Дослідження усталених крутних коливань біматеріалу ”півпростір з тріщиною — шар” з використанням ефективних крайових умов: Fìz.-mat. model. ìnf. tehnol. 2018, 27:103-111

• Дата: 2019
• Автор: Stankevych, Volodymyr
• Формат: Стаття
• Мова: Українська
• Опубліковано: Інститут прикладних проблем механіки і математики ім. Я. С. Підстригача НАН України 2019
• Теми: півпростір з тріщиною; накладка; усталені коливання; ефективні крайові умови; граничні інтегральні рівняння; динамічний коефіцієнт інтенсивності напружень
• Онлайн доступ: https://www.fmmit.lviv.ua/index.php/fmmit/article/view/120
• Назва журналу: Physico-mathematical modeling and informational technologies

The dynamic problem of steady-state vibrations of an elastic bimaterial with a crack is considered. Using effective boundary conditions on the interface surface of the body and Helmholtz potentials, the problem is reduced to a system of 2-D boundary integral equations with the unknown functions defect opening surface. Using the solutions of the equations, the values of the dynamic stress intensity factors were obtained and their frequency dependences on the ratio of the components of the bimaterial components rigidity were analyzed. References Mohamood, R.M., Akinlabi, E.T. (2017). Functionally Graded Materials. Springer International Publishing, 103.https://doi.org/10.1007/978-3-319-53756-6 Gopalakrishnan, S. (2016). Wave Propagation in Materials and Structures. CRC Press.https://doi.org/10.1201/9781315372099 Bovik, P. (1996). A comparison between the Tiersten model and O(h) boundary conditions for elastic surface waves guided by thin layers. ASME J. Appl. Mech., 63, 162–167.https://doi.org/10.1115/1.2787193 Craster, R.V., Kaplunov, J. (2013). Dynamic Localization Phenomena in Elasticity, Acoustics and Electromagnetism. Springer International Publishing, 547, 260.https://doi.org/10.1007/978-3-7091-1619-7 Niklasson, J., Datta, S. K., Dunn, M. L. On approximating guided waves in plates with thin anisotropic coating by means of effective boundary conditions. J. Acoust. Soc. Am., 108, 924–933.https://doi.org/10.1121/1.1286882 Ahmad, M., Nolde, E., Pichugin, A.V. (2011). Explicit asymptotic modelling of transient Love waves propagated along a thin coating. Z. Angew. Math. Phys., 62, 173–181.https://doi.org/10.1007/s00033-010-0095-y Andreeva, D., Miszuris, W. (2017). Nonlinear transmission conditions for thin curvilinear low-conductive interphases. Continuum Mech. Thermodyn., 29, 345–358.https://doi.org/10.1007/s00161-016-0532-z Vinh, P.C., Anh, V.T. (2016). Efective boundary condition method and and approximate secular equations of Rayleigh waves in orthotropic half-space coated by a thin layer. J. of Mech. of Materials and Struct, 11(3), 259-277.https://doi.org/10.2140/jomms.2016.11.259 Rekik, M., Neifar, M., El-Borgi, S. (2010). An axisymmetric problem of an embedded crack in a graded layer bonded to a homogeneous half-space. Int. J. of Solids and Struct., 47, 2043-2055.https://doi.org/10.1016/j.ijsolstr.2010.04.006 Wang, B.L., Han, J.C., Du, S.Y. (2000). Fracture mechanics for multilayers with penny-shaped cracks subjected to dynamic torsional loading. Int. J. of Eng. Science, 38, 893-901.https://doi.org/10.1016/S0020-7225(99)00068-3 Stankevych, V.Z. (2008). Stress intensity near a crack in the composition of a half space and a layer under harmonic loading. Material Science, 44(2), 175-182.https://doi.org/10.1007/s11003-008-9065-3 Hansen, E.V. (2014). Fourier Transforms. Principles and Applications. John Wiley & Sons, Inc. Stankevych, V.Z. (1995). Calculation of some two-dimensional integrals for the dynamic problems of the cracks in the half-space body. Math. Methods Phys. Mech. Fields, 39, 56-61 (in Ukrainian). Stankevych, V.Z. (2017). Tryvymirna dynamichna zadacha teorii pruzhnosti pro ustaleni krutni kolyvannia bimaterialu “pivprostir — shar z trishchynoiu”. Fiz.-mat. modeliuvannia ta inform. tekhnolohii, 25, 141-150