Peculiarities of Lyave wave propagation in elastic functionally graded coatings

In the framework of the linear theory of elasticity, a problem on harmonic oscillations of a coating which are excited by a surface source is considered. The coating is modeled by a functionally graded layer with a monotone change of properties, the lower bound is rigidly fixed, an isotropic elastic material is used as a base material. The boundary problem for a system of partial differential equations is reduced to a system of ordinary differential equations with variable coefficients by means of methods of operational calculus. The use of a special substitution allows one to reduce the system of ordinary differential equations of the second order with variable coefficients to the system of initial Cauchy problems with the matrix whose elements do not contain derivatives of the functions which describe the properties of a medium material. To solve the initial boundary problem, a modified Runge-Kutta method that allows one to control a calculation error effectively is used. Using the problem on shear oscillations of a functionally graded layer as an example, the influence of the character, intensity and localization of the change of the material physical parameters on the structure and peculiarities of surface wave propagation is investigated. The cases of “acoustically” homogeneous coatings, in which velocities of space waves are not changed with respect to thickness, and the cases of “acoustically” inhomogeneous coatings are considered. The influence of the region of localization and of the character of the change of the material physical parameters is investigated in detail. It is determined that in some cases the dispersion characteristics can coincide for the coatings with different characters and regions of inhomogeneity localization. It is shown that unlike the dispersion characteristics, such integral characteristics as amplitude frequency characteristics (AFC) of the displacement of some surface waves and AFC of the surface are more sensitive to the character and localization of the coating inhomogeneity. The influence of the intensity of the change of the coating material density on the structure of the surface wave field is investigated. The possibility of controlling the resonance effects, i.e., the shear of resonance frequency, the increase or the suppression of the amplitude of the surface displacement beyond the resonance regions by means of changing the coating material properties is demonstrated.