An Efficient and Accurate Method for Calculating Nonlinear Diffraction Beam Fields

Jeong, Hyunjo;Cho, Sungjong;Nam, Kiwoong;Lee, Janghyun

  • 투고 : 2016.02.02
  • 심사 : 2016.04.05
  • 발행 : 2016.04.30


This study develops an efficient and accurate method for calculating nonlinear diffraction beam fields propagating in fluids or solids. The Westervelt equation and quasilinear theory, from which the integral solutions for the fundamental and second harmonics can be obtained, are first considered. A computationally efficient method is then developed using a multi-Gaussian beam (MGB) model that easily separates the diffraction effects from the plane wave solution. The MGB models provide accurate beam fields when compared with the integral solutions for a number of transmitter-receiver geometries. These models can also serve as fast, powerful modeling tools for many nonlinear acoustics applications, especially in making diffraction corrections for the nonlinearity parameter determination, because of their computational efficiency and accuracy.


Nonlinear Beam Field;Quasilinear Theory;Integral Solution;Multi-Gaussian Beam;Diffraction


  1. A. Kumar, C. J. Torbet, J. W. Jones and T. M. Pollock, "Nonlinear ultrasonics for in situ damage detection during high frequency fatigue," J. Appl. Phys., Vol. 106, 024904 (2009)
  2. J.-Y. Kim, L. J. Jacobs, J. Qu and J. W. Littles, "Experimental characterization of fatigue damage in a nickel-base superalloy using nonlinear ultrasonic waves," J. Acoust. Soc. Am., Vol. 120, pp. 1266-1273 (2006)
  3. J. H. Cantrell, "Substructural organization, dislocation plasticity and harmonic generation in cyclically stressed wavy slip metals," Proc. Royal Soc. London Series A - Math. Phys. Eng. Sci., Vol. 460, pp. 757-780 (2004)
  4. K. D. Wallace, C. W. Lloyd, M. R. Holland and J. G. Miller, "Finite amplitude measurements of the nonlinear parameter B/A for liquid mixtures spanning a range relevant to tissue harmonic mode," Ultrasound Med. Biol., Vol. 33, pp. 620-629 (2007)
  5. L. Bjorno, "Characterization of biological media by means of their nonlinearity," Ultrasonics, Vol. 24, pp. 254-259 (1986)
  6. F. Prieur, S. P. Nasholm, A. Austeng, F. Tichy and S. Holm, "Feasibility of second harmonic imaging in active sonar: measurements and simulations," IEEE J. Oceanic Eng., Vol. 37, pp. 467-477 (2012)
  7. L. K. Zarembo and V. A. Krasil'nikov, "Nonlinear phenomena in the propagation of elastic waves in solids," Sov. Phys. Uspekhi, Vol. 13, pp. 778-797 (1971)
  8. H. Jeong, S. Cho, K. Nam and J. Lee, "Diffraction corrections for second harmonic beam fields and effects on the nonlinearity parameter evaluation," Journal of the Korean Society for Nondestructive Testing, Vol. 36, No. 2, pp. 112-120 (2016)
  9. M. F. Hamilton and C. L. Morfey, "Model Equations," Nonlinear Acoustics, M. F. Hamilton and D. T. Blackstock, Eds., Academic Press, San Diego, USA, pp. 41-63 (2008)
  10. M. Cervenka and M. Bednarik, "Nonparaxial model for a parametric acoustic array," J. Acoust. Soc. Am., Vol. 134, pp. 933-938 (2013)
  11. S. R. Best, A. J. Croxford and S. A. Neild, "Modelling harmonic generation measurements in solids," Ultrasonics, Vol. 54, pp. 442-450 (2014)
  12. X. Zhao and T. Gang, "Nonparaxial multi-Gaussian beam models and measurement models for phased array transducers," Ultrasonics, Vol. 49, pp. 126-130 (2009)
  13. H. Jeong and L. W. Schmerr, Jr., "Ultrasonic transducer fields modeled with a modular multi-Gausssian beam and application to a contact angle beam testing," Research in Nondestructive Evaluation, Vol. 19, pp. 87-103 (2008)
  14. L. W. Schmerr Jr. and S.-J. Song, "Ultrasonic Nondestructive Evaluation Systems - Models and Measurements," Springer, New York, USA, pp. 179-234 (2007)
  15. H. Jeong, M.-C. Park and L. W. Schmerr, Jr., "Application of a modular multi-Gaussian beam model to ultrasonic wave propagation with multiple interfaces," Journal of the Korean Society for Nondestructive Testing, Vol. 25, pp. 163-170 (2005)
  16. H. Jeong and L. W. Schmerr, Jr., "Effects of material anisotropy on ultrasonic beam propagation: Diffraction and beam skew," Journal of the Korean Society for Nondestructive Testing, Vol. 26, pp. 198-205 (2006)
  17. V. Labat, J. P. Remenieras, O. Bou Matar, A. Ouahabi and F. Patat, "Harmonic propagation of finite amplitude sound beams: experimental determination of the nonlinearity parameter B/A," Ultrasonics, Vol. 38, pp. 292-296 (2002)
  18. J. J. Wen and M. A. Breazeale, "A diffraction beam field expressed as the superposition of Gaussian beams," J. Acoust. Soc. Am., Vol. 83, pp. 1752-1756 (1988)
  19. H.-J. Kim, L. W. Schmerr, Jr. and A. Sedov, "Generation of the basis sets for multi-Gaussian ultrasonic beam models-An overview," J. Acoust. Soc. Am., Vol. 119, pp. 1971-1978 (2006)
  20. D. Huang and M. A. Breazeale, "A Gaussian finite-element method for description of sound diffraction," J. Acoust. Soc. Am., Vol. 106, pp. 1771-1781 (1999)

피인용 문헌

  1. Diffraction Corrections for Second Harmonic Beam Fields and Effects on the Nonlinearity Parameter Evaluation vol.36, pp.2, 2016,


연구 과제 주관 기관 : National Research Foundation of Korea (NRF)