keywords

• elastic diffusion
• laplace transform
• fourier series
• green's functions
• polar symmetric problems
• unsteady problems
• bessel functions
• cylinder