Computational structural acoustics applied to scattering of sound by spherical shells

Abstract

Computational structural acoustics is the use of exact large-scale computations and computer graphics to study the behavior of elastic waves in structures. This approach is applied here to the scattering of sound by spherical shells in water. It is shown that rotational waves, found earlier in solid spheres and cylinders [Hickling et al., J. Acoust. Soc. Am. 89, 971–979 (1991)], continue to occur even for shells that are quite thin. In particular, when a thin shell in water is excited by incident continuous sound waves, small rotational waves occur, whose center of rotation and surrounding rotational displacement are inside the boundaries of the shell structure. For a thin shell, it appears to be impossible to excite a natural mode of the shell. This is probably due to the dense confluence of the frequencies of the fundamentals of the natural or free modes of vibration that occurs as the shell becomes thin. Radiation damping will cause these fundamentals to overlap, making it difficult to excite any particular natural mode. This is in contrast to the results obtained previously with the solid sphere, where it appeared to be possible to excite natural modes with continuous sound in water. The results for a thin shell are shown to be consistent with thin-shell theory for low and intermediate values of ka.