In the present paper, solutions of the equations of uncoupled thermoelastodynamics of thermoelastic rods are constructed for power and thermal effects. Based on the Fourier transform, the Green tensor and generalized solutions of the thermoelasticity equations are constructed in the original space-time using the apparatus of generalized functions theory. Analytical formulas for definitions of the thermal stress-strain state of the rods taking into account its thermoelastic parameters are obtained. Shock thermoelastic waves are considered and conditions on their fronts are obtained. The results of numerical calculations of Green tensor are presented.
Rod structures are widely used in mechanical engineering as connecting and transmission links for structural elements of a wide variety of machines and mechanisms. During operation, they are subject-ed to variable mechanical and thermal influences, which create a complex stress-strain state in structur-al elements, depending on their temperature, and affecting their strength and reliability. Therefore, the determination of the thermally stressed state of rod structures, taking into account their mechanical properties (in particular, elasticity and thermal conductivity) is one of the topical scientific and tech-nical problems. Here, spatially one-dimensional unsteady boundary value problems (BVPs) of uncoupled ther-moelasticity are considered, which can be used to study various bar structures. This model describes well thermodynamic processes at low strain rates and here a unified technique is proposed for solving various BVPs typical of practical applications. Problems of determining the thermally stressed state of a thermoelastic rod using a model of uncoupled thermoelasticity are considered. Generalized solutions of non-stationary and stationary direct and semi-inverse BVPs under the action of power and heat sources of various types are con-structed on the basis of the method of generalized functions. Acting sources can also be specified by singular generalized functions, under different boundary conditions at the ends of the rod. Con-sidered are shock elastic waves that arise in such structures under the action of shock loads. Regu-lar integral representations of generalized solutions are obtained, which give an analytical solution to the stated BVPs.
The non-stationary boundary-value problems of the dynamics of thermoelastic rods are considered. Based on the method of generalized functions, generalized solutions of boundary value problems are constructed using a model of unbound thermoelasticity under the influence of non-stationary power and thermal loads of various types. The integral representations of the solution of the boundary-value problem are given, which make it possible to determine the thermally stressed state of the rod under the influence of various power and thermal influences from the known boundary displacements, stresses, temperature, and heat fluxes at the ends of the rod.
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