Acoustic waves that are incident on this submarine will have complex interactions with it. Inside the hull are many smaller structures and equipment. As is the case with electromagnetics, the analysis of the scattering and radiation of sound waves by such complex structures into the surrounding fluid medium or into its passenger cabin can also use asymptotically valid methods. This asymptotic analysis is possible for small or large values of the ratio of characteristic dimensions to acoustic wavelengths.

However, there is a large intermediate range in which this capability is severely limited. The difficulties involved can be illustrated by considering a simple example of an empty submarine hull submerged in water. The surrounding water supports the acoustic wavelength while the steel shell of the hull supports multiple elastic waves with wavelengths ranging from one-fifth of the acoustic wavelength to orders of magnitude larger than the acoustic wavelength. Thus the analysis of this system involves a very wide range of wavelengths that are amenable to widely differing analytic techniques. Due to the strong coupling between wave types, all interactions at different wavelengths must be treated accurately.

The comprehensive analysis of acoustic scattering by large complex structures has long had importance for the Navy. Furthermore, U.S. industry is under increasing pressure to develop analytic and modeling capabilities for complex structural acoustic systems with high strength, light weight, and low noise and vibration. The recognition of these needs has made it imperative to optimize the strength-to-weight and vibration-to-weight ratios.

Whether the interest is noise in submarines, aircraft, or automobiles, engineers and scientists are still unable to predict accurately and reliably the midfrequency acoustic behavior of large complex structures. These needs, coupled with the opportunities offered by broadening computational horizons, have renewed interest in analytical models of systems that in principle are understood, but the analysis of which is limited in practice by complexity.

Large-scale structures in acoustics and electromagnetics exemplify this trend. The VLSI chip and the submarine indicate the general characteristics of large-scale complex structures that need to be better understood:

  • First, models of these large-scale complex structures require the coherent combination of asymptotic, computational, empirical, and exact analysis.

  • Second, the analysis of large-scale systems generally is multidisciplinary in nature.

  • Third, efficiency and accuracy of the analytic techniques are essential for models of realistic large-scale systems.

At this symposium, the ONR looks forward to learning how cooperative research and development in different sciences and technologies will lead to a greater understanding of large-scale systems. I am impressed with the high quality of the abstracts and the breadth of the technical material to be presented. This symposium is indeed appropriate for the National Academy of Sciences because of the excellence of the speakers and their subjects. I am sure you will advance our knowledge of large-scale structures during your time here.

Thank you and best wishes for a successful symposium.

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