Exxon Res. and Eng. Co., 79 Rte. 22 East, Annadale, NJ 08801-0998
Recent experiment by L. Ye et al. on Lucite--steel composite system [Phys. Rev. Lett. 69, 3080 (1992)] has demonstrated the localization of bending waves. This is particularly surprising on first sight because the huge acoustic impedance mismatch between Lucite and steel would seem to imply that Lucite should have very little effect on the steel. A dynamic finite-element approach was used to calculate the excitation modes in a 2-D periodic structure consisting of a steel plate decorated by a checkerboard pattern of Lucite blocks. The results show that the coupling between the steel plate bending wave and the flexural resonances of the Lucite blocks can drastically alter the dispersion relation of the bending wave, whereas the effect of periodicity is minimal. Since the Lucite flexural resonance frequencies depend on the Lucite block height, its effect on the bending wave can be tuned in terms of the frequency as demonstrated experimentally by Ye et al. This talk will also report the results of calculations on a random 1-D Lucite--steel system. In particular, the localization characteristics will be emphasized.