KOSSER DOIRAVIY SILINDRIDA BUROVCHI TO‘LQINLAR: CHASTOTA TENGLAMASI VA UZUN TO‘LQIN TEZLIGINING O‘LCHAM EFFEKTI
DOI:
https://doi.org/10.5281/zenodo.23301939Abstract
Kosser (mikropolyar) muhit mikrostrukturali materiallarda to‘lqinlarning o‘lchamga bog‘liq tarqalishini tasvirlaydi, biroq silindrik to‘lqin o‘tkazgichdagi burovchi to‘lqinlar uchun yopiq ko‘rinishdagi natijalar yetarli emas. Ishda chiziqli izotrop Kosser materialidan yasalgan, yon sirti erkin doiraviy silindrda o‘qqa simmetrik burovchi tipdagi to‘lqinlar o‘rganilgan. Siljish va mikroburilish maydonlari potensiallar orqali ajratilib, Bessel funksiyalaridagi aniq yechim qurilgan; chastota tenglamasi 3×3 determinant ko‘rinishida yozilgan; uzun to‘lqin limiti chegaraviy qatlamli statik buralish yechimi orqali topilgan. Hajmiy xarakteristik tenglamaning ikkala ildizi haqiqiy ekani isbotlangan. Uzun to‘lqin tezligi uchun burash qattiqligining o‘lcham effekti va mikroinersiyani oshkor hisobga oluvchi yopiq formula olingan, kesim chastotalari ikki mustaqil qismga ajralishi ko‘rsatilgan. Model parametrlarining qabul qilingan to‘plamida (R=3 mm) c0 /cT =0,8745; bunda burash qattiqligi klassik qiymatdan 3,7% yuqori, aylanma inersiya esa 35,6% katta. Yopiq formula va aniq determinant 3⋅10-10 dan yaxshi aniqlikda mos keladi. Natijalar Kosser sterjenlarda burovchi to‘lqinlar tezligini radius bo‘yicha baholash va mikrostruktura doimiylarini to‘lqin o‘lchovlaridan aniqlash uchun asos bo‘ladi.Keywords
Kosser (mikropolyar) elastikligi, silindrik to‘lqin o‘tkazgich, burovchi to‘lqinlar, chastota tenglamasi, kesim chastotasi, o‘lcham effekti, mikroinersiyaReferences
Cosserat, E., & Cosserat, F. (1909). Théorie des corps déformables. Paris: A. Hermann et Fils, 1909.
Eringen, A. C. (1999). Microcontinuum Field Theories I: Foundations and Solids. New York: Springer, 1999.
Nowacki, W. (1986). Theory of Asymmetric Elasticity. Oxford: Pergamon Press, 1986.
Toupin, R. A. (1962). Elastic materials with couple-stresses. Archive for Rational Mechanics and Analysis, 11(1), 385–414. https://doi.org/10.1007/BF00253945
Mindlin, R. D., & Tiersten, H. F. (1962). Effects of couple-stresses in linear elasticity. Archive for Rational Mechanics and Analysis, 11(1), 415–448. https://doi.org/10.1007/BF00253946
Achenbach, J. D. (1973). Wave Propagation in Elastic Solids. Amsterdam: North-Holland, 1973.
Graff, K. F. (1975). Wave Motion in Elastic Solids. Oxford: Clarendon Press, 1975.
Willson, A. J. (1972). The micropolar elastic vibrations of a circular cylinder. International Journal of Engineering Science, 10(1), 17–22. https://doi.org/10.1016/0020-7225(72)90071-7
Krishna Reddy G.V., Venkatasubramanian N.K. Saint-Venant’s problem for a micropolar elastic circular cylinder. (1976). International Journal of Engineering Science, 14(11), 1047–1057. https://doi.org/10.1016/0020-7225(76)90099-9
Khudoynazarov, K., Yalgashev, B. F., & Mavlonov, T. (2021). Mathematical modelling of torsional vibrations of the three-layer cylindrical viscoelastic shell. IOP Conference Series: Materials Science and Engineering, 1030. https://doi.org/10.1088/1757-899X/1030/1/012098
Khalmuradov, R. I., Yalgashev, B. F., & Akhatov, Kh. N. (2022). Refined equations of torsional vibrations of a three-layer cylindrical viscoelastic shell. AIP Conference Proceedings, 2637. https://doi.org/10.1063/5.0121480
Khudoynazarov, Kh. (2024). Longitudinal-radial vibrations of a viscoelastic cylindrical three-layer structure. Facta Universitatis, Series: Mechanical Engineering, 22. https://doi.org/10.22190/FUME231219010K
Ruziyev, T., Safarov, I. I., Teshayev, M. Kh., et al. (2026). Longitudinal–transverse natural waves in a cylindrical shell in contact with a viscous fluid. Journal of Composites Science, 10(3). https://doi.org/10.3390/jcs10030121
Ruziyev, T., Safarov, I. I., Teshayev, M. Kh., Boltayev, Z. I., et al. (2026). Assessment of the dissipative properties of viscoelastic hollow cylindrical bodies with filler during the propagation of natural waves. Journal of Composites Science, 10(8).
DOI: 10.3390/jcs10080437.
Downloads
Published
Issue
Section
License
Copyright (c) 2026 MUHANDISLIK VA IQTISODIYOT
This work is licensed under a Creative Commons Attribution 4.0 International License.
