INTEGRAL CHARACTERISTICS OF SOLUTIONS OF SPATIAL PROBLEMS ON THE DYNAMIC IMPRESSION OF SOLID BODIES IN CONTINUOUS MEDIA

Spatial problems of the impression of arbitrary bodies into a half-spa ce occupied by a continuous medium are examined in a geometrically lin ear formulation. It is shown that if the governing relationships are l inear, while the medium is homogeneous inhomogeneous only in depth, th en in the initial interaction stage the problem of determining the int egral characteristics of the solutions (the integral displacements and resultant forces) is equivalent to the problem of plane-wave propagat ion in this same medium. Expressions are obtained for the interaction forces between the body and the medium (resultant forces) in a number of specific cases: a non-linear elastic medium with initial stresses, viscoelastic media, and an isotropic elastic medium, smoothly inhomoge neous in depth. It is shown that all the results hold for both vertica l impression and for impression with rotation. Expressions for the res ultant forces have been obtained earlier by other methods in the follo wing problems: vertical impression for an acoustic medium /1/ and an i sotropic elastic medium /2, 3/, impression with rotation for an isotro pic elastic medium /4/ and vertical impression in an anisotropic elast ic medium /5/.