The Cauchy problem for elastic waves in an anisotropic medium

摘要: The propagation of elastic waves in a homogeneous solid is governed by hyperbolic system three linear second-order partial differential equations with constant coefficients. When the also isotropic, form these well known and provides foundation conventional theory elasticity (Love 1944). explicit solution initial value, or Cauchy, problem for isotropic case was found Poisson, different way Stokes (1883). If disturbance sharp concentrated, resulting at field point will consist an pressure wave, continuous wave certain period, final shear wave. then ceases. Here we shall consider medium which but not describe, using Fourier transforms, produced local disturbance. again consists lasts definite period time, number waves, detailed nature may, highly anisotropic media, be very much more complicated. may arrive advance first though it always terminate last exceed 75. appears as sum modes, correspond to sheets surface. geometry this surface, quite complicated (Musgrave 1954 ), qualitatively determines solution. These calculations serve study time-dependent waves. There mathematical interest example surface have types singularities usually considered existing general equations.