Method of Green’s Functions for the Problem of Sound Diffraction on Elastic Shell of Non-Analytical Form

Authors

  • S. L. Ilmenkov Saint – Petersburg State Navy Technical University, 190008, Saint, Petersburg, Lotsmanskaya st, 3, Russia
  • A. A. Kleshchev Saint – Petersburg State Navy Technical University, 190008, Saint, Petersburg, Lotsmanskaya st, 3, Russia
  • A. S. Klimenkov Saint – Petersburg State Navy Technical University, 190008, Saint, Petersburg, Lotsmanskaya st, 3, Russia

DOI:

https://doi.org/10.15379/2408-977X.2014.01.01.2

Keywords:

Diffraction, Method of Green’s functions, Non–analytical surface, Boundary conditions, Scatterer

Abstract

The real scatterers have a non–analytical form and, therefore, the variable separation method (Fourier series method) for calculation of the reflected sound field cannot be applied to them. This article presents the method of Green’s functions and methods of the dynamic theory of elasticity for the solution of the problem of sound diffraction on elastic shell of a non–analytical surface. Furthermore, this work includes the detailed analysis of the solution of this problem and calculation of the angular characteristics of the sound scattering by non-analytical scatterers

References

Ionov AV, Mayorov VS. Sonar characteristics of underwater objects. St. Petersburg. Publishing of Central Research Institute. Acad. Krylov, 2011.

Seybert AF, Wu TW, Wu X. F. Radiation and scattering of acoustic waves from elastic solids and shells using the boundary element method. // J. A. S. A. 1988; 84(5); 1906 - 1912.

Varadan VV, Varadan VK, Dragonette LRC. Computation of a rigid body scattering by prolate spheroids using the T - matrics approach. // J. A. S. A. 1982; 84(1): 22 - 25.

Brebbia K, Walker S. The Application of the boundary element method in engineering. M: Mir. 1982.

Aben MK, Lage AI. Calculation of diffraction of elastic shells in the liquid by the methods of boundary and finite elements. Tallinn, 1989.

Kees AL. Sound diffraction on shells with complicated form. Tallinn 1989.

Lage AI. Algorithm of the finite element method for calculation of echo signals from the shells in the liquid. // Proceedings of the Tallinn Polytechnic Institute 1984; (575): 65 - 67.

Kupradze VD. Method of potentials in theory of elasticity. M. Fizmatfiz, 1963.

Tetukhin MY, Fedoruk M. Plane wave diffraction on elongated solid body in liquid. // Acoustic Journal 1989; 34(1): 126 - 131.

Su J-H, Varadan VV, Varadan VK, Flax L. Acoustic wave scattering by a finite elastic cylinder in water. // J. A. S. A. 1980; 68(2): 685 - 691.

Dushin AY, Ilmenkov SL, Kleshchev. AA, Postnov VA. The application of finite elements method to the solution of elastic shells radiation problem. All-Union Symposium, Tallinn.1989. P. 89 - 91.

Kleshchev AA. Sound scattering by ideal bodies of non-analytical form. // Proceedings of Leningrad Shipbuilding Institute. 1989. Ship systems. P. 95 - 99.

Kleshchev AA. Hydroacoustic scatterers. First publication, St. Petersburg, Shipbuilding, 1992, second publication, St. Petersburg, Prima, 2012 [in Russian].

Kleshchev AA. Method of Integral Equations in Problem of Sound Diffraction on Bodies of Non - analytical Form. // MECH. 2012; 2(6): 124 - 128.

Peterson B, Strom S. Matrix Formulation of Acoustic Scattering from Multilaytred Scatterers. // J. A. S. A. 1975; 57(1): 2 - 13.

Numrich SK, Varadan VV, Varadan VK. Scattering of acoustic waves by a finite elastic cylinder immersed in water. // J. A. S. A. 1981; 70(5): 1407 - 1411.

Babich VM, Boldyrev VS. Asymptotic methods in diffraction problems of short waves. Etalon problems method. M.: Science, 1972.

Kravtsov UN, Orlov UN. Geometrical optics of heterogeneous mediums. M.: Science, 1980.

Kaminetzky L, Keller J B. Diffraction coefficients for higher order edges and vertices. // SLAM. J. Appl. Math. 1972; 22(1): 109 - 134.

Keller JB. Diffraction by smooth cylinder. // Trans. IRE AP-4. 1956; (3): 312 - 321.

Keller JB, Lewis RM, Secler BD. Asymptotic solution of some diffraction problems. // Comm. Pure and Appl. Math. 1956; 9(2): 207 - 265.

Kleshchev AA. Sound diffraction on bodies with mixed boundary conductions. // Acoustic Journal 1974; 20(4): 632 - 634.

Kleshchev AA. About accuracy of Green functions method. // Proceedings of Leningrad Shipbuilding Institute. Problems of acoustics of ships and oceans. 1984. P. 19 - 24.

Kleshchev AA, Klukin II. Foundations of hydroacoustics, 1987, Sudostroenie [in Russian].

Ilmenkov SL, Kleshchev AA. Solution of Problem of Sound Scattering on Bo-dies of Non-analytical Form with Help of Method of Green’s Functions. // A.S.P. 2014; 2(2): 50 - 54.

Fan Y, Sinclair AN, Honorvar F. Scattering of a plane acoustic wave from a tran-svesely isotropic cylinder encased in a solid elastic medium. // J. A. S. A. 1999; 106(3): Pt. 1. P. 1229 - 1236.

Kleshchev AA. Diffraction and propagation of waves in elastic mediums and bodies. St. Petersburg. 2002.

Kleshchev AA. Diffraction, radiation and propagation of elastic waves. St. Petersburg.: Profprint.

Kleshchev AA, Klimenkov A.S. Sound diffraction on elastic isotropic bodies of spherical form. Strict solution. // Morskoy vestnik. 2013; 2(125): 74 - 76.

Kleshchev AA, Klimenkov AS. Sound diffraction on elastic isotropic bodies of spherical form (strict solution). // Proceedings of XXVI - th session of Russian Acoustic Society. M.: GEOS, 2013. P. 130 - 133.

Kleshchev AA, Klimenkov AS. Diffraction of Sound Impulses on Isotropic Bo-dies of Spherical Form (Strict Solution). // A. S. P. 2013; 1(4): 68 - 77.

Debye P. Das Verhalten von Lichtwellen in der Nahe Brennpunktes oder Brennline. // Ann. Phys. 1909; 30(4): 775 - 776.

Fok VA. Problems of diffraction and propagation of electromagnetic waves. M.: Sovetskoe radio, 1970.

Kleshchev AA, Klukin II. About flexural waves in elastic cylindrical pivot. // Proceedings of Leningrad Shipbuilding Institute. 1976; 109: P. 3 - 5.

Schenderov EL. Wave problems of hydroacoustics. Leningrad: Sudostroenie, 1972. [in Russian].

Downloads

Published

2014-08-28

Issue

Vol. 1 No. 1 (2014)

Section

Articles

License

Policy for Journals/Articles with Open Access

Authors who publish with this journal agree to the following terms:
    1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.

  1. Authors are permitted and encouraged to post links to their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work

Policy for Journals / Manuscript with Paid Access

Authors who publish with this journal agree to the following terms:
    1. Publisher retain copyright .

  1. Authors are permitted and encouraged to post links to their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work .