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Arxiv / №1 · 2026 / Maqola
01.00.00 – FIZIKA-MATEMATIKA FANLARI

BURALISH-EGILISH TO‘LQININI QOVUSHOQ-ELASTIK STERJENGA TARQALISHI XUSUSIYATLARI

Annotatsiya
O'ZBEKCHA

Bu ishda buralish-egilish to‘lqinini qovushoq-elastik sterjenga tarqalishida sodda-lashtirilgan tenglamasini olish masalasi ko‘riladi. Sterjenni differensial yondashuv bo‘yicha olingan teng-lamalarini turlicha soddalashtirilgan holidagi bir va ikki o‘lchamli tenglamalari olingan. Materiallarning qovushoqligi irsiy, ya’ni, Boltsman-Volterra integral munosabati bilan olingan. Qovushqoq yadrosi sifa-tida uch parametrli relaksatsiya yadrosi olingan. Dispersion tenglama olinib, uni sonli yechishi topilib tah-lil qilingan

Kalit so'zlar: sterjen, buralish-egilish to‘lqini, qovushoq-elastiklik, inersiya momenti, buralish bur-chagi
РУССКИЙ

В данной работе рассматривается задача получения упрощенного уравнения распространения крутильно-изгибной волны в вязкоупругом стержне. Получены одномерные и дву-мерные уравнения стержня, полученные дифференциальным методом в различных упрощенных случаях. Вязкость материалов определяется с помощью наследственного, то есть интегрального соотношения Больцмана-Вольтерры. В качестве ядра вязкости используется трехпараметричес-кое ядро релаксации. Получено дисперсионное уравнение, найдено и проанализировано его численное решение.

Ключевые слова: стержень, кручение-изгибная волна, вязкая упругость, момент инерции, угол кручения.
ENGLISH

This work deals with the problem of obtaining a simplified equation for the propagation of a torsional-flexural wave in a viscous-elastic rod. One-and two-dimensional equations of the rod obtained by the differential approach in various simplified cases are obtained. The viscosity of materials is obtained by the hereditary, that is, Boltzmann-Volterra integral relation. A three-parameter relaxation kernel is taken as the viscous kernel. The dispersion equation is obtained, its numerical solution is found and analyzed.

Keywords: rod, torsion-bending wave, viscous elasticity, moment of inertia, torsion angle
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Foydalanilgan adabiyotlar

  1. Бабич Ю.Н. Трёхмерные волновые процессы в составных полей цилиндров, взаимодействующих с окружающей средой. Пробл. прочности. 1980, № 3, c. 101–104.
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  3. Safarov I.I., Teshaev M.Kh., Boltayev Z.I. Propagation of linear waves in multilayered structural – Inho-mogeneous cylindrical shells. Journal of Critical Reviews, 2020, 7(12), р. 893–904 http://jcreview.com/
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  5. Teshaev, M.Kh. Realization of Servo-Constraints by Electromechanical Servosystems. 2010, RUSSIAN MATHEMATICS. 54 (12), pp. 38-44. DOI 10.3103/S1066369X10120042
  6. Safarov I.I. and Teshaev M.Kh. Dynamic damping of vibrations of a solid body mounted on viscoelastic supports. Izvestiya vysshikh uchebnykh zavedeniy-prikladnaya nelineynaya dinamika. 31 (1), pp. 63–74.
  7. Teshaev M.Kh., Karimov I.M., Umarov A.O., Zhuraev Sh.I. Diffraction of Harmonic Shear Waves on an Elliptical Cavity Located in a Viscoelastic Medium. Russian Mathematics, vol. 67(8), pp. 44–48, 2023
  8. Safarov I.I., Teshaev M.Kh. Control of resonant oscillations of viscoelastic systems. Theoretical and Ap-plied Mechanics, 2024, 51(1), pp. 1–12 https://doi.org/10.2298/TAM220510007S
  9. Durdiyev D.Q., Safarov I.I., Teshaev M.Kh. Propagation of Waves in a Fluid in a Thin Elastic Cylindrical Shell. WSEAS TRANSACTIONS on FLUID MECHANICS DOI: 10.37394/232013.2024.19.11, pp. 113–119.
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