Diffraction of Pulses by Obstacles of Arbitrary Shape with a Robin Boundary Condition. Part B. Semi-Free Case

摘要

The velocity field resulting from the diffraction of a plane acoustic wave by a scattering obstacle of arbitrary shape with a Robin boundary condition, is found as the solution to an integro-differential equation. Numerical values are found for the velocity on the surface of a long cylinder of square cross section struck longitudinally by a plane pulse through an approximation of the integral by finite summations over specified steps in space and time. Comparison with exact solutions available for certain regions of space-time indicate good agreement. The solution for small values of K does not differ greatly from that for K = 0 indicating that the free boundary condition is a reasonable approximation for many physical problems. Values of K up to 1.0 (in appropriate nondimensional form) seem to give most reasonable rsults in terms of velocity; for K > 10 a formulation in terms of pressure seems more appropriate and for values 1 > K > 10 either form will do. (Author)