Formulas for the velocity of Stoneley waves at the unbonded interface between two micropolar elastic half-spaces
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https://doi.org/10.15625/0866-7136/22643Keywords:
Stoneley waves, micropolar half-spaces, the complex function method, formulas for the Stoneley wave velocity, unbonded interfaceAbstract
In this paper, we investigate the propagation of Stoneley waves along the unbonded interface between two micropolar elastic half-spaces. Using the complex function method, we derive explicit formulas for the wave velocity. These formulas have applications in various scientific fields, particularly in non-destructive evaluation. Two numerical examples illustrate how the obtained wave velocity formulas can be used to evaluate material parameters non-destructively.
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[1] R. Stoneley. Elastic waves at the surface of separation of two solids. Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, 106, (1924), pp. 416–428. https://doi.org/10.1098/rspa.1924.0079.
[2] 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.
[3] Q. Gu, Y. Liu, and T. Liang. Stoneley wave at the interface of elastic-nematic elastomer half spaces. Physica B: Condensed Matter, 652, (2023). https://doi.org/10.1016/j.physb.2022.414629.
[4] D. Nkemzi. A new formula for the velocity of Rayleigh waves. Wave Motion, 26, (1997), pp. 199–205. https://doi.org/10.1016/s0165-2125(97)00004-8.
[5] P. G. Malischewsky. Comment to “A new formula for the velocity of Rayleigh waves” by D. Nkemzi [Wave Motion 26 (1997) 199–205]. Wave Motion, 31, (2000), pp. 93–96. https://doi.org/10.1016/s0165-2125(99)00025-6.
[6] P. C. Vinh and R. W. Ogden. On formulas for the Rayleigh wave speed. Wave Motion, 39, (2004), pp. 191–197. https://doi.org/10.1016/j.wavemoti.2003.08.004.
[7] P. C. Vinh and R. W. Ogden. Formulas for the Rayleigh wave speed in orthotropic elastic solids. Archive of Mechanics, 56, (2004), pp. 247–265.
[8] P. C. Vinh. On formulas for the velocity of Rayleigh waves in prestrained incompressible elastic solids. Journal of Applied Mechanics, 77, (2010), pp. 1–9. https://doi.org/10.1115/1.3197139.
[9] P. C. Vinh. On formulas for the Rayleigh wave velocity in pre-stressed compressible solids. Wave Motion, 48, (2011), pp. 614–625. https://doi.org/10.1016/j.wavemoti.2011.04.015.
[10] P. C. Vinh and N. Q. Xuan. Rayleigh waves with impedance boundary condition: Formula for the velocity, existence and uniqueness. European Journal of Mechanics - A/Solids, 61, (2017), pp. 180–185. https://doi.org/10.1016/j.euromechsol.2016.09.011.
[11] P. T. H. Giang and P. C. Vinh. On the existence of Rayleigh waves with full impedance boundary condition. Mathematics and Mechanics of Solids, 30, (2024), pp. 927–941. https://doi.org/10.1177/10812865241266809.
[12] P. C. Vinh and P. T. H. Giang. On formulas for the velocity of Stoneley waves propagating along the loosely bonded interface of two elastic half-spaces. Wave Motion, 48, (2011), pp. 647–657. https://doi.org/10.1016/j.wavemoti.2011.05.002.
[13] P. C. Vinh, P. G. Malischewsky, and P. T. H. Giang. Formulas for the speed and slowness of Stoneley waves in bonded isotropic elastic half-spaces with the same bulk wave velocities. International Journal of Engineering Science, 60, (2012), pp. 53–58. https://doi.org/10.1016/j.ijengsci.2012.05.002.
[14] R. S. Lakes. Experimental microelasticity of two porous solids. International Journal of Solids and Structures, 22, (1), (1986), pp. 55–63. https://doi.org/10.1016/0020-7683(86)90103-4.
[15] G. Hassen and P. de Buhan. A two-phase model and related numerical tool for the design of soil structures reinforced by stiff linear inclusions. European Journal of Mechanics A/Solids, 24, (2005), pp. 987–1001. https://doi.org/10.1016/j.euromechsol.2005.06.009.
[16] N. P. Kruyt. On weak and strong contact force networks in granular materials. International Journal of Solids and Structures, 92–93, (2016), pp. 135–140. https://doi.org/10.1016/j.ijsolstr.2016.02.039.
[17] J. F. C. Yang and R. S. Lakes. Experimental study of micropolar and couple stress elasticity in compact bone in bending. Journal of Biomechanics, 15, (1982), pp. 91–98. https://doi.org/10.1016/0021-9290(82)90040-9.
[18] A. C. Eringen. Linear theory of micropolar elasticity. Journal of Mathematics and Mechanics, 15, (6), (1966), pp. 909–923.
[19] C. Eringen. Theory of microcontinuum field theories. Springer, (1999).
[20] S. K. Tomar and D. Singh. Propagation of Stoneley waves at an interface between two microstretch elastic half-spaces. Journal of Vibration and Control, 12, (2006), pp. 995–1009. https://doi.org/10.1177/1077546306068689.
[21] M. Tajuddin. Existence of Stoneley waves at an unbonded interface between two micropolar elastic half-spaces. Journal of Applied Mechanics, 62, (1995), pp. 255–257. https://doi.org/10.1115/1.2895919.
[22] P. T. H. Giang and P. C. Vinh. Existence and uniqueness of micropolar elastic Stoneley waves with sliding contact and formulas for the wave slowness. Journal of Applied Mechanics, 92, (2025). https://doi.org/10.1115/1.4066956.
[23] N. I. Muskhelishvili. Singular integral equations. Noordhoff-Groningen, (1953). https://doi.org/10.1007/978-94-009-9994-7.
[24] N. I. Muskhelishvili. Some basic problems of mathematical theory of elasticity. Noordhoff, Netherlands, (1963). https://doi.org/10.1007/978-94-017-3034-1.
[25] P. T. H. Giang and P. C. Vinh. Existence and uniqueness of Rayleigh waves with normal impedance boundary conditions and formula for the wave velocity. Journal of Engineering Mathematics, 130, (2021). https://doi.org/10.1007/s10665-021-10170-y.
[26] P. T. H. Giang. The velocity formulas of Rayleigh waves and Stoneley waves. Phd thesis, VNU University of Science, (2017).
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National Foundation for Science and Technology Development
Grant numbers 107.02-2021.13
