A thermal shock problem for a viscoelastic annular disk using novel L–S phase-lag models

This paper demonstrates a comprehensive study of generalized coupled thermoelastic responses in annular disks, formulated within the framework of the Lord–Shulman generalized theory of thermoelasticity. The governing system of coupled thermoelastic equations is first established in cylindrical coordinates and solved in the Laplace domain. A numerical inversion technique is then employed to transform the solutions back into the physical time domain, enabling the analysis of transient thermoelastic fields. The dynamic thermoelastic response of viscoelastic annular disks subjected to thermal shock loading can be estimated with the help of the established models. A clear picture of the transient thermo-mechanical response is provided by the study, which gives the time histories of displacement, temperature, dilatation, and stress distributions within the disk. The outcomes anticipated by the simpler theory are compared with those derived from the improved models. It is demonstrated that more realistic transient properties, including finite propagation speeds, stress localization, and relaxation behaviour, are captured by the improved Lord–Shulman formulations.