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Acoustic Scattering and Radiation Force Function Experienced by Functionally Graded Cylindrical Shells

Published online by Cambridge University Press:  16 June 2011

J. Jamali,
M.H. Naei,
F. Honarvar and
M. Rajabi
J. Jamali*
Affiliation:
Department of Mechanical Engineering, Tehran University and Azad Shoushtar University, Tehran, Iran
M.H. Naei
Affiliation:
Department of Mechanical Engineering, Tehran University and Azad Shoushtar University, Tehran, Iran
F. Honarvar
Affiliation:
Department of Mechanical Engineering, K. N. Toosi University, Tehran, Iran
M. Rajabi
Affiliation:
School of Mechanical Engineering, Sharif University of Technology, Tehran, Iran
*
*Assistant Professor, corresponding author

Abstract

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A body insonified by a sound field is known to experience a steady force that is called the acoustic radiation force. In this paper, the method of wave function expansion is adopted to study the scattering and the radiation force function caused by a plane normal harmonic acoustic wave incident upon an arbitrarily thick-walled functionally graded cylindrical shell submerged in and filled with compressible ideal fluids. A laminate approximate model and the so-called state space formulation in conjunction with the classical transfer matrix (T-matrix) approach are employed to present an analytical solution based on the two-dimensional exact equations of elasticity. Two typical models, representing the elastic properties of FGM interlayer, are considered. In both models, the mechanical properties of the graded shell are assumed to vary smoothly and continuously with the change of volume concentrations of the constituting materials across the thickness of the shell. In the first model, the simple rule of mixture governs. In the second, an elegant self-consistent micromechanical model which assumes an interconnected skeletal microstructure in the graded region is employed. Particular attention is paid on dynamical response of these models in a wide range of frequency and for different shell wall-thicknesses. In continue, by focusing on the second model, the normalized radiation force function and the form function amplitude are calculated and compared for different shell wall thicknesses and various profile of variations. Limiting cases are considered and good agreements with the solutions available in the literature are obtained.

Keywords

Sound scatteringFGM cylindrical shellState-space methodSurface wavesRadiation force function

Information

Type
Articles
Information
Journal of Mechanics , Volume 27 , Issue 2 , June 2011, pp. 227 - 243
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2011

References

1. Yamanouchi, M., Koizumi, M., Hirai, T. and Shiota, I., Proceedings of the First International Symposium on Functionally Gradient Materials, Sendai, Japan (1990).Google Scholar
2. Holt, J. B., Koizumi, M., Hirai, T. and Munir, Z. A., Ceramic Transaction: Functionally Gradient Materials, 34, Ohio, Westerville, The American Ceramic Society (1993).Google Scholar
3. Koizumi, M., The Concept of FGM, in J.B. Holt, M.Koizumi, T., Hirai, Z. A. Munir Eds., Ceramic Transaction: Functionally Gradient Materials, 34, Ohio, Westerville, The American Ceramic Society, pp. 3–10 (1993).Google Scholar
4. Suresh, S. and Mortensen, A., Fundamentals of Functionally Graded Materials, IOM Communications, London (1998).Google Scholar
5. Miyamoto, Y., Kaysser, W. A., Rabin, B. H., Kawasaki, A. and Ford, R. G., Functionally Graded Materials: Design, Processing and Applications, Chapman Hall (1999).CrossRefGoogle Scholar
6. Talmant, M. and Batard, H., “Material Characterization and Resonant Scattering by Cylinders,” Proceedings of the IEEE Ultrasonics Symposium, 3, pp. 1371–1380 (1994).CrossRefGoogle Scholar
7. Migliori, A. and Sarrao, J. L., “Resonant Ultrasound Spectroscopy: Applications to Physics,” Materials Measurements and Nondestructive Evaluation, Wiley, New York (1997).Google Scholar
8. Tesei, A., Fox, W. L. J., Maguer, A. and Lovik, A., “Target Parameter Estimation Using Resonance Scattering Analysis Applied to Air-Filled, Cylindrical Shells in Water,” Journal of the Acoustical Society of America, 108, pp. 2891–2910 (2000).CrossRefGoogle Scholar
9. Guicking, D., Goerk, K. and Peine, H., “Recent Advances in Sonar Target Classification,” Proceedings of SPIE, International Society for Optical Engineering, 1700, pp. 2–15 (1992).Google Scholar
10. Honarvar, F. and Sinclair, A. N., “Nondestructive Evaluation of Cylindrical Components by Resonance Acoustic Spectroscopy,” Ultrasonic, 36, pp. 845–854 (1998).CrossRefGoogle Scholar
11. Gaunaurd, G. C., “Elastic and Acoustic Resonance Wave Scattering,” Applied Mechanical Review, 42, pp. 143–192 (1989).CrossRefGoogle Scholar
12. Uberall, H., Acoustic Resonance Scattering, Gordon and Breach Science, Philadelphia (1992).Google Scholar
13. Veksler, N. D., Resonance Acoustic Spectroscopy, Springer Series on Wave Phenomena, Springer Verlag, Berlin (1993).CrossRefGoogle Scholar
14. Honarvar, F. and Sinclair, A. N., “Acoustic Wave Scattering from Transversely Isotropic Cylinders,” Journal of the Acoustical Society of America, 100, pp. 57–63 (1996).CrossRefGoogle Scholar
15. Hasheminejad, S. M. and Rajabi, M., “Acoustic Scattering Characteristics of Thick-Walled Orthotropic Cylindrical Shell at Oblique Incidence,” Ultrasonics, 47, pp. 32–48 (2007).CrossRefGoogle Scholar
16. Hasheminejad, S. M. and Rajabi, M., “Acoustic Resonance Scattering from a Submerged Functionally Graded Cylindrical Shell,” Journal of Sound and Vibration, 302, pp. 208–228 (2007).CrossRefGoogle Scholar
17. Rajabi, M. and Hasheminejad, S. M., “Acoustic Resonance Scattering from a Multilayered Cylindrical Shell with Imperfect Bonding,” Ultrasonics, (2009).CrossRefGoogle Scholar
18. Lee, C. P. and Wang, T. G., “Acoustic Radiation Pressure,” Journal of the Acoustical Society of America, 94, pp. 1099–1109 (1993).CrossRefGoogle Scholar
19. Nightingale, K., Soo, M. S., Nightingalo, R. and Trahey, G., “Acoustic Radiation Force Impulse Imaging: In Vivo Demonstration of Clinical Feasibility,” Ultrasonic Medical Biology, 28, pp. 227–235 (2002).CrossRefGoogle ScholarPubMed
20. Sarvazyan, R. P., Rudenko, O. V., Swanson, S. D., Fowlkes, J. B. and Emelianov, S. Y., “Shear Wave Elasticity Imaging: A New Ultrasonic Technology of Medical Diagnostics,” Ultrasonic Medical Biology, 24, pp. 1419–1435 (1998).CrossRefGoogle ScholarPubMed
21. Fatemi, M. and Greenleaf, J. F., “Ultrasound Stimulated Vibro-Acoustic Spectroscopy,” Science, 280, pp. 82–85 (1998).CrossRefGoogle Scholar
22. Fatemi, M. and Greenleaf, J. F., “Vibro-Acoustography: An Imaging Modality Based on Ultrasound-Stimulated Acoustic Emission,” Natural Academic of Science of USA, 96, pp. 6603–6608 (1999).CrossRefGoogle ScholarPubMed
23. Dunn, F., Averbach, A. J. and O'Brein, D. J., “A Primary Method for the Determination of Ultrasonic Intensity with the Elastic Sphere Radiometer,” Acustica, 38, pp. 58–61 (1977).Google Scholar
24. Rayleigh, R. W. S., On the Pressure of Vibrations, Philosophical Magazine, 3, pp. 338–346 (1902).Google Scholar
25. Awatani, J., “Study on Acoustic Radiation Pressure (IV), Radiation Pressure on a Cylinder,” Memoirs of the Institute of Scientific and Industrial Research, Osaka University, 12, pp. 95–102 (1955).Google Scholar
26. Zhuk, A. P., “Radiation Force Acting on a Cylindrical Particle in a Sound Field,” International Applied Mechanics, 22, pp. 689–693 (1986).Google Scholar
27. Hasegawa, T., Saka, K., Inoue, N. and Matsuzawa, K., “Acoustic Radiation Force Experienced by a Solid Elastic Cylinder in a Plane Progressive Sound Field,” Journal of the Acoustical Society of America, 83, pp. 1770–1775 (1988).CrossRefGoogle Scholar
28. Hasegawa, T., Hino, Y., Annou, A., Noda, H. and Kato, M., “Acoustic Radiation Pressure Acting on Spherical and Cylindrical Shells,” Journal of the Acoustical Society of America, 93, pp. 154–161 (1993).CrossRefGoogle Scholar
29. Mitri, F. G., “Radiation Force Acting on an Absorbing Cylinder Placed in an Incident Plane-Progressive Acoustic Field,” Journal of Sound and Vibration, 284, pp. 494–502 (2005).CrossRefGoogle Scholar
30. Mitri, F. G., “Theoretical Calculation of the Acoustic Radiation Force Acting on Elastic and Viscoelastic Cylinders Placed in a Plane Standing or Quasistanding Wave Field,” European Physical Journal B, 44, pp. 71–78 (2005).CrossRefGoogle Scholar
31. Mitri, F. G., “Theoretical and Experimental Determination of the Acoustic Radiation Force Acting on an Elastic Cylinder in a Plane Progressive WaveFar-Field Derivation Approach,” New Journal of Physics, 8, p. 138 (2006).CrossRefGoogle Scholar
32. Pierce, A. D., “Acoustics; An Introduction to its Physical Principles and Applications,” American Institute of Physics, New York (1991).Google Scholar
33. Chen, W. Q., Bian, Z. G. and Ding, H. J., “Three Dimensional Vibration Analysis of Fluid Filled Orthotropic FGM Cylindrical Shells,” International Journal of Mechanical Science, 46, pp. 159–171 (2004).CrossRefGoogle Scholar
34. Nayfeh, A. H. and Nagy, P. B., “General Study of Axisymmetric Waves in Layered Anisotropic Fibers and Their Composites,” Journal of the Acoustical Society of America, 99, pp. 931–941 (1996).CrossRefGoogle Scholar
35. Achenbach, J. D., Wave Propagation in Elastic Solids, North-Holland, New York (1976).Google Scholar
36. Musgrave, M. J. P., Crystal Acoustics, Holden-Day Series in Mathematical Physics (1970).Google Scholar
37. Shuvalov, A. L., “A Sextic Formalism for ThreeDimensional Elasto-Dynamics of Cylindrically Anisotropic Radially Inhomogeneous Materials,” Proceeding of Royal Society of London, 459, pp. 1611–1639 (2003).CrossRefGoogle Scholar
38. Chang, H. H. and Tarn, J. Q., “A State Space Approach for Exact Analysis of Composite Laminates and Functionally Graded Materials,” International Journal of Solids and Structures, 44, pp. 1409–1422 (2007).CrossRefGoogle Scholar
39. Lee, W. M. and Chen, J. T., “Scattering of Flexural Wave in Thin Plate with Multiple Circular Holes by Using the Multipole Trefttz Method,” International Journal of Solids and Structures, 47, pp. 1118–1129 (2010).CrossRefGoogle Scholar
40. Gantmakher, F. R., The Theory of Matrices, New York, Chelsea (1959).Google Scholar
41. Pease, M. C., Methods of Matrix Algebra, Academic (1965).Google Scholar
42. Chen, W. Q. and Ding, H. J., “Free Vibration of Multi-Layered Spherically Isotropic Hollow Spheres,” International Journal of Mechanical Science, 43, pp. 667–680 (2001).CrossRefGoogle Scholar
43. Chen, J. T., Chen, C. T., Chen, P. Y. and Chen, I. L., “A Semi-Analytical Approach for Radiation and Scattering Problems with Circular Boundaries,” Computational Methods and Applications in Mechanical Engineering, 196, pp. 2751–2764 (2007).CrossRefGoogle Scholar
44. Hill, R., “A Self-Consistent Mechanics of Composite Materials,” Journal of Mechanics and Physics of Solids, 13, pp. 213–222 (1965).CrossRefGoogle Scholar
45. Reiter, T., Dvorak, G. J. and Tvergaard, V., “Micromechanical Models for Graded Composite Materials,” Journal of Mechanics and Physics of Solids, 45, pp. 1281–1302 (1997).CrossRefGoogle Scholar
46. Lee, W. M. and Chen, J. T., “Scattering of Flexural Wave in Thin Plate with Multiple Inclusions by Using Null-Field Integral Equation Approach,” Journal of Sound and Vibration, 329, pp. 1042–1061 (2010).CrossRefGoogle Scholar
47. Yosioka, K. and Kawasima, Y., “Acoustic Radiation Pressure on a Compressible Sphere,” Acustica, 5, pp. 167–173 (1955).Google Scholar
48. Mitri, F. G., “Frequency Dependence of the Acoustic Radiation Force Acting on Absorbing Cylindrical Shells,” Ultrasonics, 43, pp. 271–277 (2005).CrossRefGoogle ScholarPubMed
49. Joo, Y. S., Ih, J. G. and Choi, M. S., “Inherent Background Coefficients for Acoustic Resonance Scattering from Submerged, Multilayered, Cylindrical Structures,” Journal of the Acoustical Society of America, 103, pp. 900–910 (1998).CrossRefGoogle Scholar
50. Murphy, J. D., Breitenbach, E. D. and Uberall, H., “Resonance Scattering of Acoustic Waves from Cylindrical Shells,” Journal of the Acoustical Society of America, 64, pp. 677–683 (1978).CrossRefGoogle Scholar