A theoretical study on propagation of guided waves in a fluid layer overlying a solid half-space


  • Phuong-Thuy Nguyen Institute of Physics, VAST, Hanoi
  • Haidang Phan Institute of Mechanics, VAST, Hanoi




layered half-space, guided waves, reciprocity theorem, quantitative ultrasound


Ultrasonic guided waves propagating in a non-viscous fluid layer of uniform thickness bonded to an elastic solid half-space is theoretically investigated in this article. Based on the boundary conditions set for the joined configuration, a characteristic dispersion equation is found and new expressions for free guided waves are introduced. Closed-form solutions of guided waves generated by a time-harmonic load are derived by the use of elastodynamics reciprocity theorems. Through calculation examples, it is shown that the obtained computation of the lowest wave mode approaches the result of the Rayleigh wave in the solid half-space as the layer thickness approaches zero. The aim of the present work is to improve the understanding of wave motions in layered half-spaces for potential applications in the area of bone quantitative ultrasound.


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Author Biography

Haidang Phan, Institute of Mechanics, VAST, Hanoi

(Corresponding Author) Email: haidangphan@imech.vast.vn


L. H. Le, Y. J. Gu, Y. Li, and C. Zhang. Probing long bones with ultrasonic body waves. Applied Physics Letters, 96, (11), (2010). https://doi.org/10.1063/1.3300474.

V. H. Nguyen, T. N. H. T. Tran, M. D. Sacchi, S. Naili, and L. H. Le. Computing dispersion curves of elastic/viscoelastic transversely-isotropic bone plates coupled with soft tissue and marrow using semi-analytical finite element (SAFE) method. Computers in Biology and Medicine, 87, (2017), pp. 371–381. https://doi.org/10.1016/j.compbiomed.2017.06.001.

P. H. F. Nicholson, P. Moilanen, T. Kärkkäinen, J. Timonen, and S. Cheng. Guided ultrasonic waves in long bones: modelling, experiment and in vivo application. Physiological Measurement, 23, (4), (2002), pp. 755–768. https://doi.org/10.1088/0967-3334/23/4/313.

G. Lowet and G. Van der Perre. Ultrasound velocity measurement in long bones: measurement method and simulation of ultrasound wave propagation. Journal of Biomechanics, 29, (10), (1996), pp. 1255–1262. https://doi.org/10.1016/0021-9290(96)00054-1.

J. J. Kaufman, G. Luo, and R. S. Siffert. Ultrasound simulation in bone. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 55, (6), (2008), pp. 1205–1218. https://doi.org/10.1109/tuffc.2008.784.

A. H. Nayfeh. Wave propagation in layered anisotropic media: With application to composites. Elsevier, (1995).

J. Achenbach. Wave propagation in elastic solids. North-Holland Publishing Company, (2012).

J. L. Rose. Ultrasonic guided waves in solid media. Cambridge University Press, (2014).

W. M. Ewing,W. S. Jardetzky, and F. Press. Elastic waves in layered media. McGraw-Hill, (1957).

T. Kundu. Ultrasonic nondestructive evaluation: engineering and biological material characterization. CRC Press, (2003).

N. T. K. Linh, P. C. Vinh, and L. T. Hue. An approximate formula for the H/V ratio of Rayleigh waves in compressible pre-stressed elastic half-spaces coated with a thin layer. Vietnam Journal of Mechanics, 40, (1), (2018), pp. 63–78. https://doi.org/10.15625/0866-7136/10417.

P. C. Vinh, V. T. N. Anh, and V. P. Thanh. Rayleigh waves in an isotropic elastic half-space coated by a thin isotropic elastic layer with smooth contact. Wave Motion, 51, (3), (2014), pp. 496–504. https://doi.org/10.1016/j.wavemoti.2013.11.008.

P. C. Vinh and V. T. N. Anh. Rayleigh waves in an orthotropic half-space coated by a thin orthotropic layer with sliding contact. International Journal of Engineering Science, 75, (2014), pp. 154–164. https://doi.org/10.1016/j.ijengsci.2013.11.004.

J. D. Achenbach and S. P. Keshava. Free waves in a plate supported by a semi-infinite continuum. Journal of Applied Mechanics, 34, (2), (1967), pp. 397–404. https://doi.org/10.1115/1.3607696.

H. F. Tiersten. Elastic surface waves guided by thin films. Journal of Applied Physics, 40, (2), (1969), pp. 770–789. https://doi.org/10.1063/1.1657463.

T. T. Tuan and T. N. Trung. The dispersion of Rayleigh waves in orthotropic layered half-space using matrix method. Vietnam Journal of Mechanics, 38, (1), (2016), pp. 27–38. https://doi.org/10.15625/0866-7136/38/1/6191.

C. L. Yapura and V. K. Kinra. Guided waves in a fluid-solid bilayer. Wave Motion, 21, (1), (1995), pp. 35–46. https://doi.org/10.1016/0165-2125(94)00043-5.

H. Phan, Y. Cho, and J. D. Achenbach. Verification of surface wave solutions obtained by the reciprocity theorem. Ultrasonics, 54, (7), (2014), pp. 1891–1894. https://doi.org/10.1016/j.ultras.2014.05.003.

H. Phan, Y. Cho, and J. D. Achenbach. Validity of the reciprocity approach for determination of surface wave motion. Ultrasonics, 53, (3), (2013), pp. 665–671. https://doi.org/10.1016/j.ultras.2012.09.007.

H. Phan, Y. Cho, and J. D. Achenbach. A theoretical study on scattering of surface waves by a cavity using the reciprocity theorem. In Nondestructive Testing of Materials and Structures. Springer Netherlands, (2013), pp. 739–744.

H. Phan, Y. Cho, T. Ju, and J. D. Achenbach. Multiple scattering of surface waves by cavities in a half-space. In AIP Conference Proceedings, Vol. 1581. AIP, (2014), pp. 537–541. https://doi.org/10.1063/1.4864866.

O. Balogun and J. D. Achenbach. Surface waves generated by a line load on a halfspace with depth-dependent properties. Wave Motion, 50, (7), (2013), pp. 1063–1072. https://doi.org/10.1016/j.wavemoti.2013.03.001.

S. S. Kulkarni and J. D. Achenbach. Application of the reciprocity theorem to determine line-load-generated surface waves on an inhomogeneous transversely isotropic half-space. Wave Motion, 45, (3), (2008), pp. 350–360. https://doi.org/10.1016/j.wavemoti.2007.07.001.

J. D. Achenbach. Reciprocity in elastodynamics. Cambridge University Press, (2003).

J. D. Achenbach, A. K. Gautesen, and H. McMaken. Ray methods for waves in elastic solids: with applications to scattering by cracks. Pitman Advanced Publishing Program, (1982).

A. T. de Hoop. Handbook of radiation and scattering of waves: Acoustic waves in fluids, elastic waves in solids, electromagnetic waves. Academic Press, (1995).

L. R. F. Rose, W. K. Chiu, N. Nadarajah, and B. S. Vien. Using reciprocity to derive the far field displacements due to buried sources and scatterers. The Journal of the Acoustical Society of America, 142, (5), (2017), pp. 2979–2987. https://doi.org/10.1121/1.5009666.

H. Phan, T. Q. Bui, H. T. L. Nguyen, and C. V. Pham. Computation of interface wave motions by reciprocity considerations. Wave Motion, 79, (2018), pp. 10–22. https://doi.org/10.1016/j.wavemoti.2018.02.008.

H. Phan, Y. Cho, Q. H. Le, P. C. Vinh, H. T. L. Nguyen, P. T. Nguyen, and T. Q. Bui. A closed-form solution to propagation of guided waves in a layered half-space under a time-harmonic load: An application of elastodynamic reciprocity. Ultrasonics, (2019). https://doi.org/10.1016/j.ultras.2019.03.015.

H. Phan, Y. Cho, and J. D. Achenbach. Application of the reciprocity theorem to scattering of surface waves by a cavity. International Journal of Solids and Structures, 50, (24), (2013), pp. 4080–4088. https://doi.org/10.1016/j.ijsolstr.2013.08.020.

H. Phan, Y. Cho, and W. Li. A theoretical approach to multiple scattering of surface waves by shallow cavities in a half-space. Ultrasonics, 88, (2018), pp. 16–25. https://doi.org/10.1016/j.ultras.2018.02.018.

H. Phan, Y. Cho, T. Ju, J. D. Achenbach, S. Krishnaswamy, and B. Strom. A novel approach of using the elastodynamic reciprocity for guided wave problems. In AIP Conference Proceedings, Vol. 1511. AIP, (2013), pp. 107–112. https://doi.org/10.1063/1.4789037

W. Liu, Y. Cho, H. Phan, and J. D. Achenbach. Study on the scattering of 2-D Rayleigh waves by a cavity based on BEM simulation. Journal of Mechanical Science and Technology, 25, (3), (2011), pp. 797–802. https://doi.org/10.1007/s12206-011-0133-5.

S. Hao, B. W. Strom, G. Gordon, S. Krishnaswamy, and J. D. Achenbach. Scattering of the lowest Lamb wave modes by a corrosion pit. Research in Nondestructive Evaluation, 22, (4), (2011), pp. 208–230. https://doi.org/10.1117/12.880534.




How to Cite

Nguyen, P.-T., & Phan, H. (2019). A theoretical study on propagation of guided waves in a fluid layer overlying a solid half-space. Vietnam Journal of Mechanics, 41(1), 51–62. https://doi.org/10.15625/0866-7136/12710



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