This review analyzes following numerical methods of a solution of problems of a sound diffraction on ideal and elastic scatterers of a non-analytical form: a method of integral equations, a method of Green’s functions, a method of finite elements, a boundary elements method, a method of Kupradze, a T-matrix method and a method of a geometrical theory of a diffraction.
References
[1]
Honl, H., Maue, A. and Westpfahl, K. (1961) Theorie der Beugung. Springer, Berlin.
[2]
Kleshchev, A.A. (2012) Hydroacoustic Scatterers. Prima, St. Petersburg.
[3]
Kleshchev, A.A. (2012) Method of Integral Equations in Problem of Sound Diffraction on Bodies of Non-Analytical Form. International Journal of Mechanics and Applications, 2, 124-128. https://doi.org/10.5923/j.mechanics.20120206.04
[4]
Kleshchev, A.A. (2013) Method of Integral Equations in Problem of Sound Diffraction on Bodies of Non-Analytical Form. Journal Marine Gazette, 2, 94-98.
[5]
Kleshchev, A.A. (1995) Method of Integral Equations in Problem of Sound Diffraction on Elastic Shell of Non-Analytical Form. Journal of Technical Acoustics, 2, 29-30.
[6]
Kleshchev, A.A. (1989) Sound Scattering by Ideal Bodies of Non-Analytical Form. Proceedings of LKI “The Сommon Ship’s Systems”, 95-99.
[7]
Seybert, A.F., Wu, T.W. and Wu, X.F. (1988) Radiation and Scattering of Acoustic Waves from Elastic Solids and Shells Using the Boundary Element Method. Journal of Acoustical Society of America, 84, 1906-1912. https://doi.org/10.1121/1.397156
[8]
Podstrigach, J.S. and Poddubniak, A.P. (1986) Scattering of Sound Beams at Bodies of Spherical and Cylindrical Form. Naukova Dumka, Kiev.
[9]
Varadan, V.V., Varadan, V.K. and Dragonette, I.R. (1982) Computation of a Rigid Body Scattering by Prolate Spheroids Using the T-Matrix Approach. Journal of Acoustical Society of America, 84, 22-25. https://doi.org/10.1121/1.387311
[10]
Grinblat, G.A., Kleshchev, A.A. and Smirnov, K.V. (1993) Sound Fields of Spheroidal Scatterers and Radiators in Plane Waveguide. Acoustical Journal, 39, 72-76.
[11]
Bostrom, A., Varadan, V.K. and Varadan, V.V. (1980) Acoustic, Electromagnetic and Elastic Wave Scattering—Focus on the Matrix Approach. Pergamon Press, New York.
[12]
Grinblat, G.A. and Kleshchev, A.A. (1994) The Scattering and the Emission of the Bodies Placed in the Plane Waveguide. Journal of Technical Acoustics, 1, 3-6.
[13]
Kharkevich, A.A. (1995) Spektrum and Analysis. Springer-Verlag, Berlin.
[14]
Kleshchev, A.A. (2015) Diffraction of Pulsed Sound Signals by Elastic Bodies of Analytical and Non-Analytical Forms, Put in Plane Waveguide. Zeitschrift fur Naturforschung A, 6, 419-427. https://doi.org/10.1515/zna-2015-0062
[15]
Brebbia, K. and Walker, C. (1982) Application of the Boundary Element Method in Engineering. MIR, Moscow. https://doi.org/10.1007/978-3-662-11273-1
[16]
Kupradzc, V.D. (1963) Methods of Potentials in the Theory of Elasticity. Fizmatgiz, Moscow.
[17]
Su, J.-H., Varadan, V.V., Varadan, V.K. and Flax, L.J. (1980) Acousic Wave Scattering by a Finite Elastic Cylinder in Water. Journal of Acoustical Society of America, 68, 685-691.
https://doi.org/10.1121/1.384727
[18]
Dushin, A., Il’mcnkov, S.L., Kleshchev, A.A. and Postnov, V.A. (1989) Use of Finite Element Method to Solution of Problems of Sound Radiating Elastic Shells. Proceedings Symposium “Interaction of Acoustic Waves with Elastic Bodies”, Tallinn, 26-27 October 1989, 89-91.
[19]
Peterson, B. and Strom, S. (1975) Matrix Formulation of Acoustic Scattering from Multilayered Scatterers. Journal of Acoustical Society of America, 57, 2-13.
https://doi.org/10.1121/1.380397
[20]
Numrich, S.K., Varadan, V.V. and Varadan, V.K. (1981) Scattering of Acoustic Waves by a Finite Cylinder Immersed in Water. Journal of Acoustical Society of America, 70, 1407-1411. https://doi.org/10.1121/1.387131
[21]
Kleshchev, A.A. (1974) Sound Diffraction on Bodies with Mixed Boundary Conditions. Acoustical Journal, 20, 632-634.
[22]
Kleshchev, A.A. (1984) Accuracy of Green’s Functions Method. Proceedings of LKI “Acoustics of Ships and Oceans”, 19-24.
[23]
Kleshchev, A.A. (1993) Method of Integral Equations for Solution of Problem of Sound Diffraction on Elastic Shell of Non-Analytical Form. Journal of Technical Acoustics, 2, 66-67.
[24]
Il’menkov, S.L. (2014) Green’s Functions Method in Problem of Sound Diffraction on Bodies of Non-Analytical Form. Journal Marine Intellectual Technologies, 2, 32-36.
[25]
Kleshchev, A.A. and Klukin, I.I. (1987) Principles of Hydroacoustis. Shipbuiilding, Leningrad.
[26]
Kleshchev, A.A. (2002) Diffraction and Propagation of Waves in Elastic Mediums and Bodies. Vlas, St Petersburg.
[27]
Il’menkov, S.L. and Kleshchev, A.A. (2014) Solution of Problems of Sound Scattering on Bodies of Non-Analytical form with Help of Method of Green’s Unctions. Journal Advances in Signal Processing, 2, 50-54.
[28]
Il’menkov, S.L., Kleshchev, A.A. and Klimenkov, S.L. (2016) Green’s Functions Method in Problem of Sound Diffraction on Elastic Shell of Non-Analytical Form. Proceedings of the 15th L. M. Brekhovskikh’s Conference, Moscow, 123-126.
[29]
Il’menkov, S.L. Kleshchev, A.A. and Klimenkov, A.S. (2014) The Green’s Function Method in the Problem of Sound Diffraction by an Elastic Shell of Noncanonical Shape. Journal Acoustical Physics, 60, 617-623. https://doi.org/10.1134/S1063771014060062
[30]
Kleshchev, A.A. and Klimenkov, A.S. (2013) Diffraction of Sound Impulses on Isotropic Bodies of Spherical Form (Strict Solution). Journal Advances in Signal Processing, 1, 68-77.
[31]
Kleshchev, A.A. (2006) Diffraction, Radiation and Propagation of Elastic Waves. Profprint, St Petersburg.
[32]
Kleshchev, A.A. (2012) Debye and Debye-Type Potentials in Diffraction, Radiation and Elastic Waves Propagation Problems. Journal Physical Acoustics, 58, 308-311.
https://doi.org/10.1134/S106377101202008X
[33]
Kaminetzky, L. and Keller, J.B. (1972) Diffraction Coefficients for Higher Order Edges and Vertices. Journal Applied Mathematics, 22, 109-134. https://doi.org/10.1137/0122013
[34]
Il’menkov, S.L. (2015) Calculation of Sound Scattering Characteristics of Elastic Body of Non-Analytical Form Using Boundary Element Method. Journal Marine Intellectual Technologies, 1, 30-36.
