Abstract
Contact problems for functionally graded (FG) materials of complex structure are of traditional research interest due to various practical applications in the chemical industry, materials science, etc. In this article, we consider the dynamic response of such materials with FG or stepwise layered coatings. Numerical analysis is carried out based on the explicit integral and asymptotic representations obtained in terms of Green’s matrix for elastic half-spaces with periodic coverages. Their soft interlayers form internal waveguide channels, which leads to unusual wave and energy transfer effects in response to dynamic surface loading.
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References
Aizikovich SM (1982) Asymptotic solutions of contact problems of elasticity theory for media inhomogeneous in depth. J Appl Math Mech 46:116–124
Aizikovich SM, Alexandrov VM (1982) Properties of compliance functions for a layered and continuously nonuniform halfspace. Sov Phys Doklady 27:765–767
Aizikovich SM, Krenev LI, Trubchik IS (2008) The deformation of a half-space with a gradient elastic coating under arbitrary axisymmetric loading. J Appl Math Mech 72:461–467
Aizikovich SM, Vasil’ev AS, Krenev LI et al (2011) Contact problems for functionally graded materials of complicated structure. Mech Compos Mater 47(5):539–548
Alekseev AS, Mikhailenko BG (1976) Solution of Lamb’s problem for a vertically inhomogeneous elastic half-space. Izv Akad Nauk SSSR Fiz Zemli 12:11–25
Babeshko VA, Glushkov EV, Glushkova NV (1987) Methods of constructing Green’s matrix of a stratified elastic half-space. USSR Comput Math Math Phys 27(1):60–65
Gentilleau B, Bertin M, Touchard F et al (2011) Stress analysis in specimens made of multi-layer polymer/composite used for hydrogen storage application: comparison with experimental results. Compos Struct 93:2760–2767
Glushkov EV (1978) Dynamic contact problems for arbitrarily shaped stamps on inhomogeneous media. Dis. Cand. fiz.-mat.nauk, 01.02.04, 134 p. Rostov State University
Glushkov EV (1983) Energy distribution of a surface source in an inhomogeneous half-space. PMM U.S.S.R. 47(1):70–75
Glushkov EV, Glushkova NV, Fomenko SI, Zhang C (2012) Surface waves in materials with functionally gradient coatings. Acoust Phys 58(3):339–353
Glushkov E, Glushkova N, Fomenko S (2015) Wave energy transfer in elastic half-spaces with soft interlayers. J Acoust Soc Am 137(4):1802–1812
Glushkova NV (1981) Propagation of elastic waves in stratified media and their interaction with surface objects. Dis. Cand. fiz.-mat.nauk, 01.02.04, 204 p. Rostov State University
Haskell NA (1953) The dispersion of surface waves on multilayered media. Bull Seismol Soc Am 43:17–34
Knopoff L (1964) A matrix method for elastic waves problems. Bull Seismol Soc Am 54:431–438
Mikhasev GI, Botogova MG, Eremeyev VA (2021) On the influence of a surface roughness on propagation of anti-plane short-length localized waves in a medium with surface coating. Int J Eng Sci 158:103428
Petrashen’ GI (1952) Propagation of elastic waves in an isotropic-layered media, divided by parallel planes. Uch Zap LGU, Leningrad 26:162
Thomson WT (1950) Transmission of elastic waves through a stratified medium. J Appl Phys 21:89–93
Vasiliev A, Volkov S, Aizikovich S et al (2014) Axisymmetric contact problems of the theory of elasticity for inhomogeneous layers. ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik 94:705–712
Vasiliev AS, Swain MV, Aizikovich SM, Sadyrin EV (2016) Torsion of a circular punch attached to an elastic half-space with a coating with periodically depth-varying elastic properties. Arch Appl Mech 86:1247–1254
Volkov S, Aizikovich S, Wang Y-S et al (2013) Analytical solution of axisymmetric contact problem about indentation of a circular indenter into a soft functionally graded elastic layer. Acta Mechanica Sinica/Lixue Xuebao 29:196–201
Vorovich II, Babeshko VA (1979) Dynamic mixed problems of elasticity for non-classical domains. Nauka, Moscow [in Russian]
Vorovich II, Aleksandrov VM, Babeshko VA (1974) Non-classical mixed problems of elasticity theory. Nauka, Moscow [in Russian]
Zharnikov TV, Syresin DE (2015) Repulsion of dispersion curves of quasidipole modes of anisotropic waveguides studied by finite element method. J Acoust Soc Am 137(6):EL396–EL402
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The work is supported by the Russian Science Foundation (Project No. 17-11-01191).
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Glushkov, E., Glushkova, N., Fomenko, S. (2022). Surface Wave Propagation in Elastic Half-Spaces with Periodic Coatings. In: Altenbach, H., Eremeyev, V.A., Galybin, A., Vasiliev, A. (eds) Advanced Materials Modelling for Mechanical, Medical and Biological Applications. Advanced Structured Materials, vol 155. Springer, Cham. https://doi.org/10.1007/978-3-030-81705-3_10
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DOI: https://doi.org/10.1007/978-3-030-81705-3_10
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