Образец для цитирования:
Kaplunov J. D., Prikazchikova L. A. Low-Frequency Vibration Modes of Strongly Inhomogeneous Elastic Laminates [Каплунов Ю. Д., Приказчикова Л. А. Длинноволновые моды колебаний сильно неоднородных упругих слоистых конструкций] // Изв. Сарат. ун-та. Нов. сер. Сер. Математика. Механика. Информатика. 2018. Т. 18, вып. 4. С. 447-457. DOI: https://doi.org/10.18500/1816-9791-2018-18-4-447-457
Low-Frequency Vibration Modes of Strongly Inhomogeneous Elastic Laminates
[Длинноволновые моды колебаний сильно неоднородных упругих слоистых конструкций]
В статье изучается динамика тонких многослойных конструкций с контрастными мягкими и жесткими слоями. Разработана асимптотическая процедура для анализа малых частот среза. Получено полиномиальное частотное уравнение, а также линейные уравнения для собственных форм толщинных колебаний. В случае пятислойной пластины с зажатыми лицевыми поверхностями выведены двухчленные асимптотические разложения для собственных частот и форм, которые сопоставляются с точным решением исходной задачи о свободных толщинных колебаниях.
1. Kossovich L. Yu. Nestacionarnye zadachi teorii uprugih tonkih obolochek [Nonstationary problems in the theory of elastic thin shells]. Saratov, Saratov Univ. Press, 1986 (in Russian).
2. Kaplunov J. D., Kossovich L. Y., Nolde E. V. Dynamics of thin walled elastic bodies. Academic Press, 1998.
3. Beresin V. L., Kossovich L. Y., Kaplunov J. D. Synthesis of the dispersion curves for a cylindrical shell on the basis of approximate theories. Journal of sound and vibration, 1995, vol. 186, no. 1, pp. 37–53. DOI: https://doi.org/10.1006/jsvi.1995.0432
4. Le K. C. Vibrations of shells and rods. Berlin, Springer, 1999.
5. Berdichevsky V. Л. Variacionnye principy mekhaniki sploshnoj sredy [Variational Principles of Continuum Mechanics]. Moscow, Nauka, Glav. red. fiz.-mat. lit., 1983 (in Russian).
6. Kaplunov J., Prikazchikov D. A., Prikazchikova L. A. Dispersion of elastic waves in a strongly inhomogeneous three-layered plate. International Journal of Solids and Structures, 2017, vol. 113–114, pp. 169–179. DOI: https://doi.org/10.1016/j.ijsolstr.2017.01.042
7. Kossovich L. Yu., Shevtsova Yu. V. Asymptotic approximations of three-dimensional dynamic equations of elasticity theory in case of two-layered plates. Problems of strenght and plasticity, 2005, vol. 76, pp. 102–111 (in Russian). DOI: https://doi.org/10.32326/1814-9146-2005-67-1-102-110
8. Prikazchikova L., Ece Aydın Y., Erba¸ s B., Kaplunov J. Asymptotic analysis of an anti-plane dynamic problem for a three-layered strongly inhomogeneous laminate. Mathematics and Mechanics of Solids, 2018. DOI: https://doi.org/10.1177/1081286518790804
9. Kaplunov J., Prikazchikov D., Sergushova O. Multi-parametric analysis of the lowest natural frequencies of strongly inhomogeneous elastic rods. Journal of Sound and Vibration, 2016, vol. 366, pp. 264–276. DOI: https://doi.org/10.1016/j.jsv.2015.12.008
10. Vinson J. R. The behavior of sandwich structures of isotropic and composite materials. CRC Press, 1999.
11. Ivanov I. V. Analysis, modelling, and optimization of laminated glasses as plane beam. International Journal of Solids and Structures, 2006, vol. 43, no. 22–23, pp. 6887–6907. DOI: https://doi.org/10.1016/j.ijsolstr.2006.02.014
12. Schulze S.-H., Pander M., Naumenko K., Altenbach H. Analysis of laminated glass beams for photovoltaic applications. International Journal of Solids and Structures, 2012, vol. 49, pp. 2027–2036. DOI: https://doi.org/10.1016/j.ijsolstr.2012.03.028
13. Lee P., Chang N. Harmonic waves in elastic sandwich plates. Journal of Elasticity, 1979, vol. 9, pp. 51–69. DOI: https://doi.org/10.1007/BF00040980
14. Kaplunov J. D. Long-wave vibrations of a thinwalled body with fixed faces. The Quarterly Journal of Mechanics and Applied Mathematics, 1995, vol. 48, no. 3, pp. 311–327. DOI: https://doi.org/10.1093/qjmam/48.3.311
15. Kaplunov J. D., Nolde E. V. Long-wave vibrations of a nearly incompressible isotropicplate with fixed faces. The Quarterly Journal of Mechanics and Applied Mathematics, 2002, vol. 55, no. 3, pp. 345–356. DOI: https://doi.org/10.1093/qjmam/55.3.345
16. Kaplunov J. D., Kossovich L. Yu., Rogerson G. A. Direct asymptotic integration of the equations of transversely isotropic elasticity for a plate near cut-off frequencies. Quarterly Journal of Mechanics and Applied Mathematics, 2000, vol. 53, no. 2, pp. 323–341.
17. Nolde E. V., Rogerson G. A. Long wave asymptotic integration of the governing equations for a pre-stressed incompressible elastic layer with fixed faces. Wave Motion, 2002, vol. 36, no. 3, pp. 287–304. DOI: https://doi.org/10.1016/S0165-2125(02)00017-3
18. Rogerson G. A., Sandiford K. J., Prikazchikova L. A. Abnormal long wave dispersion phenomena in a slightly compressible elastic plate with non-classical boundary conditions. International Journal of Non-Linear Mechanics, 2007, vol. 42, no. 2, pp. 298–309. DOI: https://doi.org/10.1016/j.ijnonlinmec.2007.01.005
