Theoretical analysis of monochromatic waves propagating in elastic layer with gradient properties

The paper studies the wave propagation in an inhomogeneous flat layer using a linear law of variation of elastic properties along the layer thickness. Analytical solutions previously obtained for the case of gradient changes in density and modulus of elasticity and arbitrary relative changes of these quantities are supplemented by the solution found for changing the modulus at a constant density. The distribution of displacements and strains over the layer thickness is constructed and analyzed based on the found solutions determined by special functions. The distribution patterns are identified for displacements and strains from the frequency of external loading and gradients of the relative change in elastic parameters. The coordinate dependence is studied for the elastic wave velocity at linear variation of various elastic parameters. Research findings provide the basis for studying the non-uniform surface and transition layers with gradient elastic parameters and can be used to verify computer models of composite materials and materials with reinforcing coatings.