A solution of the problem of oscillations of a die on a two-phase base under a seismic impact

A method of studying nonstationary seismic oscillations of a cylindrical die on a two-phase base is developed, which is modeled with an application of the theory of M. Bio-Ya. I. Frenkel'—V.N. Nikolaevskii. In the solution of the problem integral transforms are used in combination with the method of orthogonal polynomials for a representation of required contact stresses. Numerical results are given, which characterize a change of coefficients of expansion of the series of contact stresses with respect to time, including their resultant, under different masses of the die. Transformations of the projection diagram of normal contact stresses are shown as time passes.Translated from Dinamicheskie Sistemy, No. 7, pp. 32–41, 1988.