Dynamics of a Thermoelastic Rod Under Unsteady Thermal and Force Influences

Abstract

Rod elements are extensively utilized in various technological fields. An unsteady temperature field induces a time-varying stress field within the rod structure, impacting its strength and reliability during operation. Determining the thermally stressed state of rod structures, considering their mechanical properties (especially elasticity), is a significant scientific and technical challenge. The application of mathematical modeling methods enables the study of thermodynamic processes occurring within a structure and its elements, allowing for the determination of their dynamic and strength characteristics during the design phase. This paper addresses the Cauchy problem for the dynamics of a thermoelastic rod under arbitrary initial conditions and subjected to force and thermal influences. By employing the Green’s tensor for thermoelasticity equations, an analytical solution is derived, which determines deformations, stresses, and temperatures at any point along the rod at any given time, provided the initial state and the acting force and heat sources are known. Numerical calculations of temperature and displacement are presented for cases involving pulsed concentrated force and heat sources. Additionally, solutions to Cauchy problems under the influence of regular force and heat sources distributed along the rod are computed. The developed program allows for the investigation of thermodynamic processes in rods with various physical and mechanical properties, under the influence of both distributed and concentrated pulsed thermal and force sources, described by singular generalized functions.