### ASA 125th Meeting Ottawa 1993 May

## 2aPA3. Dynamic finite-element calculation of excitation modes in periodic
and disordered Lucite--steel composite systems.

**Ping Sheng
**

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Minyao Zhou
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*Exxon Res. and Eng. Co., 79 Rte. 22 East, Annadale, NJ 08801-0998
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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.