Skip to main content
SpringerLink
Log in

Nonaxisymmetric elastoacoustic analysis of a submerged eccentric hollow sphere: an exact solution

  • Published:
Acta Mechanica Aims and scope Submit manuscript

Abstract

The classical Navier equations of linear elasticity and the Helmholtz equation for the internal/external acoustic domains in conjunction with the translational addition theorem for spherical vector wave functions are employed to present an exact solution for three-dimensional nonaxisymmetric steady-state sound radiation from an eccentric hollow elastic sphere, immersed in and filled with acoustic fluids, and subjected to arbitrary time-harmonic mechanical drives at its internal/external surface. The analytical results are illustrated with numerical examples in which air-filled, water-submerged, thick-walled concentric and eccentric steel spheres are driven by harmonic concentrated or distributed radial internal/external loads. The numerical results reveal the important effects of sphere eccentricity, loading configuration, and excitation frequency on the sound radiation characteristics of the submerged structure. Limiting cases are considered and the validity of results is established with the aid of a commercial finite element package as well as by comparison with the data in the existing literature.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Junger M.C., Feit D.: Sound, Structures and their Interaction. MIT Press, Cambridge (1986)

    Google Scholar 

  2. Qatu M.S.: Recent research advances in the dynamic behavior of shells: 1989–2000. Part [2] homogeneous shells. Appl. Mech. Rev. 169, 415–434 (2002)

    Article  Google Scholar 

  3. Amabili M., Paidoussis M.P.: Review of studies on geometrically nonlinear vibrations and dynamics of circular cylindrical shells and panels, with and without fluid-structure interaction. Appl. Mech. Rev. 56, 349–356 (2003)

    Article  Google Scholar 

  4. Hu J., Qiu Z., Su T.C.: Axisymmetric vibrations of a viscous-fluid-filled piezoelectric spherical shell and the associated radiation of sound. J. Sound Vib. 330, 5982–6005 (2011)

    Article  Google Scholar 

  5. Cao X., Hua H., Ma C.: Acoustic radiation from shear deformable stiffened laminated cylindrical shells. J. Sound Vib. 331, 561–670 (2012)

    Google Scholar 

  6. Hasheminejad S.M., Mirzaei Y.: Free vibration analysis of an eccentric hollow cylinder using exact 3D elasticity theory. J. Sound Vib. 326, 687–702 (2010)

    Article  Google Scholar 

  7. Hasheminejad S.M., Mirzaei Y.: Exact 3D elasticity solution for free vibrations of an eccentric hollow sphere. J. Sound Vib. 330, 229–244 (2011)

    Article  Google Scholar 

  8. Hasheminejad S.M., Ahamdi-Savadkoohi A.: Vibro-acoustic behavior of a hollow FGM cylinder excited by on-surface mechanical drives. J. Compos. Struct. 92, 86–96 (2010)

    Article  Google Scholar 

  9. Hasheminejad S.M., Malakooti S., Mousavi-Akbarzadeh H.: Acoustic radiation from a submerged hollow FGM sphere. Arch. Appl. Mech. 81, 1889–1902 (2011)

    Article  Google Scholar 

  10. Dassios G., Hadjinicolaou M., Kamvyssas G.: The penetrable coated sphere embedded in a point source excitation field. Wave Motion 32, 319–338 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  11. Anagnostopoulos K.A., Mavratzas S., Charalambopoulos A., Fotidadis D.I.: Scattering of a spherical acoustic field from an eccentric spheroidal structure simulating the kidney-stone system. Act. Mech. 161, 39–52 (2003)

    Article  MATH  Google Scholar 

  12. Yan, B., Han, X., Fang Ren, K.: Scattering of a shaped beam by a spherical particle with an eccentric spherical inclusion. J. Opt. A: Pure Appl. Opt. (2009). doi:10.1088/14644258/11/1/015705

  13. Friedman B., Russek J.: Addition theorems for spherical waves. Q. Appl. Math. 12, 13–23 (1954)

    MathSciNet  MATH  Google Scholar 

  14. Stein S.: Additions theorems for spherical wave functions. Q. Appl. Math. 19, 15–24 (1961)

    MATH  Google Scholar 

  15. Cruzan O.R.: Translational addition theorems for spherical vector wavefunctions. Q. Appl. Math. 20, 33–40 (1962)

    MathSciNet  MATH  Google Scholar 

  16. Fikioris J.G., Uzunoglu N.K.: Scattering from an eccentrically stratified dielectric sphere. J. Opt. Soc. Am. 69, 1359–1366 (1979)

    Article  Google Scholar 

  17. Roumeliotis J.A., Kanellopoulos J.D., Fikioris J.G.: Acoustic resonance frequency shifts in a spherical cavity with an eccentric inner small sphere. J. Acoust. Soc. Am. 90, 1144–1148 (1991)

    Article  Google Scholar 

  18. Roumeliotis J.A., Kanellopoulos J.D.: Acoustic eigenfrequencies and modes in a soft-walled spherical cavity with an eccentric inner small sphere. J. Frankl. Inst. 329, 727–735 (1992)

    Article  Google Scholar 

  19. Borghese F., Denti P., Saija R., Sindoni O.I.: Optical properties of spheres containing a spherical eccentric inclusion. J. Opt. Soc. Am. 9, 1327–1335 (1992)

    Article  Google Scholar 

  20. Roumeliotis J.A., Kakogiannos N.B., Kanellopoulos J.D.: Scattering from a sphere of small radius embedded into a dielectric one. IEEE Trans. Microw. Theory Tech. 43, 155–168 (1995)

    Article  Google Scholar 

  21. Lim K., Lee S.S.: Analysis of electromagnetic scattering from an eccentric multilayered sphere. IEEE Trans. Antennas Propag. 43, 1325–1328 (1995)

    Google Scholar 

  22. Ngo D., Videen G., Chylek P.: A Fortran code for the scattering of EM-waves by a sphere with a nonconcentric spherical inclusion. Comput. Phys. Commun. 1077, 94–112 (1996)

    Article  Google Scholar 

  23. Gouesbet G., Grehan G.: Generalized Lorenz–Mie theory for a sphere with an eccentrically located-spherical inclusion. J. Mod. Opt. 47, 821–837 (2000)

    MathSciNet  MATH  Google Scholar 

  24. Hasheminejad S.M., Azarpeyvand M.: Eccentricity effects on acoustic radiation from a spherical source suspended within a thermoviscous fluid sphere. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 50, 1444–1454 (2003)

    Article  Google Scholar 

  25. Videen G.: Seismic scattering from a spherical inclusion eccentrically located within a homogeneous, spherical host: theoretical derivation. Waves Random Media 13, 177–190 (2003)

    Article  Google Scholar 

  26. Moneda A.P., Chrissoulidis D.P.: Dyadic Green’s function of a sphere with an eccentric spherical inclusion. J. Opt. Soc. Am. 24, 1695–1703 (2007)

    Article  MathSciNet  Google Scholar 

  27. Yan, B., Han, X., Fang Ren, K.: Scattering of a shaped beam by a spherical particle with an eccentric spherical inclusion. J. Opt. A: Pure Appl. Opt. A (2009). doi:10.1088/1464-4258/11/1/015705

  28. Lou Y.K., Klosner J.M.: Dynamics of a submerged ring-stiffened spherical shell. Proc. SPIE Int. Soc. Opt. Eng. 1700, 2–15 (1992)

    Google Scholar 

  29. Tung, C.C.: Seismic response of submerged oil storage tank. In: Proceedings of the 4th Engineering Mechanics Division Specialty Conference: Recent Advances in Engineering Mechanics and their Impact on Civil Engineering Practice, ASCE, IN, USA, pp. 299–302 (1983)

  30. Yumoto, H., Yamamoto, N., Matsunaga, S., Suzuki, T.: Model test of spherical shell of submersible. ASME, Conference: Fifth International Conference on Pressure Vessel Technology, Volume III: Lectures and Discussions. San Francisco, CA, USA, pp. 151–168 (1985)

  31. http://en.wikipedia.org/wiki/Deep_Submergence_Vehicle (2012). Accessed 22 Jan 2012

  32. http://www.google.com/patents/US4302291 (2012). Accessed 22 Jan 2012

  33. Guicking D., Klaus G., Harald P.: Recent Advances in Sonar Target Classification, Automatic Object Recognition II. Orlando, FL, USA (1992)

    Google Scholar 

  34. Gaunaurd G.C., Uberall H.: Identification of cavity fillers in elastic solids using the resonance scattering theory. J. Appl. Mech. 38, 408–417 (1971)

    Article  Google Scholar 

  35. Jellison, J., Kess, H. R., Adams, D. E., Nelson, D. C.: Vibration-based NDE technique for identifying non-uniformities in manufacture parts with degeneracies. In: Proceedings of IMECE, New Orleans, pp. 621–628 (2002)

  36. Haïat G., Lhémery A., Calmon P., Lasserre F.: A model-based inverse method for positioning scatterers in a cladded component inspected by ultrasonic waves. Ultrasonics 43, 619–628 (2005)

    Article  Google Scholar 

  37. Kaufman R.N.: Compression of an elastic sphere with a nonconcentric spherical cavity. J. Appl. Math. Mech. 28, 957–961 (1964)

    Article  MATH  Google Scholar 

  38. Kolesov V.S, Vlasov N.M., Tisovskii L.O., Shatskii I.P.: The stress concentration in an elastic ball with nonconcentric spherical cavity. J. Math. Sci. 63, 335–339 (1993)

    Article  Google Scholar 

  39. Hasheminejad S.M., Bahari A., Abbasion S.: Modelling and simulation of acoustic pulse interaction with a fluid-filled hollow elastic sphere through numerical Laplace inversion. Appl. Math. Model. 35, 22–49 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  40. Pierce A.D.: Acoustics, An Introduction to its Physical Principles and Applications. American Institute of Physics, New York (1994)

    Google Scholar 

  41. Pao Y.H., Mow C.C.: Diffraction of Elastic Waves and Dynamics Stress Concentration. Crane Russak, New York (1971)

    Google Scholar 

  42. Shah A.H., Ramakrishnan C.V., Datta S.K.: Three dimensional and shell theory analysis of elastic waves in a hollow sphere, Part I. Analytical foundation. J. Appl. Mech 36, 431–439 (1969)

    Article  MATH  Google Scholar 

  43. Williams E.G.: Fourier Acoustics: Sound Radiation and Nearfield Acoustical Holography. Academic Press, Cambridge (1999)

    Google Scholar 

  44. Abramowitz M., Stegun I.A.: Handbook of Mathematical Functions. National Bureau of Standards, Washington DC (1964)

    MATH  Google Scholar 

  45. Einspruch N.G., Witterholt E.J., Truell R.: Scattering of a plane transverse wave by a spherical obstacle in an elastic medium. J. Appl. Phys. 5, 806–818 (1960)

    Article  MathSciNet  Google Scholar 

  46. Arfken G.B., Hans J.W., Harris F.: Mathematical Methods for Physicists. Harcourt Academic, San Diego, CA (2001)

    MATH  Google Scholar 

  47. Sato H., Shindo Y.: Multiple scattering of plane elastic waves in a particle-reinforced-composite medium with graded interfacial layers. Mech. Mater. 35, 83–106 (2003)

    Article  Google Scholar 

  48. Pathak G.A., Stepanishen R.P.: Acoustic harmonic radiation from fluid-loaded spherical shells using elasticity theory. J. Acoust. Soc. Am. 96, 2564–2575 (1994)

    Article  Google Scholar 

  49. Herrin D.W., Martinus F., Wu T.W., Seybert A.F.: An assessment of the high frequency boundary element and Rayleigh integral approximations. Appl. Acoust. 67, 819–833 (2006)

    Article  Google Scholar 

  50. ABAQUS, Analysis User’s Manual Version 6.9 On-line Documentation

  51. Chen J.M., Huang Y.Y.: Vibration and acoustic radiation from submerged stiffened spherical shell with deck-type internal plate. Acta. Mech. Solida Sin. 16, 210–219 (2003)

    Google Scholar 

  52. Ko S.H., Seong W., Pyo S.: Structure-borne noise reduction for an infinite, elastic cylindrical shell. J. Acoust. Soc. Am. 109, 1483–1495 (2001)

    Article  Google Scholar 

  53. Junger M.C.: Pressure radiated by an infinite plate driven by distributed loads. J. Acoust. Soc. Am. 74, 649–653 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  54. Peng H., Banks-Lee P.: Source correlation effects on the sound power radiation from spherical shells. J. Acoust. Soc. Am. 86, 1586–1594 (1989)

    Article  Google Scholar 

  55. Guo Y.P.: Radiation from cylindrical shells driven by on-surface forces. J. Acoust. Soc. Am. 95, 2014–2021 (1994)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Acoustics Research Lab., School of Mechanical Engineering, Iran University of Science and Technology, Narmak, 16846-13114, Tehran, Iran

    Seyyed M. Hasheminejad & Hessam Mousavi-Akbarzadeh

  2. Department of Mechanical Engineering, Damavand Branch, Islamic Azad University, Damavand, Iran

    Yaser Mirzaei

Authors
  1. Seyyed M. Hasheminejad
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hessam Mousavi-Akbarzadeh
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yaser Mirzaei
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Seyyed M. Hasheminejad.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hasheminejad, S.M., Mousavi-Akbarzadeh, H. & Mirzaei, Y. Nonaxisymmetric elastoacoustic analysis of a submerged eccentric hollow sphere: an exact solution. Acta Mech 223, 1397–1416 (2012). https://doi.org/10.1007/s00707-012-0659-3

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-012-0659-3

Keywords

Search

Navigation