IV 157 2. Transform Inversion at the Epicenter for Materials Satisfying Condition (1) of Table 11 162 3. Discussion of the <.v-Plane Branch Points and the Cagniard Path When the Real <.v-Axis is Not Free of Branch Points 166 4. Transform Inversion at the Epicenter for Materials Satisfying Conditions (2) and (3) of Table 11 169 5. Discussion of the Epicenter Vertical Displacement for Some Hexagonal Crystals
Two problems connected with the transient motion of an elastic body acted upon by a moving-point force are solved by an application of the dynamic Betti-Rayleigh reciprocal theorem. This theorem, which is the analogue of Green’s theorem for the scalar wave equation, permits the solution to be written as a single expression, irrespective of the value of the (constant) moving-force velocity
v
v
. In particular, the displacement field in an infinite elastic body, due to a transient-point body force moving, in a straight line, is given in a simple form. Next the surface motion of an elastic half-space acted upon by a transient pressure spot moving in a straight line is analyzed for a material for which Poisson’s ratio is one-fourth. The normal displacement is expressed in a simple manner, but the tangential displacement is quite complicated and is not fully expressible in terms of elementary functions. Singularities of the displacement fields are identified and discussed.
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