Time-shift operators with exponential growth in generalized thermoelasticity

A generalized framework of exponential thermoelasticity is used to study the coupled thermal-mechanical behavior of elastic media under time-harmonic thermal excitation. The proposed formulation unifies exponential time-shift operators of various orders and provides a unified and flexible extension that includes the classical thermoelastic model as well as several generalized theories as special examples. By carefully examining its influence, the paper demonstrates that the operator order has a significant impact on the temporal and spatial evolution of temperature, displacement, and stress fields. In particular, increasing the operator order results in response profiles that are smoother and more physically consistent, enhances wave attenuation, and effectively suppresses spurious and nonphysical oscillations. From a physical viewpoint, the exponential operator introduces delayed constitutive effects associated with finite thermal-wave propagation and memory-dependent material behavior.