Differaction of a pulsed longitudinal shear wave in an orthrotropic massif with a cavita

Abstract

We propose a method for numerical-analytic solution of a boundary-value problem for diffraction of a longitudinal shear wave in the form of a triangular pulse on a cylindrical tunnel cavity of circular crosssection in an unbounded rectilinearly orthotropic massif. The basis of the proposed approach consists of methods of spectral decomposition of periodically continued pulses with the introduction of small correcting perturbations of the elastic constants of the massif. The characteristics of the stress-strain state in the basic stationary problems are ezpressed in terms of the generalized wave potentials which become the classical potentials of longitudinal and transverse waves for an isotropic medium. We study the influence of the space-time structure of the pulse on the concentration of the contour dynamical stresses under different phases of mutual position of the leading edge of the pulse and the contour of the section of the cavity in a massif of isotropic and anisotropic basalt. 4 Figures. Bibliography: 6 titles.