Nonlinear Rayleigh wave propagation in a layered half-space in dual-phase-lag

Area of Science:

• Solid Mechanics
• Thermoelasticity
• Wave Propagation

Background:

• Nonlinear wave propagation in layered media is crucial for understanding material behavior under thermal stress.
• Dual-phase-lag (DPL) theory accounts for microstructural effects in heat conduction, offering a more realistic model than classical theories.
• Temperature-dependent thermal properties significantly influence heat transfer and wave dynamics in materials.

Purpose of the Study:

• To investigate nonlinear Rayleigh wave propagation in a thermoelastic layered medium (slab on a half-space).
• To analyze the impact of temperature-dependent heat conductivity and thermal relaxation times on wave propagation.
• To assess the nonlinear coupling effects and interface phenomena in the layered system.

Main Methods:

• Utilizing dual-phase-lag (DPL) theory for heat conduction analysis.
• Applying Poincaré expansion to solve nonlinear wave equations and generate higher harmonics.
• Numerical evaluation of wave propagation characteristics and interface behavior.

Main Results:

• Temperature, heat flux, and one stress component exhibit jumps at the interface between the slab and half-space.
• The jump in heat flux is primarily observed in the first order of nonlinearity.
• The presence of the slab accelerates the damping of wave solutions with increasing depth in the half-space.

Conclusions:

• Interface jumps in thermal and mechanical quantities are significant features of nonlinear wave propagation in layered thermoelastic media.
• The temperature dependence of heat conductivity and thermal relaxation times play a crucial role in nonlinear wave dynamics.
• The layered structure, specifically the slab, enhances the dissipative behavior of the system, leading to faster wave damping.