Sturm–Liouville Problem for a One-Dimensional Thermoelastic Operator in Cartesian, Cylindrical, and Spherical Coordinate Systemsстатья
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Дата последнего поиска статьи во внешних источниках: 15 мая 2024 г.
Аннотация: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.