Use of the Green's function method in the hyperbolic heat conduction theory and non-Fourier analysis of non-stationary thermoelastic fields (moving) deformed media/bodies and composite materials
DOI:
https://doi.org/10.32347/2410-2547.2026.116.207-219Keywords:
Green's function method, hyperbolic heat conduction theory, analysis, non-stationarity, thermoelastic fields, mobile deformed media, composite materials, non-Fourier analysis, short wave video pulsesAbstract
The work develops precisely solvable models of pulse optics for dispersive, dissipative deformed media (bodies) and composite materials during their laser processing with short wave pulses. Unsteady thermoelastic fields excited by video pulses in these media (bodies) and materials are presented analytically thanks to exact periodic and unsteady solutions of thermoelasticity equations obtained directly in the time domain outside the limits of Fourier series by analogy with the well-known results of A.B. Schwarzburg.
This study also obtained a hyperbolic heat conduction equation for a moving body and a solution to this equation in a cylindrical coordinate system using Green's functions. The solution obtained in this work corresponds to the hyperbolic theory of heat conduction, which takes into account the finiteness of the heat propagation velocity and allows for a more accurate assignment of strength standards for parts operating under thermodynamic stresses, and in technological processes, for example, in the problem of temperature field distribution in cylindrical samples during their processing with a grinding tool, to optimize the processing mode parameters.
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