State‐Space Approach to Characterize Rayleigh Waves in Nonlocal Piezothermoelastic Orthotropic Medium With Phase‐Lags

ABSTRACT This manuscript uses Eringen's nonlocal thermoelasticity theory to study Rayleigh wave propagation in a homogeneous piezo‐thermoelastic orthotropic half‐space. This subject is discussed using the three‐phase‐lag (TPL) model of hyperbolic thermoelasticity and the state‐space method via the Cayley‐Hamilton theorem. The fundamental constitutive relations for nonlocal piezo‐thermoelastic orthotropic media have been established. Thermally insulated, or isothermal, surfaces and stress‐free, open, or closed circuits are instances of boundary conditions. The Rayleigh wave's frequency equations are obtained in various kinds of instances. Certain special and particular instances have been deduced and compared with earlier studies. The particle path on the surface during Rayleigh wave propagation is elliptical. To illustrate and validate the analytical developments, the frequency equations, specific loss factor, eccentricities, and inclination of particle trajectories with wave normals are numerically solved. The computer‐simulated results are then shown graphically. The various Rayleigh wave properties, such as propagation speed, attenuation coefficient, penetration depth, and specific loss against wave number, are graphically compared for various conditions in the presence and absence of nonlocal parameters. The effects of nonlocal parameters on various Rayleigh wave characteristics and a comparison of three hyperbolic thermoelasticity models including Lord‐Shulman (LS), dual‐phase‐lag (DPL), and three‐phase‐lag (TPL) are presented. Subsequently, a comparison of the GN‐III and GN‐II models has been shown in both local and nonlocal settings. Propagation speed and specific loss exhibit the opposite tendency when comparing the GN‐II and GN‐III models. Additionally, the famous Rayleigh wave frequency in classical elasticity has been derived as a result of this investigation.