Analytical Model of Three-Dimensional Ultrasonic Beam Interaction with an Immersed Plate

• Autorzy: Soucrati H. , Chitnalah A. , Aouzale N. , Jakjoud H.

Identyfikatory

DOI

10.24425/aoa.2018.125160

• Języki publikacji: EN

Abstrakty

EN

This paper proposes an analytical model to describe the interaction of a bounded ultrasonic beam with an immersed plate. This model, based on the Gaussian beams decomposition, takes into account multiple reflections into the plate. It allows predicting three-dimensional spatial distributions of both transmitted and reflected fields. Thereby, it makes it easy to calculate the average pressure over the receiver’s area taking into account diffraction losses. So the acoustical parameters of the plate can be determined more accurately. A Green’s function for the interaction of an ultrasonic beam with the plate is derived. The obtained results are compared to those given by the angular spectrum approach. A good agreement is seen showing the validity of the proposed model.

Słowa kluczowe

EN

ultrasonic modeling; immersed plate; Gaussian beams decomposition; Green’s functions; NDUT

• Wydawca: Instytut Podstawowych Problemów Techniki PAN ; Komitet Akustyki PAN ; Polskie Towarzystwo Akustyczne
• Czasopismo: Archives of Acoustics
• Rocznik: 2018
• Tom: Vol. 43, No. 4
• Strony: 669--679
• Opis fizyczny: Bibliogr. 52 poz., rys., tab., wykr.

Twórcy

autor

Soucrati H.

• Electrical Systems and Telecommunications Laboratory, Cadi Ayyad University, BP 549, Av. Abdelkarim Elkhattabi, Guéliz Marrakesh, Morocco

autor

Chitnalah A.

• Electrical Systems and Telecommunications Laboratory, Cadi Ayyad University, BP 549, Av. Abdelkarim Elkhattabi, Guéliz Marrakesh, Morocco

autor

Aouzale N.

• Electrical Systems and Telecommunications Laboratory, Cadi Ayyad University, BP 549, Av. Abdelkarim Elkhattabi, Guéliz Marrakesh, Morocco

autor

Jakjoud H.

• Energy Engineering Materials and Systems Laboratory, Ibn Zohr University, BP 1136, Agadir, Morocco

Bibliografia

• 1. Aouzale N., Chitnalah A., Jakjoud H. (2010), Moroccan oil characterization using pulse-echo ultrasonic technique, Physical & Chemical News, 54, 1-8.
• 2. Babich V. M., Pankratova T. F. (1973), On discontinuities of the Green function of mixed problem for wave equation with variable coefficients, Problems of Mathematical Physics, Leningrad University Press, 6, 9-27.
• 3. Blitz J., Simpson G. (1996), Ultrasonic methods of non-destructive testing, Chapman & Hall, London.
• 4. Carcione J. M. (1996), Wave propagation in anisotropic, saturated porous media: Plane-wave theory and numerical simulation, The Journal of the Acoustical Society of America, 99, 5, 2655-2666.
• 5. Cartz L. (1995), Nondestructive testing, ASM International, Materials Park, OH, United States.
• 6. Cerveny V., Popov M. M., Psencik I. (1982), Computation of wave fields in inhomogeneous media – Gaussian beam approach, Geophysical Journal of Royal Astronomical Society, 70, 109-128.
• 7. Deschamps M., Hosten B. (1992), The effects of viscoelasticity on the reflection and transmission of ultrasonic waves by an orthotropic plate, The Journal of the Acoustical Society of America, 91, 4, 2007-2015.
• 8. Du Y., Jensen H., Jensen J. A. (2009), Angular spectrum simulation of pulsed ultrasound fields, IEEE International Ultrasonics Symposium Proceedings, 2379-2382.
• 9. Du Y., Jensen H., Jensen J. A. (2013), Investigation of an angular spectrum approach for pulsed ultrasound fields, Ultrasonics, 53, 6, 1185-1191.
• 10. El Mouhtadi A., Duclos J., Duflo H. (2012), Ultrasonic modeling of a viscoelastic homogeneous plate, Acoustics 2012 Proceedings, Société Française d’Acoustique, Nantes, France, 2611-2616.
• 11. Glauser A. R., Robertson P. A., Lowe C. R. (2001), An electrokinetic sensor for studying immersed surfaces, using focused ultrasound, Sensors and Actuators B: Chemical, 80, 1, 68-82.
• 12. Goodman J. W. (1968), Introduction to fourier optics, McGraw-Hill, New York, USA.
• 13. Green G. (1852), An essay on the application of mathematical analysis to the theories of electricity and magnetism, Journal für die reine und angewandte Mathematik, 44, 356-374.
• 14. Gunarathne G. P. P., Christidis K. (2002), Material characterization in situ using ultrasound measurements, IEEE Transactions on Instrumentation and Measurement, 51, 2, 368-373.
• 15. Hamilton M. F., Blackstock D. T. (1998), Nonlinear acoustics, San Diego, Academic Press.
• 16. Hull J. B., Langton C. M., Barker S., Jones A. R. (1996), Identification and characterization of materials by broadband ultrasonic attenuation analysis, Journal of Materials Processing Technology, 56, 148-157.
• 17. Ingard K. U., Morse P. M. (1968), Theoretical acoustics, Princeton University Press, Princeton, New Jersey.
• 18. Jakjoud H., Chitnalah A., Aouzale N. (2014), Transducer profile effect on the second harmonic level, Acoustical Physics, 60, 3, 261-268.
• 19. Kachalov A. P., Popov M. M. (1981), Application of the method of summation of Gaussian beams for calculation of high-frequency wave fields, Soviet Physics – Doklady, 26, 604-606.
• 20. Kinra V. K., Dayal V. (1988), A new technique for ultrasonic-nondestructive evaluation of thin specimens, Experimental Mechanics, 33, 2, 288-297.
• 21. Kinra V. K., Iyer V. R. (1995), Ultrasonic measurement of the thickness, phase velocity, density or attenuation of a thin-viscoelastic plate. Part I. The forward problem, Ultrasonics, 33, 2, 95-109.
• 22. Kinsler L. E., Frey A. R., Coppens A. B., Sanders J. V. (1999), Fundamentals of acoustics, 4th Edition, Wiley-VCH.
• 23. Kline R. A. (1984), Measurement of attenuation and dispersion using an ultrasonic spectroscopy technique, The Journal of the Acoustical Society of America, 76, 2, 498-504.
• 24. Korenev B. G. (2002), Bessel functions and their applications, Taylor & Francis, CRC Press.
• 25. Langenberg K. J., Marklein R., Mayer K. (2012), Ultrasonic nondestructive testing of materials: theoretical foundations, Taylor & Francis, CRC Press.
• 26. Lee B. C., Staszewski W. J. (2003a), Modelling of Lamb waves for damage detection in metallic structures. Part I. Wave propagation, Smart Materials and Structures, 12, 5, 804-814.
• 27. Lee B. C., Staszewski W. J. (2003b), Modelling of Lamb waves for damage detection in metallic structures: Part II. Wave interactions with damage, Smart Materials and Structures, 12, 5, 815-824.
• 28. Lee B. C., Staszewski W. J. (2007a), Lamb wave propagation modelling for damage detection. I. Two-dimensional analysis, Smart Materials and Structures, 16, 2, 249-259.
• 29. Lee B. C., Staszewski W. J. (2007b), Lamb wave propagation modelling for damage detection. II. Damage monitoring strategy, Smart materials and structures, 16, 2, 260-274.
• 30. Leiderman R., Braga A. M. B., Barbone P. E. (2005), Scattering of ultrasonic waves by defective adhesion interfaces in submerged laminated plates, The Journal of the Acoustical Society of America, 118, 4, 2154-2166.
• 31. Lowe M. J. S. (1995), Matrix techniques for modeling ultrasonic waves in multilayered media, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 42, 4, 525-542.
• 32. Makin I. R. S., Averkiou M. A., Hamilton M. F. (2000), Second-harmonic generation in a sound beam reflected and transmitted at a curved interface, The Journal of the Acoustical Society of America, 108, 4, 1505-1513.
• 33. Moilanen P., Nicholson P. H. F., Kilappa V., Cheng S., Timonen J. (2006), Measuring guided waves in long bones: Modeling and experiments in free and immersed plates, Ultrasound in Medicine & Biology, 32, 5, 709-719.
• 34. Orofino D. P., Pedersen P. C. (1993a), Efficient angular spectrum decomposition of acoustic sources. Part I. Theory, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 40, 3, 238-249.
• 35. Orofino D. P., Pedersen P. C. (1993b), Efficient angular spectrum decomposition of acoustic sources. Part II. Results, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 40, 3, 250-257.
• 36. Perdijon J. (1993), Ultrasonic non-destructive testing [in French: Le contrôle non destructif par ultrasons], Hermès.
• 37. Popov M. M. (1982a), A new method of computation of wave fields using Gaussian beams, Wave Motion, 4, 85-97.
• 38. Popov M. M. (1982b), A new method of computing wave fields in the high-frequency approximation, Journal of Mathematical Sciences, 20, 1869-1882.
• 39. Popov M. M., Psencik I., Cerveny V. (1980), Uniform ray asymptotics for seismic wave fields in laterally inhomogeneous media, Prog. Abstr. XVII General Assembly of the European Seismological Commission, Hungarian Geophysical Society, Budapest, 143.
• 40. Rose J. L. (1999), Ultrasonic waves in solid media, Cambridge University Press, Cambridge.
• 41. Rossi M. (1986), Electro-acoustique, Edit. Dunod.
• 42. Schmerr L. W., Jr. (2013), Fundamentals of ultrasonic nondestructive evaluation: a modeling approach, Springer Science & Business Media.
• 43. Seki H., Granato A., Truell R. (1956), Diffraction effects in the ultrasonic field of a piston source and their importance in the accurate measurement of attenuation, The Journal of the Acoustical Society of America, 28, 2, 230-238.
• 44. Shankar P. M. (2001), Ultrasonic tissue characterization using a generalized Nakagami model, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 48, 6, 1716-1720.
• 45. Soucrati H., Chitnalah A., Jakjoud H., El Idrissi A. (2013), Application of the wavelets transform to the determination of the geometrical characteristics of a plate by analysis of the diffused acoustic field, Revue Méditerranéenne des Télécommunications, 3, 2, 152-156.
• 46. Van Hemelrijck D., Anastassopoulos A. (1996), Non destructive testing, A.A. Balkema, Rotterdam, Netherlands.
• 47. Wen J. J., Breazeale M. A. (1988), A diffraction beam field expressed as the superposition of Gaussian beams, The Journal of the Acoustical Society of America, 83, 5, 1752-1756.
• 48. Westervelt P. J. (1963), Parametric acoustic array, The Journal of the Acoustical Society of America, 35, 4, 535-537.
• 49. Williams E. G., Maynard J. D. (1982), Numerical evaluation of the Rayleigh integral for planar radiators using the FFT, The Journal of the Acoustical Society of America, 72, 6, 2020-2030.
• 50. Wu P., Kazys R., Stepinski T. (1996a), Analysis of the numerically implemented angular spectrum approach based on the evaluation of two-dimensional acoustic fields. Part I. Errors due to the discrete Fourier transform and discretization, The Journal of the Acoustical Society of America, 99, 3, 1339-1348.
• 51. Wu P., Kazys R., Stepinski T. (1996b), Analysis of the numerically implemented angular spectrum approach based on the evaluation of two-dimensional acoustic fields. Part II. Characteristics as a function of angular range, The Journal of the Acoustical Society of America, 99, 3, 1349-1359.
• 52. Wu P., Kazys R., Stepinski T. (1997), Optimal selection of parameters for the angular spectrum approach to numerically evaluate acoustic fields, The Journal of the Acoustical Society of America, 101, 1, 125-134.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).