(untitled) (European Journal of Pure and Applied Mathematics, 2026)
The present study develops a generalised version of the exponential Lord-Shulman thermoelasticity theory that takes into account the combined effects of body forces and time-harmonic thermal sources. The appropriate governing equations are generated and analytically solved by means of the harmonic wave technique, assuming that the medium under discussion is traction-free. Displacements, dilatation, temperature distribution, and stress components are among the non-dimensional findings for field variables. Comprehensive numerical evaluations are used to support the explicit analytical formulas developed for these variables. Examining how the operator expansion order and temporal evolution affect the physical fields’ behaviour is assumed particular attention. The significance of higher-order modelling in capturing complex dynamic thermoelastic responses is highlighted by graphical representations that unequivocally show that the operator expansion order plays a crucial role in influencing all thermoelastic parameters.