state space approach to characterize rayleigh waves in a nonlocal thermoelastic layer lying over a half-space with voids under three-phase-lag model

The paper deals with the propagation of rayleigh waves in a nonlocal thermoelastic isotropic layer that is lying over a nonlocal thermoelastic isotropic half-space within the framework of eringen's nonlocal elasticity in the three-phase-lag model with voids present. a vector matrix differential equation is obtained by using the state space method to the considered equations. the field equations for an isotropic homogeneous nonlocal thermoelastic material with voids are developed by first constructing the energy density function from the fundamental variables and then deriving constitutive relations. this study also yielded certain special situations, which are then contrasted with the findings of other researchers. the rayleigh wave frequency equation is calculated, and many specific instances are also inferred. a graphic representation of the effects of voids and nonlocality on several rayleigh wave properties is shown. the behavior of granular materials, such as rock, soils, and artificially created porous things, appears to be adequately described by this hypothesis. the attenuation coefficient, penetration depth, specific loss, and propagation speed are among the various rayleigh wave properties for which numerical values are calculated and displayed graphically.