Archives of Acoustics, 41, 3, pp. 461–472, 2016
10.1515/aoa-2016-0045

Acoustic Scattering of 3D Complex Systems Having Random Rough Surfaces by Scalar Integral Equations

Juan Antonio GUEL-TAPIA
Centro de Investigaciones en Óptica
Mexico

Francisco VILLA-VILLA
Centro de Investigaciones en Óptica
Mexico

Alberto MENDOZA-SUÁREZ
Universidad Michoacana de San Nicolás de Hidalgo
Mexico

Héctor PÉREZ-AGUILAR
Universidad Michoacana de San Nicolás de Hidalgo
Mexico

We propose a numerical surface integral method to study complex acoustic systems, for interior and exterior problems. The method is based on a parametric representation in terms of the arc’s lengths in curvilinear orthogonal coordinates. With this method, any geometry that involves quadric or higher order surfaces, irregular objects or even randomly rough surfaces can be considered. In order to validate the method, the modes in cubic, spherical and cylindrical cavities are calculated and compared to analytical results, which produced very good agreement. In addition, as examples, we calculated the scattering in the far field and the near field by an acoustic sphere and a cylindrical structure with a rough cross-section.
Keywords: integral equations; Helmholtz equation; acoustic scattering.
Full Text: PDF

References

Arfken G.B., Weber H.J., Harris F.E. (2013), Mathematical Methods for Physicists, 7th edition, Academic Press, USA.

Burton A.J., Miller G.F. (1971), The application of integral equation methods to the numerical solution of some exterior boundary-value problems, Proc. Roy. Soc. Lond., 323, 201–210.

Chowdhury N.M.A., Takada J.I., Hirose M. (2004), 3D scalar-formulation of IE-MEI for acoustic scattering, IEEE Conf. Antennas Propag. Soc. Int. Symp., 3, 2251–2254.

Hanninen I., Taskinen M., Sarvas J. (2006), Singularity substraction formulaes for surface integral equations with rwg, rooftop and hybrid basis functions, Progr. Electromag. Res., 63, 243–278.

Huacasi W., Mansur W.J., Azevedo J.P.S. (2003), A novel hypersingular B.E.M. formulation for three-dimensional potential problems, J. of the Braz. Soc. of Mech. Sci. & Eng., 25, 364–372.

Iturarán-Viveros U., Sánchez-Sesna F.J., Luzón F. (2007), Boundary element simulation of scattering of elastic waves by 3D cracks, J. Appl. Gephys., 64, 70–82.

Jun L., Beer G., Meek J.J. (1985), Efficient evaluation of integrals of order 1/r, 1/r2, 1/r3 using a gaussian quadrature, Eng. Analysis, 2, 118–123.

Junger M.C., Feit D. (2004), Sound, structures, and their Interaction, MIT Press, USA.

Kirkup S. (1998), The boundary element method in acoustics, Integrated Sound Software.

Li S., Huang Q. (2011), A new fast multipole boundary element method for two-dimensional acoustic problems, Comp. Meth. Appl. Mech. Eng., 200, 1333–1340.

Maradudin A.A., Méndez E.R., Michel T. (1990), Enhanced backscattering of light from a random grating, Ann. Phys., 203, 255–307.

Mendoza-Suárez A., Méndez E.R. (1977), Light scattering by a reentrant fractal surface, Appl. Opt., 36, 3521–3531.

Mendoza-Suárez A., Pérez-Aguilar H. (2015), Optical response of a photonic crystal waveguide that includes a dispersive left-handed material, Photonic. Nanostruct., 14, 93–100.

Mendoza-Suárez A., Corona U.R., Luna R.E. (2004), Effects of wall random roughness on te and tm modes in a hollow conducting waveguide, Opt. Commun., 238, 291–299.

Mendoza-Suárez A., Villa-Villa F., Gaspar-Armenta J.A. (2006), Numerical method based on the solution of integral equations for the calculation of the band structure and reflectance of one and two-dimensional photonic crystals, J. Opt. Soc. Am. B, 23, 2249–2256.

Mendoza-Suárez A., Villa-Villa F., Gaspar-Armenta J.A. (2007), Band structure of two-dimensional photonic crystals that include dispersive left-handed materials and dielectrics in the unit cell, J. Opt. Soc. Am. B, 24, 3091–3098.

Mendoza-Suárez A., Pérez-Aguilar H., Villa-Villa F. (2011), Optical response of a perfect conductor waveguide that behaves as a photonic crystal, Prog. Electromagn. Res., 121, 433–452.

Morse P.M., Ingard K.U. (1968), Theoretical acoustics, Princeton University Press, USA.

Pedersen H.A., Sánches-Sesma F.J., Campillo M. (1994), Three-dimensional scattering by two-dimensional topologies, Bulletin of the Seismological Society of America, 84, 1169–1183.

Pérez-Aguilar H., Mendoza-Suárez A., Tututi E., Herrera-Gonzalez I. (2013), Chaotic behavior of a quantum waveguide, Physica B, 411, 93–98.

Piscoya R., Ochmann M. (2014), Acoustical boundary elements: theory and virtual experiments, Archives Acoustics, 39, 4, 453–465.

Pointer T., Liu E., Hudson J. (1998), Numerical modelling of seismic waves scattered by hydrofractures: application of indirect boundary element method, Geophys. J. Int., 135, 289–303.

Tadeu A.J.B., Goginho L., Santos P. (2001), Performance of the BEM solution in 3D acoustic wave scattering, Adv. Eng. Soft., 32, 629–639.

Tong M.S., Chew W.C. (2010), Novel approach for evaluating hypersingular and strongly singular surface integrals in electromagnetics, IEEE Trans. Antenn. Prop., 58, 3593–3601.

Ursell F. (1973), On the exterior problems of acoustics, Proc. Camb. Phil. Soc., 74, 117–125.

Zaman S.I. (2000), A comprehensive review of boundary integral formulations of acoustic scattering problems, Sci. Tech. Special Review, pp. 281–310.




DOI: 10.1515/aoa-2016-0045

Copyright © Polish Academy of Sciences & Institute of Fundamental Technological Research (IPPT PAN)