Unsteady coupled elastic diffusion processes in an orthotropic cylinder taking into account diffusion fluxes relaxation

N. A. Zverev ; A. V. Zemskov ; D. V. Tarlakovskii

Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2022), pp. 25-37.

Résumé

We considered the one-dimensional problem of stress-strain state determining of a orthotropic multicomponent cylinder. The cylinder is affected by unsteady surface elastic diffusive perturbations. The coupled system of elastic diffusion equations in the polar coordinate system is used as a mathematical model. Diffusion relaxation effects, implying finite rates of diffusion flux propagation, are taken into account. The problem solution is sought in the integral form and is represented as convolutions of Green's functions with functions defining surface elastodiffusive perturbations. We used the Laplace transform by time, and Fourier series expansion in first kind Bessel functions to find the Green's functions. The Laplace transform inversion is done analytically due to residues and operational calculus tables. An analytical solution to the problem is obtained. Numerical study of the mechanical and diffusion fields interaction in a continuous orthotropic cylinder is performed. We used three-component material as an example. The cylinder is under pressure uniformly distributed over the surface. We used three-component material as an example.

Détail

Mots-clés : elastic diffusion, Laplace transform
Keywords: Fourier series, Green's function, polar-symmetric problem, unsteady problem, Bessel function.

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