Wave propagation through an interface between dissimilar media with a doubly periodic array of arbitrary shaped planar delaminations. (English) Zbl 1447.74022
Summary: This paper considers the scattering of elastic waves by a doubly periodic array of three-dimensional planar delaminations at the interface between two dissimilar media. The delaminations are modelled in terms of the spring boundary conditions, which are employed to formulate a boundary integral equation. The problem is solved using the Bubnov-Galerkin scheme and the integral approach, taking into account geometrical periodicity. The effects of distribution and shape of periodic delaminations on wave transmission and diffraction are analysed. The specific phenomenon of pass-bands or an ‘opening’ interface for wave propagation by a periodic array of delaminations is revealed.
MSC:
| 74J20 | Wave scattering in solid mechanics |
| 74R10 | Brittle fracture |
| 74S99 | Numerical and other methods in solid mechanics |
Keywords:
spring boundary condition; diffraction; Bubnov-Galerkin method; pass-band effect; boundary integral equation methodReferences:
| [1] | [1] Khelif, A, Adibi, A. Phononic crystals: fundamentals and applications. New York: Springer-Verlag, 2016. |
| [2] | [2] Zhao, S, Wang, Y, Zhang, C. High-transmission acoustic self-focusing and directional cloaking in a graded perforated metal slab. Sci Rep 2017; 7: 4368. |
| [3] | [3] Sotiropoulos, DA, Achenbach, JD. Ultrasonic reflection by a planar distribution of cracks. J Nondestr Eval 1988; 7: 123-129. |
| [4] | [4] Boström, A, Wickham, GR. On the boundary conditions for ultrasonic transmission by partially closed cracks. J Nondestr Eval 1991; 10: 139-149. |
| [5] | [5] Mori, N, Biwa, S, Hayashi, T. Reflection and transmission of Lamb waves at an imperfect joint of plates. J Appl Phys 2013; 113(7): 074901. |
| [6] | [6] Golub, MV, Doroshenko, OV, Boström, A. Effective spring boundary conditions for a damaged interface between dissimilar media in three-dimensional case. Int J Solids Struct 2016; 81: 141-150. |
| [7] | [7] Baik, JM, Thompson, RB. Ultrasonic scattering from imperfect interfaces: a quasi-static model. J Nondestr Eval 1984; 4: 177-196. |
| [8] | [8] Wickham, G. A polarization theory for the scattering of sound at imperfect interfaces. J Nondestr Eval 1992; 11: 199-210. |
| [9] | [9] Achenbach, JD, Kitahara, M, Mikata, Y. Reflection and transmission of plane waves by a layer of compact inhomogeneities. Pure Appl Geophys 1988; 128: 101-118. |
| [10] | [10] Scarpetta, E, Sumbatyan, MA. One-mode wave propagation through a periodic array of interface cracks: explicit analytical results. J Math Anal Appl 2008; 337(1): 576-593. · Zbl 1293.74250 |
| [11] | [11] Golub, MV. Propagation of elastic waves in layered composites with microdefect concentration zones and their simulation with spring boundary conditions. Acoust Phys 2010; 56(6): 848-855. |
| [12] | [12] Lekesiz, H, Katsube, N, Rokhlin, SI. Effective spring stiffness for a planar periodic array of collinear cracks at an interface between two dissimilar isotropic materials. Mech Mater 2011; 43(2): 87-98. · Zbl 1269.74196 |
| [13] | [13] Golub, MV, Zhang, C, Wang, YS. SH-wave propagation and scattering in periodically layered composites with a damaged layer. J Sound Vib 2012; 331(8): 1829-1843. |
| [14] | [14] Golub, MV, Zhang, C. In-plane time-harmonic elastic wave motion and resonance phenomena in a layered phononic crystal with periodic cracks. J Acoust Soc Am 2015; 137(1): 238-252. |
| [15] | [15] Scarpetta, E, Sumbatyan, MA. On wave propagation in elastic solids with a doubly periodic array of cracks. Wave Motion 1997; 25(1): 61-72. · Zbl 0954.74524 |
| [16] | [16] Shi, PP. Interaction between the doubly periodic interfacial cracks in a layered periodic composite: simulation by the method of singular integral equation. Theor Appl Fract Mech 2015; 78: 25-39. |
| [17] | [17] Kachanov, M. Elastic solids with many cracks and related problems. Adv Appl Mech 1994; 30: 259-445. · Zbl 0803.73057 |
| [18] | [18] Eriksson, A, Boström, A, Datta, S. Ultrasonic wave propagation through a cracked solid. Wave Motion 1995; 22(3): 297-310. · Zbl 0968.74543 |
| [19] | [19] Zhang, C, Gross, D. Wave attenuation and dispersion in randomly cracked solids-II. Penny-shaped cracks. Int J Eng Sci 1993; 31(6): 859-872. · Zbl 0775.73086 |
| [20] | [20] Scarpetta, E, Tibullo, V. Explicit results for scattering parameters in three-dimensional wave propagation through a doubly periodic system of arbitrary openings. Acta Mech 2006; 185(1): 1-9. · Zbl 1099.74036 |
| [21] | [21] Lekesiz, H, Katsube, N, Rokhlin, SI. The stress intensity factors for a periodic array of interacting coplanar penny-shaped cracks. Int J Solids Struct 2013; 50(1): 186-200. |
| [22] | [22] Mykhas’kiv, V, Zhbadynskyi, I, Zhang, C. Dynamic stresses due to time-harmonic elastic wave incidence on doubly periodic array of penny-shaped cracks. J Math Sci 2014; 203: 114-122. |
| [23] | [23] Remizov, MY, Sumbatyan, MA. Three-dimensional one-mode penetration of elastic waves through a doubly periodic array of cracks. Math Mech Solids 2017. Epub ahead of print: 5January2017. DOI: 10.1177/1081286516684902. · Zbl 1395.74047 |
| [24] | [24] Lekesiz, H, Katsube, N, Rokhlin, SI. Effective spring stiffness for a periodic array of interacting coplanar penny-shaped cracks at an interface between two dissimilar isotropic materials. Int J Solids Struct 2013; 50(18): 2817-2828. |
| [25] | [25] Glushkov, EV, Glushkova, NV. On the efficient implementation of the integral equation method in elastodynamics. J Comput Acoust 2001; 9(3): 889-898. |
| [26] | [26] Glushkov, YV, Glushkova, NV. Diffraction of elastic waves by three-dimensional cracks of arbitrary shape in a plane. J Appl Math Mech 1996; 60: 277-283. · Zbl 0883.73023 |
| [27] | [27] Trofimov, A, Drach, B, Kachanov, M. Effect of a partial contact between the crack faces on its contribution to overall material compliance and resistivity. Int J Solids Struct 2017; 108: 289-297. |
| [28] | [28] Brekhovskikh, LM Waves in layered media. New York: Academic Press, 1960. |
| [29] | [29] Glushkov, YV, Glushkova, NV. Resonant frequencies of the scattering of elastic waves by three-dimensional cracks. J Appl Math Mech 1998; 62(5): 803-806. |
| [30] | [30] Glushkov, E. Energy distribution of a surface source in an inhomogeneous half-space. J Appl Math Mech 1983; 47(1): 70-75. · Zbl 0526.73019 |
| [31] | [31] Sveshnikov, V. The limit absorption principle for a waveguide. Dokl Akad Nauk USSR 1951; 80(3): 345-347. · Zbl 0044.22204 |
| [32] | [32] Boström, A. Review of hypersingular integral equation method for crack scattering and application to modeling of ultrasonic nondestructive evaluation. Appl Mech Rev 2003; 56: 383-405. |
| [33] | [33] Kiselev, A. Energy flux of elastic waves. J Sov Math 1982; 19(4): 1372-1375. |
| [34] | [34] Boström, A. Acoustic scattering by a sound-hard rectangle. J Acoust Soc Am 1991; 90(6): 3344-3347. |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
