Analysis of resonant excitation of layered and block media on the basis of discrete models

Resonant processes in structurally inhomogeneous materials of layered and block microstructure are studied in the framework of discrete models. Natural frequencies of longitudinal motion in a linear monatomic chain modeling a layered medium are determined for various boundary conditions. In order to analyze the behavior of the chain near resonant frequencies, the spectral portraits of the corresponding matrices are specified. It is shown that a special resonant frequency of rotational motion is observed when passing to the limit from a model of a monatomic chain with elastic connections to a moment continuum model. The particle rotation resistance is taken into account in this passage to the limit. This special resonant frequency does not depend on the chain length.