Theoretical study of three dimensional elastic band gaps with the finite-difference time-domain method

This work presents results on finite-difference time-domain (FDTD) integration of the full three dimensional elastic wave equation in nonhomogenous periodic media, for understanding the propagation and gap existence in these media. Extensive calculations are compared with plane wave expansion (PWE) data for different three dimensional systems consisting of Pb spheres in epoxy matrix forming an fcc lattice. The method of solving the wave equation provides good convergence and the agreement with the PWE method is excellent. The FDTD method, however, can handle cases such as fluids in solids which cannot be treated with the PWE method. Transmission results are presented for the case of Hg spheres in Al with fcc lattice, in order to prove the general use of the FDTD method.