Keywords
sound field
spherical shell
ellipsoid of rotation
dual equations
spherical radiator
spherical shell
ellipsoid of rotation
dual equations
spherical radiator
How to Cite
Shushkevich, G. (2016). Propagation of the sound wave by an unclosed spherical shell and a penetrable ellipsoid. Advances in Mechanical and Materials Engineering, 33(293 (3), 221-232. https://doi.org/10.7862/rm.2016.18
Abstract
In this paper the result of solution of axisymmetric problem of propagation of sound wave by an unclosed spherical shell and a penetrable ellipsoid of rotation is presented. A spherical radiator is located in a thin unclosed spherical shell as a source of acoustic field. The equation of the spheroidal boundary is given in spherical coordinates. A scattered pressure field is expressed in terms of spherical wave functions. Using corresponding additional theorems the solution of boundary value problem is reduced to solving of dual equations in Legendre's polynomials, which are converted to infinite system of linear algebraic equations of the second kind. The formula for calculation of the far field and numerical results for different values of parameters are obtained.
References
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10. Varadan V.K., Varadan V.V., Dragonette L.R., Flax L.: Computation of rigid body by prolate spheroids using the T-matrix approach, J. Acoust. Soc. America, 71 (1982) 22-25.
11. Sammelmann G.S., Trivett D.H., Hackmann R.H.: High-frequency scattering from rigid prolate spheroids, J. Acoust. Soc. America, 83 (1988) 46-54.
12. Barton J.P., Wolf N.L., Zhang H., Tarawneh C.: Near-field calculations for a rigid spheroid with an arbitrary incident acoustic field, J. Acoust. Soc. America, 103 (2003) 1266-1222.
13. Burke J.E.: Scattering by penetrable spheroids, J. Acoust. Soc. America, 43 (1968) 871-875.
14. Kotsis A.D., Roumeliotis J.A.: Acoustic scattering by a penetrable spheroid, Acoust. Phys., 54 (2008) 153-167.
15. Kleshchev A.A., Rostovcev D.M.: Scattering of a sound by elastic and liquid ellipsoidal shells of revolution, Acoustic J., 32 (1986) 691-694 (in Russian).
16. Kleshchev A. A.: With reference to low frequency resonances of elastic spheroidal bodies, J. Techn. Acoust., 2 (1995) 27-28.
17. Bao X.L., Uberall H., Niemiec J.: Experimental study of sound scaterring by elastic spheroids, J. Acoust. Soc. America, 102 (1997), 933-942.
18. Tolokonnikov L. A., Lobanov A. V.: About scattering of plane sound wave by inhomogeneous elastic spheroid, Proc. Tula State University, Natural Sciences, 3 (2011) 119-125 (in Russian).
19. Tolokonnikov L. A.: Diffraction of plane sound wave on elastic spheroid with arbitrary located spherical vacuity, Proc. Tula State University, Natural Sciences, 2 (2011) 169-175 (in Russian).
20. Grinchenko V.T., Vovk I.V., Matsipura V.T.: Fundamentals of acoustics, Naukova dumka, Kiev 2007 (in Russian).
21. Ivanov E. A.: Diffraction of electromagnetic waves on two bodies, Springfield, Washington 1970.
22. Shushkevich G.Ch., Kiselyova N.N.: Penetration of sound field through multi-layered spherical shell, Computer Sci., 3 (2013) 47-57 (in Russian).
23. Erofeenko V.T.: Addition theorems, Nauka and Technika, Minsk 1989.
24. Shushkevich G.Ch., Shushkevich S.V.: Computer technology in mathematics, The system Mathcad 14: in 2 parts, Grevsova, Minsk 2012 (in Russian).
2. Fuchs H. V.: Applied Acoustics: Concepts, Absorbers, and Silencers for Acoustical Comfort and Noise Control, Springer-Verlag, Berlin, Heidelberg 2013.
3. Erofeenko V.T., Demidchik V.I., Malyi S.V., Kornev R.V.: Penetration of electromagnetic waves through composite screens containing ideally conducting helices, J. Eng. Physics Thermophysics, 84 (2011) 799-806.
4. Ivanov N.I.: Engineering acoustics. Theory and practice of noise control, Logos, Moscow 2008 (in Russian).
5. Kleshchev A.A., Sheiba L.S.: Scattering of a sound wave by ideal prolate spheroids. Acoustic J., 16 (1970) 264-268 (in Russian).
6. Sidman R.D.: Scattering of acoustical waves by a prolate spherical obstacle, J. Acoust. Soc. America, 52 (1972), 879-883.
7. Abramov A.A., Dyshko A.L, Konyukhova N.B., Levitina T.V.: On a numerical-analytic investigation of problems of the diffraction of a plane sound wave by ideal prolate spheroids and triaxial ellipsoids, Comput. Math. Math. Phys., 35 (1995) 1103-1123
8. Lauchle G.C.: Short-wavelength acoustic diffraction by prolate spheroids. J. Acoust. Soc. America, 58 (1975) 568-575.
9. Germon A., Lauchle G.C.: Axisymmetric diffraction of spherical waves by a prolate spheroid, J. Acoust. Soc. America, 65 (1979) 1322-1327.
10. Varadan V.K., Varadan V.V., Dragonette L.R., Flax L.: Computation of rigid body by prolate spheroids using the T-matrix approach, J. Acoust. Soc. America, 71 (1982) 22-25.
11. Sammelmann G.S., Trivett D.H., Hackmann R.H.: High-frequency scattering from rigid prolate spheroids, J. Acoust. Soc. America, 83 (1988) 46-54.
12. Barton J.P., Wolf N.L., Zhang H., Tarawneh C.: Near-field calculations for a rigid spheroid with an arbitrary incident acoustic field, J. Acoust. Soc. America, 103 (2003) 1266-1222.
13. Burke J.E.: Scattering by penetrable spheroids, J. Acoust. Soc. America, 43 (1968) 871-875.
14. Kotsis A.D., Roumeliotis J.A.: Acoustic scattering by a penetrable spheroid, Acoust. Phys., 54 (2008) 153-167.
15. Kleshchev A.A., Rostovcev D.M.: Scattering of a sound by elastic and liquid ellipsoidal shells of revolution, Acoustic J., 32 (1986) 691-694 (in Russian).
16. Kleshchev A. A.: With reference to low frequency resonances of elastic spheroidal bodies, J. Techn. Acoust., 2 (1995) 27-28.
17. Bao X.L., Uberall H., Niemiec J.: Experimental study of sound scaterring by elastic spheroids, J. Acoust. Soc. America, 102 (1997), 933-942.
18. Tolokonnikov L. A., Lobanov A. V.: About scattering of plane sound wave by inhomogeneous elastic spheroid, Proc. Tula State University, Natural Sciences, 3 (2011) 119-125 (in Russian).
19. Tolokonnikov L. A.: Diffraction of plane sound wave on elastic spheroid with arbitrary located spherical vacuity, Proc. Tula State University, Natural Sciences, 2 (2011) 169-175 (in Russian).
20. Grinchenko V.T., Vovk I.V., Matsipura V.T.: Fundamentals of acoustics, Naukova dumka, Kiev 2007 (in Russian).
21. Ivanov E. A.: Diffraction of electromagnetic waves on two bodies, Springfield, Washington 1970.
22. Shushkevich G.Ch., Kiselyova N.N.: Penetration of sound field through multi-layered spherical shell, Computer Sci., 3 (2013) 47-57 (in Russian).
23. Erofeenko V.T.: Addition theorems, Nauka and Technika, Minsk 1989.
24. Shushkevich G.Ch., Shushkevich S.V.: Computer technology in mathematics, The system Mathcad 14: in 2 parts, Grevsova, Minsk 2012 (in Russian).