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Analytical and Non – analytical Scatterers in Plane Waveguide with Hard Elastic Bottom, Irradiated by Pulse Sound Signal

Received: 19 May 2017     Accepted: 1 June 2017     Published: 7 July 2017
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Abstract

Based on the method of imagenary sources and imagenary scatterers is the solution of the problem of the sound diffraction by pulse signals at ideal (soft) prolate spheroid, put in the plane waveguide with the hard elastic bottom. In the work is proved that with such a formulation of problems eliminated possibility of using the method of normal waves because pulses are bundies of energy and can therefore only be distributed to the group velocity which is inherent in just the method of imaginary sources. Calculations made in the article shoved that imagenary sources with smail numbers experienci8ng the effect of total internal reflection, as the result of the reflection coefficient V by the hard elastic bottom is complex and the real part of V is close to 1,0 which corresponds V absolutely hard bottom. Found sequences of reflected pulses for the elastic hard bottom and the absolutely hard bottom floor confirmed this approach. In the final part of the arti8cle on the basis of the received results given by a solution (the method integral equations) is much more complex problem of the diffraction at the elastic non-analytical scatterer, put in the plane waveguide witch the hard elastic bottom.

Published in American Journal of Modern Physics (Volume 6, Issue 4)
DOI 10.11648/j.ajmp.20170604.12
Page(s) 51-55
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2017. Published by Science Publishing Group

Keywords

Scatterer, Prolate Spheroid, Imaginary Source, Diffraction, Elastic Hard Bottom, Boundary Conditions, Group Velocity, Phase Velocity

References
[1] Kolskiy G. Waves of Stresses in Hard Bodies. M.: I L, 1956. 272 p.
[2] Kleshchev A. A.,Kuznetsova E. I. Scattering of pulse sound signals by the spheroidal body, put in plane wavegui de. / Coll. Proc. Russ. Acoust. Soc. XXIV session. M.: GEOS. 2011. V. 1. P. 743–745.
[3] Kleshchev A. A., Kuznetsova E. I. Diiffraction of Impulse Signals on Spheroidal Body, Put in Plane Waveguide/ / International Journal of Theoretical and Mathematical Physics. 2012. V. 2. № 6. P. 211–214.
[4] Kleshchev A. A. Diffraction of Pulse Sound Signals on Elastic Spheroidal Shell, Put in Plane Waveguide. / Advanced Studies in Theoretical Physics. 2013. V. 7. № 13 – 16/ P. 697–705.
[5] Kleshchev A. A, Diffraction of Sound Signals at Elastic Shell of Non-analytical Form Put in Plane Waveguide. / Advances in Signal Processing. 2014. V. 2. № 2. P. 46–49.
[6] Kleshchev A. A. Pulse Sound Signals Diffraction on Elastic Bodies of Аnalytical and Nonana-lytical Forms, Put in Plane Waveguide. / Zeitschrift fur Naturforschung A. 2015. V. 70. № 6. P. 419–427.
[7] Kleshchev A. A. Diffraction of Pulse Sound Signals on Elastic Bodies of Spheroidal Form Put in Plane Waveguide// MIT. 2015. V. 2. № 28. P. 77–81.
[8] Kleshchev A. A., Klyukin I. I. The spectral characteristics of the scattering of the sound by body, placed in the sound channel. / Sov. Phys. Acoust. 1974. V. 20. № 3. P. 470 – 473.
[9] Lekhnitskiei S. G. Theory of Elasticity of Anisotropic Elastic Body. M.: Science, 1977. 416 p.
[10] Brechovakikh L. M. Waves in Laminated Mediums. M.: Publ. Acad. Scien. SSSR, 1957. 502 p.
[11] Kleshchev A. A. Hydroacoustic Scatterers. S.-Pb.: Prima, 2012. 268 p.
[12] Кleshchev A. A. Scattering of Sound by Ideal Bodies of Non-analytical Form. / Тr. Lenin. Korablestr. Inst. 1989. Generalship. Syst. P. 95–99.
[13] Кleshchev А. А. Мethod of Integral Equations in Problem of Sound Diffraction on Elastic Shell of Non-analytical Form. / Теchn. Acoust. 1993. V. 2. № 4(6). P. 65–66..
[14] Кleshchev А. А. Мethod of Integral Equations in Problem of Sound Diffraction on Bodies of Non-analytical Form. / Мarine messenger. 2013. № 2(125). P. 94–98.
[15] Seybert A. F., Wu T. w, and Wu X. F. Radiation and scattering of acoustic waves from elas-tic solids and shells using the boundary element method. / J. A. S. A. 1988. V. 84. № 5. P. 1906–1912.
[16] Podstrigach J. S., Poddubnjak. Scattering of Sound Beams of Spherical and Cylindrical Form. Кiev: Naukova Dumka, 1986. 264 p.
[17] Brebbia C. A., Walker S. Boundary Element Techniques in Engineering. М.: Мir, 1982. 242 p.
[18] Peterson B., Strom S. Matrix Formulation of Acoustic Scattering from Multilayered Scatte-rers. / J. A. S. A. 1975. V/ 57. № 1. P. 2–13.
[19] Кupradze V. D. Methods of Potential in Theory of Elasticity. М.: Fizmatgiz, 1963. 472 p.
[20] Dushin A. Yu., Il’menkov S. L., Kleshchev A. A., Postnov V. A. Use of Finite El Sement Method to Solution of Problems of Sound Radiating by Elastic Shells. / Proc. All-Union Symp. Interaction of Acoustical Waves with Elastic Bodies. Таllinn: 1989. P. 89–91.
[21] Il’menkov S. L., Kleshchev A. A., Klimenkov A. S. The Green’s Function Method in the Problem of Sound Diffraction by an Elastic Shell of Noncanonical Shape. / Acoust. Phys. 2014. V. 60. № 6. P. 579–586.
[22] Kharcevich A. A. Spectrum and Analisis. М.: GITTL, 1957. 236 p.
[23] Кleshchev А. А. Three-Dimensional and Two-Dimensional (Axis-Symmetrical Characteris-tics of Elastic Spheroidal Scatterers. / Akust. Zh. 1986. V. 32. № 2. P. 268–270.
[24] Кleshchev A. A., Klyukin I. I. Principles of Hydroacoustics. L.: Shipbuilding, 1987, 224 p.
[25] Кleshchev A. A. Debye and Debye-Type Potentials in Diffraction, Radiation and Elastic Wave Propagation Problems. / Acoust. Phys. 2012. V. 58. № 3. P. 338–341.
[26] Кleshchev A. A. Resonance Scattering of Sound by Spheroidal Elastic Bodies and Shells. / Аcoust. Phys. 2014. V. 60. № 3. P. 253 – 261.
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  • APA Style

    Alexander Kleshchev. (2017). Analytical and Non – analytical Scatterers in Plane Waveguide with Hard Elastic Bottom, Irradiated by Pulse Sound Signal. American Journal of Modern Physics, 6(4), 51-55. https://doi.org/10.11648/j.ajmp.20170604.12

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    ACS Style

    Alexander Kleshchev. Analytical and Non – analytical Scatterers in Plane Waveguide with Hard Elastic Bottom, Irradiated by Pulse Sound Signal. Am. J. Mod. Phys. 2017, 6(4), 51-55. doi: 10.11648/j.ajmp.20170604.12

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    AMA Style

    Alexander Kleshchev. Analytical and Non – analytical Scatterers in Plane Waveguide with Hard Elastic Bottom, Irradiated by Pulse Sound Signal. Am J Mod Phys. 2017;6(4):51-55. doi: 10.11648/j.ajmp.20170604.12

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  • @article{10.11648/j.ajmp.20170604.12,
      author = {Alexander Kleshchev},
      title = {Analytical and Non – analytical Scatterers in Plane Waveguide with Hard Elastic Bottom, Irradiated by Pulse Sound Signal},
      journal = {American Journal of Modern Physics},
      volume = {6},
      number = {4},
      pages = {51-55},
      doi = {10.11648/j.ajmp.20170604.12},
      url = {https://doi.org/10.11648/j.ajmp.20170604.12},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmp.20170604.12},
      abstract = {Based on the method of imagenary sources and imagenary scatterers is the solution of the problem of the sound diffraction by pulse signals at ideal (soft) prolate spheroid, put in the plane waveguide with the hard elastic bottom. In the work is proved that with such a formulation of problems eliminated possibility of using the method of normal waves because pulses are bundies of energy and can therefore only be distributed to the group velocity which is inherent in just the method of imaginary sources. Calculations made in the article shoved that imagenary sources with smail numbers experienci8ng the effect of total internal reflection, as the result of the reflection coefficient V by the hard elastic bottom is complex and the real part of V is close to 1,0 which corresponds V absolutely hard bottom. Found sequences of reflected pulses for the elastic hard bottom and the absolutely hard bottom floor confirmed this approach. In the final part of the arti8cle on the basis of the received results given by a solution (the method integral equations) is much more complex problem of the diffraction at the elastic non-analytical scatterer, put in the plane waveguide witch the hard elastic bottom.},
     year = {2017}
    }
    

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  • TY  - JOUR
    T1  - Analytical and Non – analytical Scatterers in Plane Waveguide with Hard Elastic Bottom, Irradiated by Pulse Sound Signal
    AU  - Alexander Kleshchev
    Y1  - 2017/07/07
    PY  - 2017
    N1  - https://doi.org/10.11648/j.ajmp.20170604.12
    DO  - 10.11648/j.ajmp.20170604.12
    T2  - American Journal of Modern Physics
    JF  - American Journal of Modern Physics
    JO  - American Journal of Modern Physics
    SP  - 51
    EP  - 55
    PB  - Science Publishing Group
    SN  - 2326-8891
    UR  - https://doi.org/10.11648/j.ajmp.20170604.12
    AB  - Based on the method of imagenary sources and imagenary scatterers is the solution of the problem of the sound diffraction by pulse signals at ideal (soft) prolate spheroid, put in the plane waveguide with the hard elastic bottom. In the work is proved that with such a formulation of problems eliminated possibility of using the method of normal waves because pulses are bundies of energy and can therefore only be distributed to the group velocity which is inherent in just the method of imaginary sources. Calculations made in the article shoved that imagenary sources with smail numbers experienci8ng the effect of total internal reflection, as the result of the reflection coefficient V by the hard elastic bottom is complex and the real part of V is close to 1,0 which corresponds V absolutely hard bottom. Found sequences of reflected pulses for the elastic hard bottom and the absolutely hard bottom floor confirmed this approach. In the final part of the arti8cle on the basis of the received results given by a solution (the method integral equations) is much more complex problem of the diffraction at the elastic non-analytical scatterer, put in the plane waveguide witch the hard elastic bottom.
    VL  - 6
    IS  - 4
    ER  - 

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Author Information
  • Department of Physics, Saint-Petersburg State Navy Technical University, Saint-Petersburg, Russia

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