Надіслати цю статтю 3D dynamic analysis of layered elastic shells
Анотація
Тривимірний динамічний аналіз шаруватих пружних оболонок
Розглянуто тривимірні динамічні задачі для шаруватих ортотропних пружних оболонок із вільною верхньою поверхнею і заданими переміщеннями на одній із меж поділу шарів за умови ідеального контакту. Побудовано довгохвильовий асимптотичний розв’язок і визначено резонанси товщини. Отримані результати можуть знайти подальше застосування при оцінці певних параметрів землетрусів.
Зразок для цитування: L. A. Aghalovyan, L. G. Ghulghazaryan, J. D. Kaplunov, D. A. Prikazchikov, “3D dynamic analysis of layered elastic shells,” Мат. методи та фіз.-мех. поля, 63, No. 4, 96–108 (2020), https://doi.org/10.15407/mmpmf2020.63.4.96-108
Translation: L. A. Aghalovyan, L. G. Ghulghazaryan, J. D. Kaplunov, D. A. Prikazchikov, “Three-dimensional dynamic analysis of layered elastic shells,” J. Math. Sci., 273, No. 6, 999–1015 (2023), https://doi.org/10.1007/s10958-023-06560-5
Ключові слова
Посилання
L. A. Aghalovyan, M. L. Aghalovyan, V. V. Tagvoryan, “On solutions of dynamic three-dimensional problems of the elasticity theory for earthquake modeling,” Izv. NAN Armenii. Mekhanika, 71, No. 4, 17–29 (2018) (in Russian), https://www.doi.org/10.33018/71.4.2
L. A. Agalovyan, L. G. Gulgazaryan, “Forced vibrations of orthotropic shells: nonclassical boundary-value problems,” Prikl. Mekh., 45, No. 8, 105–122 (2009); English translation: Int. Appl. Mech., 45, No. 8, 888–904 (2009), https://doi.org/10.1007/s10778-009-0231-6
V. L. Berdichevskii, “High-frequency long-wave vibrations of plates,” Dokl. AN SSSR, 236, No. 6, 1319–1322 (1977); English translation: Sov. Phys. Dokl., 22, No. 10, 604–606 (1977).
A. L. Goldenveizer, Theory of Thin Elastic Shells [in Russian], Nauka, Moscow (1976).
Yu. D. Kaplunov, “High-frequency stress-strain states of small variability in thin elastic shells,” Izv. AN SSSR, Mekh. Tv. Tela, No. 5, 147–157 (1990) (in Russian).
L. A. Agalovyan, Asymptotic Theory of Anisotropic Plates and Shells [in Russian], Nauka, Moscow (1997).
L. A. Aghalovyan, “On one class of three-dimensional problems of elasticity theory for plates,” Proc. Razmadze Math. Inst., 155, 1–8 (2011).
L. A. Aghalovyan, M. L. Aghalovyan, “Monitoring of stress-strain state of plate-like packet of base-foundation constructions on the base of the data of seismic stations and GPS systems,” in: Proc. 5th Europ. Conf. Struct. Control, EACS–2012 (18–20 June 2012, Genoa, Italy), Paper No. 069, 8 p. (2012).
L. A. Aghalovyan, L. G. Ghulghazaryan, “Forced vibrations of a two-layered shell in the case of viscous resistance,” IOP J. Phys: Conf. Ser., 991, 012002, 10 p. (2018), https://doi.org/10.1088/1742-6596/991/1/012002
I. Argatov, G. Mishuris, Contact Mechanics of Articular Cartilage Layers, Springer, Cham (2015).
F. M. Borodich, B. A. Galanov, N. V. Perepelkin, D. A. Prikazchikov, “Adhesive contact problems for a thin elastic layer: Asymptotic analysis and the JKR theory,” Math. Mech. Solids, 24, No. 5, 1405–1424 (2019), https://doi.org/10.1177/1081286518797378
R. Chebakov, J. Kaplunov, G. A. Rogerson, “Refined boundary conditions on the free surface of an elastic half-space taking into account non-local effects,” Proc. R. Soc. A: Math., Phys. Eng. Sci., 472, No. 2186, Art. 20150800 (2016), https://doi.org/10.1098/rspa.2015.0800
B. Erbaş, E. Yusufoğlu, J. Kaplunov, “A plane contact problem for an elastic orthotropic strip,” J. Eng. Math., 70, No. 4, 399–409 (2011), https://doi.org/10.1007/s10665-010-9422-8
L. G. Ghulghazaryan, L. V. Khachatryan, “Forced vibrations of a two-layer orthotropic shell with an incomplete contact between layers,” Mech. Compos. Mater., 53, No. 6, 821–826 (2018), https://doi.org/10.1007/s11029-018-9707-y
J. D. Kaplunov, “Long-wave vibrations of a thin-walled body with fixed faces,” Quart. J. Mech. Appl. Math., 48, No. 3, 311–327 (1995), https://doi.org/10.1093/qjmam/48.3.311
J. D. Kaplunov, L. Yu. Kossovich, E. V. Nolde, Dynamics of Thin Walled Elastic Bodies, Acad. Press, San Diego (1998).
J. D. Kaplunov, E. V. Nolde, “Long-wave vibrations of a nearly incompressible isotropic plate with fixed faces,” Quart. J. Mech. Appl. Math., 55, No. 3, 345–356 (2002), https://doi.org/10.1093/qjmam/55.3.345
J. Kaplunov, D. Prikazchikov, L. Sultanova, “Justification and refinement of Winkler–Fuss hypothesis,” Z. angew. Math. Phys., 69, No. 3, Art. 80 (2018), https://doi.org/10.1007/s00033-018-0974-1
K. Kasahara, Earthquake Mechanics, Cambridge Univ. Press, Cambridge (1981).
M. I. Lashhab, G. A. Rogerson, L. A. Prikazchikova, “Small amplitude waves in a pre-stressed compressible elastic layer with one fixed and one free face,” Z. angew. Math. Phys., 66, No. 5, 2741–2757 (2015), https://doi.org/10.1007/s00033-015-0509-y
C. Le Khanh, “High frequency vibrations and wave propagation in elastic shells: Variational-asymptotic approach,” Int. J. Solids Struct., 34, No. 30, 3923–3939 (1997), https://doi.org/10.1016/S0020-7683(97)00011-5
X. Le Pichon, J. Francheteau, J. Bonnin, Plate Tectonics, Elsevier, Amsterdam (1973).
E. V. Nolde, G. A. Rogerson, “Long wave asymptotic integration of the governing equations for a pre-stressed incompressible elastic layer with fixed faces,” Wave motion, 36, No. 3, 287–304 (2002), https://doi.org/10.1016/S0165-2125(02)00017-3
A. V. Pichugin, G. A. Rogerson, “An asymptotic membrane-like theory for longwave motion in a pre-stressed elastic plate,” Proc. R. Soc. London. Ser. A: Math., Phys. Eng. Sci., 458, No. 2022, 1447–1468 (2002), https://doi.org/10.1098/rspa.2001.0932
T. Rikitake, Earthquake Prediction, Elsevier, Amsterdam (1976).
G. A. Rogerson, K. J. Sandiford, L. A. Prikazchikova, “Abnormal long wave dispersion phenomena in a slightly compressible elastic plate with non-classical boundary conditions,” Int. J. Nonlin. Mech., 42, No. 2, 298–309 (2007), https://doi.org/10.1016/j.ijnonlinmec.2007.01.005
Посилання
- Поки немає зовнішніх посилань.
Ця робота ліцензована Creative Commons Attribution 3.0 License.