ASA 126th Meeting Denver 1993 October 4-8

2pSA7. An optimized finite-difference scheme for high-loss viscoelastic materials.

Mark A. Hayner J. Robert Fricke

Dept. of Ocean Eng., Rm. 5-218, 77 Massachusetts Ave., Cambridge, MA 02139

In an effort to attenuate helical wave energy in cylindrical shells and reduce its coupling to the surrounding fluid, various constrained layer shell designs are being investigated. The shell skins being considered have an effective loss factor (eta) of order unity. As part of this effort, an efficient time-domain finite-difference scheme is being developed with the ultimate objective of constructing 3-D models of such shells. Optimization of relaxation time spectra for low-(eta) materials, done by Blanch et al. [Technical Report, Rice University, Dept. of Geology and Geophys. (1993)], is extended to high (eta) by matching both the real and imaginary parts of the complex modulus with experimental data. To improve scheme accuracy further, the matching is done again after discretization to minimize the effects of numerical dispersion and dissipation. Data has been matched for a material with (eta)=0.5 over one frequency octave using a Crank--Nicholson scheme with two relaxation times. The general applicability, accuracy, and efficiency of this numerical optimization process are subjects of continuing research. Comparison between numerical simulation and analytical solutions are given for wave propagation in a constrained layer flat plate. [Work supported by ONR.]