Transient Wave Propagation in Functionally Graded Viscoelastic Structures

Transient wave processes in viscoelastic structures built from functionally graded material (FGM) still remain almost unexplored. In this article, the problem of the propagation of nonstationary longitudinal waves in an infinite viscoelastic layer of a FGM with plane-parallel boundaries is considered. The physical and mechanical parameters of the FGM depend continuously on the transverse coordinate, while the wave process propagates along the same coordinate. The viscoelastic properties of the material are taken into account employing the linear integral Boltzmann-Volterra relations. The viscoelastic layer of the FGM is replaced by a piecewise-homogeneous layer consisting of a large number of sub-layers (a package of homogeneous layers), thus approximating the continuous inhomogeneity of the FGM. A solution of a non-stationary dynamic problem for a piecewise-homogeneous layer is constructed and, using a specific example, the convergence of the results with an increase in the number of sub-layers in the approximating piecewise-homogeneous layer is shown. Furthermore, the problem of the propagation of nonstationary longitudinal waves in the cross section of an infinitely long viscoelastic hollow FGM cylinder, whose material properties continuously change along the radius, is also considered. The cylinder composed of the FGM is replaced by a piecewise-homogeneous one, consisting of a large number of coaxial layers, for which the solution of the non-stationary dynamic problem is constructed. For both the layer and the cylinder composed of a viscoelastic FGM, the results of calculating the characteristic parameters of the wave processes for the various initial data are presented. The influence of the viscosity and inhomogeneity of the material on the dynamic processes is demonstrated.