Abstract
The article considers a new class of model representations in the theory of oscillation of systems described by the classical boundary value problems for hyperbolic equations. The peculiarity of the suggested approach consists in the introduction of an additional term into the basic equation of oscillations. This term characterizes the presence of a temperature gradient in the systems. The developed theory is applicable to longitudinal oscillations of a rod, but can be extended just as well to the problem of the vibrations of strings, membranes, shaft torsional oscillations, electromagnetic waves, etc. Numerical experiments showed a significant effect of the temperature field in the rod on the nature of the vibrations and displacements of the rod cross-sections in comparison with classical solutions.
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