Rayleigh‐type wave propagation in exponentially graded initially stressed composite structure resting on rigid and yielding foundations

•The present study aims to investigate propagation behaviour of Rayleigh-type wave in composite structure composed of exponentially graded viscoelastic materials under initial stress.•In particular, the upper stratum of the composite structure is constituted of Orthotropic viscoelastic material while lower stratum being constituted dry sandy viscoelastic sandy material.•The characteristics of Rayleigh-type wave propagating in the considered composite structure is analysed for the two distinct cases viz. when the composite structure is resting on rigid foundation (Case I), and, when the structure is resting on a yielding foundation (Case II).•Due to the dissipation involved in the system, the dispersion relation along with the attenuation coefficient for the Rayleigh type wave is obtained after using the admissible boundary conditions. As a special case of the problem, the obtained results are found in well agreement with the classical case.•The numerical results are presented owing to the material properties of Carbon-fiber, Prepreg for the upper stratum, while, Sandstone, Limestone for the lower stratum and are illustrated graphically.•The comparative analysis revealing the impact of viscoelasticity on different types of foundation on Rayleigh-type wave propagation caters to the salient feature of the study. The present study focuses on analyzing the characteristics of Rayleigh-type wave propagating in a composite structure comprised of exponentially graded orthotropic-viscoelastic stratum in welded contact with exponentially graded viscoelastic dry-sandy stratum resting on rigid (Case I) and yielding (Case II) foundations. Each stratum is under the influence of initial stresses. Employing the analytical treatment, the complex form of frequency equation has been derived for the two cases. The real part of the frequency equation represents the phase velocity profile of dispersive nature, while the imaginary part signifies the attenuation profile of Rt− wave. As a particular case of the problem, the obtained frequency equation agrees with the classical results. The numerical data of Carbon-fiber and Prepreg for the upper stratum, whereas Sandstone and Limestone for the lower stratum are considered for numerical computation and graphical illustration of the obtained results. The influence of initial stresses, functional gradient, sandiness, and width ratio (of the two strata) on the propagation of Rt− wave is examined on velocity and attenuation profiles for