Closed-form solutions for Love-wave propagation and excitation in orthotropic layered half-spaces
Author affiliations
DOI:
https://doi.org/10.15625/0866-7136/24368Keywords:
Love waves, orthotropic layered half-space, closed-form solution, elastodynamic reciprocity, dispersion analysisAbstract
Love waves are horizontally polarized shear waves guided by a surface layer and are highly sensitive to near-surface properties. While their behavior in isotropic media is well established, closed-form solutions for orthotropic layered structures under external excitation remain limited. This study presents closed-form solutions for both propagation and excitation of Love waves in an orthotropic elastic layer bonded to an orthotropic half-space. The dispersion relation is first derived within the framework of anti-plane shear motion using surface and interfacial boundary conditions. The elastodynamic reciprocity theorem is then applied to obtain explicit expressions for modal amplitudes generated by time-harmonic loading. Numerical results illustrate the dispersive characteristics and excitation behavior of the waves, highlighting the dependence of modal amplitudes on the frequency–thickness parameter. The proposed formulation provides a unified and efficient analytical framework for guided-wave analysis in anisotropic layered media.
Downloads
References
Achenbach, J. D. (1973). Wave Propagation in Elastic Solids. North-Holland Publishing Company.
Achenbach, J. D. (2003). Reciprocity in Elastodynamics. Cambridge University Press. https://doi.org/10.1017/cbo9780511550485
Babanouri, N., & Fattahi, H. (2018). Evaluating orthotropic continuum analysis of stress wave propagation through a jointed rock mass. Bulletin of Engineering Geology and the Environment, 77(2), 725–733. https://doi.org/10.1007/s10064-016-0989-9
Ebrahiminejad, A., Mardanshahi, A., & Kazemirad, S. (2022). Nondestructive evaluation of coated structures using Lamb wave propagation. Applied Acoustics, 185, 108378. https://doi.org/10.1016/j.apacoust.2021.108378
Ege, N., Erbaş, B., & Kaplunov, J. (2026). Dynamics of a FGM thin elastic coating subject to anti-plane shear. Continuum Mechanics and Thermodynamics, 38(2), 27. https://doi.org/10.1007/s00161-026-01458-4
Erbaş, B., Itskov, M., Kaplunov, J., & Prikazchikov, D. (2024). Multimode long-wave approximation for a viscoelastic coating subject to antiplane shear. Zeitschrift Für Angewandte Mathematik Und Physik, 75(6), 234. https://doi.org/10.1007/s00033-024-02382-w
Kaplunov, J., Prikazchikov, D., & Sultanova, L. (2019). Rayleigh-type waves on a coated elastic half-space with a clamped surface. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 377(2156), 20190111. https://doi.org/10.1098/rsta.2019.0111
Kulkarni, S. S., & Achenbach, J. D. (2008). Application of the reciprocity theorem to determine line-load-generated surface waves on an inhomogeneous transversely isotropic half-space. Wave Motion, 45(3), 350–360. https://doi.org/10.1016/j.wavemoti.2007.07.001
Le, D., Nguyen, Y., Quy, H. N., Le, L. H., & Phan, H. (2022). Elastodynamic response of an orthotropic layered elastic half-space to time-harmonic loading. Science Progress, 105(4). https://doi.org/10.1177/00368504221135449
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. https://doi.org/10.1109/58.393096
Nayfeh, A. H. (1995). Wave Propagation in Layered Anisotropic Media: With Applications to Composites (Vol. 39). Elsevier.
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
Panja, S. K., Alam, S., Mandal, S. C., & Craciun, E.-M. (2025). Love wave scattering by an interface crack between an orthotropic layer and an isotropic half-space. Continuum Mechanics and Thermodynamics, 37(2), 38. https://doi.org/10.1007/s00161-025-01375-y
Phan, H. (2020). Wave propagation in layered structures: Applications in Engineering and Biological Material Characterization.
Phan, H., Cho, Y., & Achenbach, J. D. (2013). Validity of the reciprocity approach for determination of surface wave motion. Ultrasonics, 53(3), 665–671. https://doi.org/10.1016/j.ultras.2012.09.007
Phan, H., Cho, Y., Le, Q. H., Pham, C. V., Nguyen, H. T.-L., Nguyen, P. T., & Bui, T. Q. (2019). 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, 96, 40–47. https://doi.org/10.1016/j.ultras.2019.03.015
Rose, J. L. (2014). Ultrasonic Guided Waves in Solid Media. Cambridge University Press. https://doi.org/10.1017/cbo9781107273610
Solie, L. P., & Auld, B. A. (1973). Elastic waves in free anisotropic plates. The Journal of the Acoustical Society of America, 54(1), 50–65. https://doi.org/10.1121/1.1913575
Tiersten, H. F. (1969). Elastic Surface Waves Guided by Thin Films. Journal of Applied Physics, 40(2), 770–789. https://doi.org/10.1063/1.1657463
Vasudevan, N., & Mal, A. K. (1985). Response of an Elastic Plate to Localized Transient Sources. Journal of Applied Mechanics, 52(2), 356–362. https://doi.org/10.1115/1.3169053
Vinh, P. C., & Ngoc Anh, V. T. (2014). Rayleigh waves in an orthotropic half-space coated by a thin orthotropic layer with sliding contact. International Journal of Engineering Science, 75, 154–164. https://doi.org/10.1016/j.ijengsci.2013.11.004
Xu, L., & Ma, M. (2022). Dynamic response of the multilayered half-space medium due to the spatially periodic harmonic moving load. Soil Dynamics and Earthquake Engineering, 157, 107246. https://doi.org/10.1016/j.soildyn.2022.107246
Downloads
Published
How to Cite
License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Funding data
-
National Foundation for Science and Technology Development
Grant numbers 107.01-2025.130
