Dynamic Response and Dispersion Analysis of a Damped Heterogeneous Coating over a Homogeneous Elastic Half-Space

This study models the dynamic response of a damped heterogeneous coating layer over a homogeneous elastic half-space via the shear horizontal equation of motion. The so-called partial nonhomogeneous has been considered in the coating, where only the density of the material features the inhomogeneity parameter. This unusual consideration, motivated by the viscoelasticity setting, gives rise to the realization of Airy's differential equation in the coating layer that poses Airy's functions of the first and the second kinds, respectively. Moreover, the resulting dispersion relation has been utilized and analyzed, assessing the impact of the involved parameters. The study realized that an increase in both the damping coefficient and the inhomogeneity parameter accelerates the dispersion of waves in the media. Additionally, once the case of the doubly coated half-space is analyzed, as an extension of the earlier setup, it is noted that the case of a doubly coated half-space is more responsive to the excitations, which is pretty geared by the composition of different layers. In addition, more modes are noted when more coatings are wrapped over the half-space.