Small-Scale Effects on the Reflection of Thermoelastic Plane Waves in an Elastic Solid with Variable Moduli

This study investigates the reflection and propagation of thermoelastic plane waves in a nonlocal elastic solid with temperature-dependent material properties, using the Lord-Shulman thermoelasticity model and Eringen’s nonlocal elasticity theory. Three wave modes are identified: two coupled longitudinal waves and one shear wave, all of which exhibit dispersion and attenuation due to elastic nonlocality. The shear wave experiences a critical frequency, while the longitudinal waves face conditional critical frequencies. Reflection at a stress-free thermally insulated boundary is analyzed, and amplitude ratios of reflected waves are derived. Numerical results for copper-like materials reveal that nonlocality significantly influences all wave modes, while thermal effects impact only the longitudinal waves. Additionally, nonlocality reduces the shear wave speed compared to classical theory. Additionally, nonlocality reduces the shear wave speed compared to classical theory. The novelty of this work lies in the combined consideration of nonlocal elasticity, temperature-dependent moduli, and Lord-Shulman thermoelasticity, which has not been previously studied for reflection of thermoelastic waves at thermally insulated/isothermal boundaries. This approach provides a more accurate representation of wave behavior in microscale thermoelastic media with varying thermal environments.