Propagation of eigenwaves in plane three-layer media

The paper considers the problem of propagation of natural stress waves in a strip that is in contact with an unbounded isotropic viscoelastic medium made of another material. It is assumed that there are no external influences during the propagation of natural waves. In some cases, the physical properties of viscoelastic materials are described by linear hereditary Boltzmann–Voltaire relations with integral differences of heredity kernels. Some of the layers can be elastic. In this case, the heredity kernels describing the rheological properties of the layers are identically zero. A system in which the rheological properties of the layers are identical (the nuclei of heredity of elements are equal to each other) will be called dissipatively homogeneous. In the particular case, when there are no external influences, the propagation of damped waves of the system is considered; — in the presence of external influences — forced. The main problem is the study of the dissipative (damping) properties of the system as a whole, as well as its stress-strain state.