Glukhov A. Propagation of the axisymmetric elastic waves in laminated materials with initial stresses at slipping layers

The thesis is devoted to study of propagation of the axisymmetric elastic waves in layered laminated materials with initial stresses at slipping layers. Composite material, which has a periodic structure and consists of layers of two alternating types, is considered. For each type of layers, the materials and the initial stress-strain states are the same. Materials of the layers are compressible or incompressible with an arbitrary form of elastic potentials. The initial stress state is homogeneous and symmetric. Only the normal stresses and movements are continuous at the boundaries of the layer, and tangential stresses equal zero. The case of wave propagation along the layers is considered. The study was conducted within the framework of a three-dimensional linearized theory of the propagation of elastic waves in bodies with initial stresses. The dispersion equations for quasi-transverse and quasi-longitudinal waves in the case of compressed materials and quasi-transverse wave in the case of incompressible materials, as well as their long-wave approximations are obtained. The analytical results are given in general terms for materials with an elastic potential of arbitrary shape. In a wide range of frequency values, numerical studies of dispersion relations for a quasi-transverse wave propagating in a highly elastic layered composite material for various contact conditions between layers of a composite material, different initial stresses, geometric parameters and elastic potentials have been carried out.