On Dynamic Behavior of “Self-Stressed” Block Media. Part I. One-Dimensional Mechanico-Mathematical Model

A mechanico-mathematical statement of the problem on dynamic behavior of "self-stressed" block geomedia within a one-dimensional model is given. The structural elements of this model are considered to be absolutely solid bodies of the same dimensions, and the displacements between them are modeled by means of tension and compression of springs, the stiffness of which depends on their elongation along the gravitational force vector. An analytical solution is obtained for the linear case, and its properties are examined. As to the nonlinear statement, a method is proposed for reducing the problem to the set of linear equations.