On antiplane waves localized in the vicinity of the interface of two elastic half-spaces in the framework of lattice dynamics
- Авторлар: Eremeyeva I.A.1, Aizikovich S.M.2
-
Мекемелер:
- University of L'Aquila
- Don State technical University
- Шығарылым: Том 89, № 6 (2025)
- Беттер: 1004-1010
- Бөлім: Articles
- URL: https://ogarev-online.ru/0032-8235/article/view/364150
- DOI: https://doi.org/10.7868/S3034575825060082
- ID: 364150
Дәйексөз келтіру
Аннотация
We consider antiplane waves that are localised in the vicinity of the interface between two elastic half-spaces. The problem is formulated within the context of the dynamics of a square lattice. Accordingly, the interface region comprises particles with a different mass to the particles in the bulk and with different elastic bonds. For this model, we demonstrate the possibility of two types of wave being localised in the vicinity of the interface. The corresponding dispersion relations are obtained. The results are compared with the Gurtin-Murdoch theory of surface elasticity.
Негізгі сөздер
Авторлар туралы
I. Eremeyeva
University of L'Aquila
Email: eremeyeva.inna@gmail.com
L'Aquila, Italy
S. Aizikovich
Don State technical University
Email: saizikovich@gmail.com
Rostov on Don, Russia
Әдебиет тізімі
- Gurtin M.E., Murdoch A.I. A continuum theory of elastic material surfaces// Arch. Rat. Mech.&Analysis. 1975. V. 57. № 4. P. 291–323. https://doi.org/10.1007/BF00261375
- Gurtin M.E., Murdoch A.I. Surface stress in solids// Int. J. of Solids&Struct. 1978. V. 14. P. 431–440. https://doi.org/10.1016/0020-7683(78)90008-2
- Gurtin M.E., Weissmüller J., Larche F. A general theory of curved deformable interfaces in solids at equilibrium// Philos. Mag. A. 1998. V. 78. № 5. P. 1093–1109. https://doi.org/10.1080/01418619808239977
- Wang J., Duan H.L., Huang Z.P. et al. A scaling law for properties of nano-structured materials// Proc. Roy. Soc. London. Ser. A. 2006. V. 462. № 2069. P. 1355–1363.
- Duan H.L., Wang J., Karihaloo B.L. Theory of elasticity at the nanoscale // Adv. in Appl. Mech. 2008. V. 42. P. 1–63. http://dx.doi.org/10.1016/S0065-2156(08)00001-X
- Альтенбах Х., Еремеев В.А., Морозов Н.Ф. Об уравнениях линейной теории оболочек при учете поверхностных напряжений // Механика твердого тела. 2010. № 3. С. 30–44. http://elibrary.ru/item.asp?id=14773884
- Устинов К.Б. Об учете поверхностных явлений при изгибе сверхтонких пластин // Механика твердого тела. 2025. № 2. С. 238–266. https://doi.org/10.31857/S1026351925020141
- Di Nino S., Rosi G., D’Annibale F. Modeling the mechanical behavior of coated masonry elements using surface stress theory // European J. of Mech.-A/Solids. 2025. V. 115. № 105779. P. 1–12. https://doi.org/10.1016/j.euromechsol.2025.105779
- Murdoch A.I. The propagation of surface waves in bodies with material boundaries // J. of the Mech.&Physics of Solids. 1976. V. 24. P. 137–146. http://dx.doi.org/10.1016/0022-5096(76)90023-5
- Murdoch A.I. The effect of interfacial stress on the propagation of Stoneley waves //J. of Sound&Vibration. 1977. V. 50. P. 1–11. https://doi.org/10.1016/0022-460X(77)90547-8
- Pal P.K., Acharya D., Sengupta P.R. Effect of surface stresses on surface waves in elastic solids // Sadhana. 1997. V. 22. №. 5. P. 659–670. https://doi.org/10.1007/BF02802553
- Steigmann D.J., Ogden R.W. Surface waves supported by thin-film/substrate interactions // IMA J. of Appl. Math. 2007. V. 72. P. 730–747. https://doi.org/10.1093/IMAMAT%2FHXM018
- Huang Z. Torsional wave and vibration subjected to constraint of surface elasticity // Acta Mechanica. 2018. V. 229. P. 1171–1182. https://doi.org/10.1007/s00707-017-2047-5
- Eremeyev V.A., Rosi G., Naili S. Surface/interfacial anti-plane waves in solids with surface energy // Mech. Res. Com. 2016. V. 74. P. 8–13. https://doi.org/10.1016/j.mechrescom.2016.02.018
- Eremeyev V.A., Rosi G., Naili S. Transverse surface waves on a cylindrical surface with coating // Int. J. of Engin. Sci. 2020. V. 147. № 103188. https://doi.org/10.1016/j.ijengsci.2019.103188
- Mikhasev G.I., Eremeyev V.A. Effects of interfacial sliding on anti-plane waves in an elastic plate imperfectly attached to an elastic half-space // Int. J. of Engin. Sci. 2024. V. 205. № 104158. https://doi.org/10.1016/j.ijengsci.2024.104158
- Ru C. Simple geometrical explanation of Gurtin-Murdoch model of surface elasticity with clarification of its related versions // Science China Physics. Mech.&Astronomy. 2010. V. 53. №. 3. P. 536–544. https://doi.org/10.1007/s11433-010-0144-8
- Murdoch A.I. Some fundamental aspects of surface modelling // J. of Elasticity. 2005. V. 80. P. 33–52. https://doi.org/10.1007/s10659-005-9024-2
- Eremeyev V.A., Sharma B.L. Anti-plane surface waves in media with surface structure: Discrete vs. continuum model // Int. J. of Engin. Sci. 2019. V. 143. P. 33–38. https://doi.org/10.1016/j.ijengsci.2019.06.007
- Eremeyev V.A. Anti-plane interfacial waves in a square lattice // Networks&Heterogeneous Media. 2025. V. 20. № 1. P. 52–64. https://doi.org/10.3934/nhm.2025004
- Brillouin L. Wave Propagation in Periodic Structures: Electric Filters and Crystal Lattices. N.-Y.: Mcgraw Hill Book Company, 1946. 247 p.
Қосымша файлдар

