Sturm–Liouville Problem for a One-Dimensional Thermoelastic Operator in Cartesian, Cylindrical, and Spherical Coordinate Systems.
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| Title: | Sturm–Liouville Problem for a One-Dimensional Thermoelastic Operator in Cartesian, Cylindrical, and Spherical Coordinate Systems. |
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| Authors: | Zemskov, A. V.1,2 (AUTHOR) azemskov1975@mail.ru, Tarlakovskii, D. V.1,2 (AUTHOR) tdvhome@mail.ru |
| Source: | Computational Mathematics & Mathematical Physics. Mar2024, Vol. 64 Issue 3, p401-415. 15p. |
| Subjects: | Spherical coordinates, Spherical functions, Thermoelasticity, Eigenfunctions, Separation of variables, Heat transfer |
| Abstract: | The problem of constructing eigenfunctions of a one-dimensional thermoelastic operator in Cartesian, cylindrical, and spherical coordinate systems is considered. The corresponding Sturm–Liouville problem is formulated using Fourier's separation of variables applied to a coupled system of thermoelasticity equations, assuming that the heat transfer rate is finite. It is shown that the eigenfunctions of the one-dimensional thermoelastic operator are expressed in terms of well-known trigonometric, cylinder, and spherical functions. However, coupled thermoelasticity problems are solved analytically only under certain boundary conditions, whose form is determined by the properties of the eigenfunctions. [ABSTRACT FROM AUTHOR] |
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| Database: | Engineering Source |
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