Memory response on thermoelastic deformation in a solid half-space with a cylindrical hole

Abstract

The present article deals with the memory response on thermal wave propagation emanating from a cylindrical hole in an unbounded thermoelastic solid. Here, we have theoretically demonstrated two aspects of thermal waves in elastic materials with memory. First, the characteristics of thermoelastic disturbances originated from the hole in an unbounded elastic solid under the light of generalized thermoelasticity theory with memory-dependent derivatives (MDDs). For numerical implementation, cylindrical polar coordinate system with radial symmetry is considered. An integral transform method and, while in inverse transformation, an efficient and pragmatic NILT (numerical inverse Laplace transform) is adopted. Second, a comparison study is being made on the memory response of thermal waves with and without energy dissipation into the medium. Finally, parameter studies are performed to evaluate the effect of the kernel function and time delay. For thermal wave, the results show appreciable differences with those in the usual thermoelasticity theory.

Keywords:

• Thermal memory
• memory-dependent derivatives
• generalized thermoelasticity
• energy dissipation
• eigenfunction expansion method