Выпуск: 1 , Том: 9 , Год издания: 2014

This paper studies properties of a continuum with structure. The characteristic size of the structure governs the fact that difference relations do not automatically transform into differential ones. It is impossible to consider an infinitesimal volume of a body, to which we could apply the major conservation laws, because the minimal representative volume of the body must contain at least a few elementary microstructures. The corresponding equations of motions are the equations of infinite order, solutions of which include, along with sound waves, the unusual waves propagating with abnormal low velocities, not bounded below. It is shown that in such media weak perturbations can increase or decrease outside the limits. The number of complex roots of the corresponding dispersion equation, which can be interpreted as the number of unstable solutions, depends on the specific surface of cracks and is an almost linear dependence on a logarithmic scale, as in the seismological law of Gutenberg-Richter. If the distance between one pore (crack) to another one is the random value with some distribution, we must write another dispersion equation and examine different scenarios depending on statistical characteristics of the random distribution. In this case, there are sufficient deviations from Gutenberg-Richter law, and this theoretical result corresponds to some field and laboratory observations