On the plane and Rayleigh-type waves propagation in the context of nonlocal two-phase-lag thermoelasticity

The principle objective of this manuscript is to investigate the propagation of time-harmonic plane as well as surface wave in an infinite linear nonlocal thermoelastic medium occupied the whole space, assuming a known wavelength. For the thermodynamic response, we adopt the dual-phase-lag (DPL) heat conduction model of generalized thermoelasticity. The study aims to analyze wave characteristics, including dispersion, damping, and coupling effects, under these advanced thermoelastic theories. Our analysis reveals six possible plane harmonic in time waves: two uncoupled transverse waves and four coupled longitudinal waves. The transverse waves propagate independently, remain undamped over time, and exhibit dispersion due to size-dependent effects, resulting in reduced wave speeds. The longitudinal waves, influenced by thermal effects, experience dispersion and temporal damping. Among these, a quasi-elastic wave and a stationary quasi-thermal wave decay exponentially to zero over time, while the presence of one or two dilatational quasi-thermal waves depends on the phase-lag parameters. For surface waves in a semi-infinite nonlocal thermoelastic medium, we derive the dispersion relation and the secular equation under a traction-free boundary condition allowing heat exchange. Numerical simulations illustrate the influence of nonlocality and DPL effects on wave behavior. The results provide deeper insights into wave propagation characteristics in advanced thermoelastic media, which may have implications for material design and wave-based applications.