Sound Scattering by an Elastic Spherical Shell and its Cancellation using a Multi-pole Approach

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Authors

  • Eldad Jitzchak AVITAL Queen Mary University of London, United Kingdom
  • Neeshtha Devi BHOLAH Queen Mary University of London, United Kingdom
  • Giuseppe Cortez GIOVANELLI Federal University of Rio de Janeiro, Brazil
  • Touvia MILOH Tel Aviv University, Ramat Aviv Israel, Israel

Abstract

The scattering and transmission of sound by an elastic spherical shell is considered when it is subject to an incoming monochromatic planar wave. It is aimed to cancel the sound scattering using combinations of multi-pole sources located at the centre of a shell filled with compressible fluid. Assuming linear acoustics and structural dynamics, exact solutions are derived for total elimination of the sound scattering for three cases: a free-space, near a hard ground or near a free-surface, where in the last two cases it is assumed that the incoming wave propagates normal to the interface to maximize sound reflection back unto the source of the incoming wave. An elastic spherical shell of 1 m radius embedded in water and filled with air or oil is analysed to show the dominance of low-mode numbers for frequencies of less than 10 kHz and thus demonstrate the ability of this approach to damp acoustic scattering by means of low-order multi-poles inside the shell. Contour and mode distribution plots are also given and analysed.

Keywords:

sound scattering, structural dynamics, sound cancellation

References

1. Avital E.J., Korakianitis T., Miloh T. (2012), Sound scattering by a flexible plate embedded on free surface, Advances in Acoustics and Vibration, 2012, Article ID 473531, https://doi.org/10.1155/2012/473531.

2. Avital E.J., Miloh T. (2011), Sound scattering by free surface piercing and fluid-loaded cylindrical shells, Philosophical Transactions of the Royal Society A: Mathematical, 369, 1947, 2852–2863.

3. Avital E.J., Miloh T. (2015), Sound scattering and its cancellation by an elastic spherical shell in free space and near a free surface, Wave Motion, 55, 35–47.

4. Barosch D., Tomas J.L., Marchiano R. (2016), Observation of a single beam gradient force acoustical trap for elastic particles: acoustical tweezers, Physical Review Letters, 116, 2, 024301.

5. Crighton D.G., Dowling A.P., Ffowcs Williams J.E., Heckl M., Leppington F.G. (1992), Modern methods in analytical acoustics, Springer-Verlag.

6. Dutrion C., Simon F. (2017), Acoustic scattering reduction using layers of elastic materials, Journal of Sound and Vibration, 388, 53–68.

7. Huang H., Gaunaurd G.C.(1997), Scattering of a plane acoustic wave by a spherical elastic shell near a free surface, International Journal of Solids and Structures, 34, 5, 591–602.

8. Junger M.C., Feit D. (1972), Sound, structures and their interaction, MIT Press.

9. Kim D., Avital E.J., Miloh T. (2014), Sound scattering and its reduction by a Janus sphere type, Advances in Acoustics and Vibration, 2014, Article ID 392138, https://doi.org/10.1155/2014/392138.

10. Meng H., Wen J., Zhao H., Wen X. (2012), Optimisation of locally resonant acoustic metamaterials on underwater sound absorption characteristics, Journal of Sound and Vibration, 331, 1, 4406–4416

11. Partridge C. (1996), Acoustic scattering from viscoelastically coated bodies, Journal of the Acoustical Society of America, 99, 1, 72–78.

12. Rayleigh J.W.S. (1945), The theory of sound – Volume II, Dover Publications.

13. Sessarego J.P., Cristine P., Grigorieva N.S., Fridman G.M. (2012), Acoustic scattering by an elastic spherical shell near the seabed, Journal of Computational Acoustics, 20, 3, 1250006.

14. Zannin P.H.T. (2000), Factors that influence the calculation of acoustic scattering by the method of source simulation, Archives of Acousics, 25, 3, 317–329.