Generalized solutions of boundary value problems ofdynamics of thermoelastic rods
DOI:
https://doi.org/10.70474/k7gyhj30Keywords:
Thermoelasticity, boundary value problems, method of generalized functions, generalized solution, Fourier transform, boundary equationsAbstract
We consider spatially one-dimensional boundary value problems of uncoupled thermoelasticity, which can be used to study various rod structures under thermal heating conditions. This model well describes thermodynamic processes at low strain rates. Here, a unified methodology has been developed for solving various boundary value problems typical of practical applications. The task is set to determine the thermo-stressed state of a thermoelastic rod under various boundary conditions at its ends, as well as the acting forces and heat sources along the entire length of the rod.
Shock elastic waves arising in such structures under the action of shock loads are considered. Based on the method of generalized functions, generalized solutions of non-stationary and stationary direct and semi-inverse boundary value problems in the class of generalized vector functions of slow growth are constructed. Regular integral representations of generalized solutions are also given, which provide analytical solutions to the posed boundary value problems. The peculiarity of the constructed solutions makes them convenient for engineering applications because make it possible to study the influence of each boundary condition, as well as the acting power and heat sources separately, which is very important when assessing the strength properties of rod structures.
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