Eigenfunction expansion method to characterize Rayleigh waves in nonlocal orthotropic thermoelastic medium with double porosity

Abstract

The present manuscript addresses the Rayleigh wave propagation in a nonlocal orthotropic thermoelastic half-space with double porosity within the dual-phase-lag model of hyperbolic thermoelasticity. An eigenvalue technique is used to solve the resulting vector-matrix differential equation. Boundary conditions include stress-free, thermally insulated, and isothermal surfaces. The frequency equations of Rayleigh waves are derived in numerous scenarios. The well-known frequency equation of the Rayleigh wave in classical elasticity is derived as a particular case from the present problem. Surface particle motion during Rayleigh wave propagation is derived. Throughout the motion, elliptical surface particle paths are observed. To illustrate and validate the analytical developments, the numerical solution of frequency equations, eccentricities, and inclination of particle trajectories with wave normal are performed, and the computer-simulated results are graphically displayed. The various Rayleigh wave characteristics, such as propagation speed, attenuation coefficient, penetration depth, and specific loss against wave number, are presented graphically.