Effect of coated hard sphere-filled metacomposite layer on Love wave propagation in an orthotropic half-space
Sourav Kumar Panja
Department of Mathematics, Jadavpur University, Kolkata, West Bengal, India
Department of Mechanical Engineering, Mahindra University, Telangana, India
Search for more papers by this authorSubhas Chandra Mandal
Department of Mathematics, Jadavpur University, Kolkata, West Bengal, India
Search for more papers by this authorCorresponding Author
Eduard-Marius Craciun
Faculty of Mechanical, Industrial and Maritime Engineering, Ovidius University of Constanta, Constanta, Romania
Academy of Romanian Scientists, Bucharest, Romania
Correspondence
Eduard-Marius Craciun, Faculty of Mechanical, Industrial and Maritime Engineering, Ovidius University of Constanta, Constanta, Romania.
Email: [email protected]
Search for more papers by this authorSourav Kumar Panja
Department of Mathematics, Jadavpur University, Kolkata, West Bengal, India
Department of Mechanical Engineering, Mahindra University, Telangana, India
Search for more papers by this authorSubhas Chandra Mandal
Department of Mathematics, Jadavpur University, Kolkata, West Bengal, India
Search for more papers by this authorCorresponding Author
Eduard-Marius Craciun
Faculty of Mechanical, Industrial and Maritime Engineering, Ovidius University of Constanta, Constanta, Romania
Academy of Romanian Scientists, Bucharest, Romania
Correspondence
Eduard-Marius Craciun, Faculty of Mechanical, Industrial and Maritime Engineering, Ovidius University of Constanta, Constanta, Romania.
Email: [email protected]
Search for more papers by this authorAbstract
An effective medium model is presented to study Love waves in an elastic metacomposite layer of coated hard spheres on an orthotropic half-space, inspired by recent developments in metasurface studies. Using specific examples, the model provides explicit equations for phase velocity and attenuation coefficients. The ramifications of these discoveries are examined both with and without the effect of damping on the local resonance of the hard spheres that are embedded. The paper provides a thorough comparison with previous findings for Love waves in an elastic half-space coated with a thin elastic layer, highlighting the effects of metasurfaces, orthotropy, and damping on the bandgap structure of Love waves. The conclusions drawn from this analysis shed important light on how surface elastic waves behave in locally resonant metamaterials.
REFERENCES
- 1Kinra, V.K., Ker, E., Datta, S.K.: Influence of particle resonance on wave propagation in a random particulate composite. Mech. Res. Commun. 9(2), 109–114 (1982)
- 2Kinra, V.K., Peining, L.: Resonant scattering of elastic waves by a random distribution of inclusions. Int. J. Solids Struct. 22(1), 1–11 (1986)
- 3Kafesaki, M., Sigalas, M., Economou, E.: Elastic wave band gaps in 3-d periodic polymer matrix composites. Solid State Commun. 96(5), 285–289 (1995)
- 4Sigalas, M., Kushwaha, M.S., Economou, E.N., Kafesaki, M., Psarobas, I.E., Steurer, W.: Classical vibrational modes in phononic lattices: Theory and experiment. Z. Kristallogr. - Cryst. Mater. 220(9-10), 765–809 (2005)
- 5Liu, Z., Zhang, X., Mao, Y., Zhu, Y.Y., Yang, Z., Chan, C.T., Sheng, P.: Locally resonant sonic materials. science 289(5485), 1734–1736 (2000)
- 6Liu, Z., Chan, C.T., Sheng, P.: Three-component elastic wave band-gap material. Phys. Rev. B 65(16), 165116 (2002)
10.1103/PhysRevB.65.165116 Google Scholar
- 7Liu, Z., Chan, C.T., Sheng, P.: Analytic model of phononic crystals with local resonances. Phys. Rev. B: Condens. Matter Mater. Phys. 71(1), 014103 (2005)
- 8Zhou, X., Hu, G.: Analytic model of elastic metamaterials with local resonances. Phys. Rev. B: Condens. Matter Mater. Phys. 79(19), 195109 (2009)
10.1103/PhysRevB.79.195109 Google Scholar
- 9Bo, Z., Li, Z.: New analytical model for composite materials containing local resonance units. J. Eng. Mech. 137(1), 1–7 (2011)
10.1061/(ASCE)EM.1943-7889.0000195 Google Scholar
- 10Mitchell, S.J., Pandolfi, A., Ortiz, M.: Metaconcrete: designed aggregates to enhance dynamic performance. J. Mech. Phys. Solids 65, 69–81 (2014)
- 11Briccola, D., Ortiz, M., Pandolfi, A.: Experimental validation of metaconcrete blast mitigation properties. J. Appl. Mech. 84(3), 031001 (2017)
- 12Kettenbeil, C., Ravichandran, G.: Experimental investigation of the dynamic behavior of metaconcrete. Int. J. Impact Eng. 111, 199–207 (2018)
- 13Xu, C., Chen, W., Hao, H.: The influence of design parameters of engineered aggregate in metaconcrete on bandgap region. J. Mech. Phys. Solids 139, 103929 (2020)
- 14Kanaun, S., Levin, V.: Propagation of longitudinal elastic waves in composites with a random set of spherical inclusions (effective field approach). Arch. Appl. Mech. 77, 627–651 (2007)
- 15Brunet, T., Merlin, A., Mascaro, B., Zimny, K., Leng, J., Poncelet, O., Aristégui, C., Mondain-Monval, O.: Soft 3d acoustic metamaterial with negative index. Nat. Mater. 14(4), 384–388 (2015)
- 16Duranteau, M., Valier-Brasier, T., Conoir, J.M., Wunenburger, R.: Random acoustic metamaterial with a subwavelength dipolar resonance. J. Acoust. Soc. Am. 139(6), 3341–3352 (2016)
- 17Willis, J.: From statics of composites to acoustic metamaterials. Philos. Trans. R. Soc. A 377(2156), 20190099 (2019)
10.1098/rsta.2019.0099 Google Scholar
- 18Ru, C.: A simplified metaelastic model for coated sphere-filled random composites. Math Mech. Solids 26(7), 939–953 (2021)
- 19Ru, C.: A simple model for elastic wave propagation in hard sphere-filled random composites. J. Acoust. Soc. Am. 152(3), 1595–1604 (2022)
- 20Nayfeh, A., Taylor, T., Chimenti, D.: Theoretical wave propagation in multilayered orthotropic media. In: Proceedings of the Joint Wave Propagation in Structural Composites on Wave Propagation in Structural Composites, vol 90, pp. 17–27. AMD (1988)
- 21Ahmed, S., Abo-Dahab, S.: Propagation of love waves in an orthotropic granular layer under initial stress overlying a semi-infinite granular medium. J. Vib. Control 16(12), 1845–1858 (2010)
- 22Panja, S.K., Mandal, S.: Propagation of love wave in multilayered viscoelastic orthotropic medium with initial stress. Waves Random Complex Medium 32(2), 1000–1017 (2022)
- 23Maznev, A., Gusev, V.: Waveguiding by a locally resonant metasurface. Phys. Rev. B 92(11), 115422 (2015)
10.1103/PhysRevB.92.115422 Google Scholar
- 24Palermo, A., Marzani, A.: Control of love waves by resonant metasurfaces. Sci. Rep. 8(1), 7234 (2018)
- 25Zeighami, F., Palermo, A., Marzani, A.: Rayleigh waves in locally resonant metamaterials. Int. J. Mech. Sci. 195, 106250 (2021)
- 26Guo, D.K., Chen, T.: Seismic metamaterials for energy attenuation of shear horizontal waves in transversely isotropic media. Mater. Today Commun. 28, 102526 (2021)
- 27Fang, X., Lou, J., Chen, Y.M., Wang, J., Xu, M., Chuang, K.C.: Broadband rayleigh wave attenuation utilizing an inertant seismic metamaterial. Int. J. Mech. Sci. 247, 108182 (2023)
- 28Ru, C.: Anti-plane surface waves of an elastic half-space coated with a metacomposite layer. J. Eng. Math. 143(1), 8 (2023)
- 29Ru, C.: Rayleigh waves in an elastic half-space with a hard sphere-filled metasurface. Mech. Res. Commun. 131, 104148 (2023)
- 30Seema, Singhal, A.: Examining three distinct rheological models with flexoelectric effect to investigate love-type wave velocity in bedded piezo-structure. ZAMM Z. fur Angew. Math. Mech. 104(11), e202400724 (2024)
- 31Panja, S.K., Alam, S., Mandal, S.C., Craciun, E.M.: Love wave scattering by an interface crack between an orthotropic layer and an isotropic half-space. Continuum Mech. Thermodyn. 37(2), 1–14 (2025)
- 32Tanwar, A., Das, S., Craciun, E.M., Altenbach, H.: Interaction among interfacial offset cracks in composite materials under the anti-plane shear loading. ZAMM Z. fur Angew. Math. Mech. 103(11), e202300081 (2023)
- 33Kundu, S., Das, A., Mistri, K.C.: Sh-waves in a complex fluid composite structure with spring membrane imperfect interfaces. ZAMM Z. fur Angew. Math. Mech. 104(12), e202301024 (2024)
- 34Santos, M.C.d., Filho, C.G.S., Miranda Jr, E.J.d., Sinatora, A.: Formulation of the extended plane wave expansion for in-plane and out-of-plane vibrations in viscoelastic phononic thin plates under a constant temperature field. ZAMM Z. fur Angew. Math. Mech. 105(1), e202400532 (2025)
10.1002/zamm.202400532 Google Scholar
- 35Singh, A., Das, S., Craciun, E.M.: Effect of thermomechanical loading on an edge crack of finite length in an infinite orthotropic strip. Mech. Compos. Mater. 55, 285–296 (2019)
- 36Singh, A., Das, S., Altenbach, H., Craciun, E.M.: Semi-infinite moving crack in an orthotropic strip sandwiched between two identical half planes. ZAMM Z. fur Angew. Math. Mech. 100(2), e201900202 (2020)
- 37Trivedi, N., Das, S., Craciun, E.M.: The mathematical study of an edge crack in two different specified models under time-harmonic wave disturbance. Mech. Compos. Mater. 58(1), 1–14 (2022)
- 38Tomczyk, B., Gołąbczak, M., Kubacka, E., Bagdasaryan, V.: Mathematical modelling of stability problems for thin transversally graded cylindrical shells. Continuum Mech. Thermodyn. 36(6), 1661–1684 (2024)
- 39Golewski, G.L.: Effect of coarse aggregate grading on mechanical parameters and fracture toughness of limestone concrete. Infrastructures 8(8), 117 (2023)
- 40Golewski, G.L.: Determination of fracture mechanic parameters of concretes based on cement matrix enhanced by fly ash and nano-silica. Materials 17(17), 4230 (2024)
- 41Golewski, G.L.: Using digital image correlation to evaluate fracture toughness and crack propagation in the mode i testing of concretes involving fly ash and synthetic nano-sio2. Mater. Res. Express 11(9), 095504 (2024)
- 42Golewski, G.L.: Comparison of fracture behavior of set concretes based on natural and crushed aggregates. Mater. Res. Express 11(10), 105509 (2024)
- 43Young, B.A., Fujii, A.M., Thiele, A.M., Kumar, A., Sant, G., Taciroglu, E., Pilon, L.: Effective elastic moduli of core-shell-matrix composites. Mech. Mater. 92, 94–106 (2016)
- 44Tiersten, H.: Elastic surface waves guided by thin films. J. Appl. Phys. 40(2), 770–789 (1969)
- 45Bövik, P.: A comparison between the tiersten model and o (h) boundary conditions for elastic surface waves guided by thin layers. J. Appl. Mech. 63(1), 162–167 (1996)
- 46Prosser, W.H., Green Jr, R.E.: Characterization of the nonlinear elastic properties of graphite/epoxy composites using ultrasound. J. Reinf. Plast. Compos. 9(2), 162–173 (1990)
