title: ÐÐ°ÑÐ¼Ð¾Ð½Ð¸ÑÐµÑÐºÐ¸Ðµ ÐºÐ¾Ð»ÐµÐ±Ð°Ð½Ð¸Ñ ÑÐ¸Ð»Ð¸Ð½Ð´ÑÐ¸ÑÐµÑÐºÐ¾Ð¹ ÑÐ¿ÑÑÐ³Ð¾Ð¹ Ð¾Ð±Ð¾Ð»Ð¾ÑÐºÐ¸ Ñ Ð½ÐµÐ¾Ð´Ð½Ð¾ÑÐ¾Ð´Ð½Ð¾Ð¹ Ð¿Ð»Ð¾ÑÐ½Ð¾ÑÑÑÑ. ÐÐ±Ð¾Ð»Ð¾ÑÐµÑÐ½ÑÐµ Ð¼Ð¾Ð´Ñ
title: Harmonic vibrations of a cylindrical elastic shell with inhomogeneous density. Shell modes
Creators: name: Ð¤Ð¸Ð»Ð¸Ð¿Ð¿ÐµÐ½ÐºÐ¾, ÐÐµÐ¾ÑÐ³Ð¸Ð¹
name: "Ð¡Ð¾Ð²ÑÐµÐ¼ÐµÐ½Ð½Ð¾Ðµ Ð¼Ð°ÑÐ¸Ð½Ð¾ÑÑÑÐ¾ÐµÐ½Ð¸Ðµ: Ð½Ð°ÑÐºÐ° Ð¸ Ð¾Ð±ÑÐ°Ð·Ð¾Ð²Ð°Ð½Ð¸Ðµ", Ð¼ÐµÐ¶Ð´ÑÐ½Ð°ÑÐ¾Ð´Ð½Ð°Ñ Ð½Ð°ÑÑÐ½Ð°Ñ ÐºÐ¾Ð½ÑÐµÑÐµÐ½ÑÐ¸Ñ (13; 2024; Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³)
Publisher: name: ÐÐÐÐÐ¢ÐÐ¥-ÐÐ ÐÐ¡Ð¡
Year: 2024
Subjects: ÐÐ±Ð¾Ð»Ð¾ÑÐºÐ¸ ÑÐ¸Ð»Ð¸Ð½Ð´ÑÐ¸ÑÐµÑÐºÐ¸Ðµ
Ð²Ð¾Ð´Ð¾ÑÐ¾Ð´Ð½Ð¾Ðµ Ð¾Ñ ÑÑÐ¿ÑÐ¸Ð²Ð°Ð½Ð¸Ðµ
Ð½ÐµÐ¾Ð´Ð½Ð¾ÑÐ¾Ð´Ð½ÑÐµ Ð¾Ð±Ð¾Ð»Ð¾ÑÐºÐ¸
Ð¼Ð½Ð¾Ð³Ð¾ÑÐ»Ð¾Ð¹Ð½ÑÐµ Ð¾Ð±Ð¾Ð»Ð¾ÑÐºÐ¸
hydrogen corrosion
non-homogeneous shells
multilayer shell

description: ÐÐºÑÑÐ°Ð»ÑÐ½ÑÐ¼Ð¸ Ð´Ð»Ñ ÑÐ¾Ð²ÑÐµÐ¼ÐµÐ½Ð½Ð¾Ð¹ Ð¿ÑÐ¾Ð¼ÑÑÐ»ÐµÐ½Ð½Ð¾ÑÑÐ¸ ÑÐ²Ð»ÑÑÑÑÑ Ð¿ÑÐ¾Ð±Ð»ÐµÐ¼Ñ Ð¿ÑÐ¸ Ð¿ÑÐ¾ÐµÐºÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð¸Ð¸ Ð¸ ÑÐºÑÐ¿Ð»ÑÐ°ÑÐ°ÑÐ¸Ð¸ ÑÐ°Ð·Ð»Ð¸ÑÐ½ÑÑ ÑÑÑÐ±Ð¾Ð¿ÑÐ¾Ð²Ð¾Ð´Ð¾Ð², ÐºÐ¾ÑÐ¾ÑÑÐµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÑÑÑÑÑ Ð½ÐµÐ¾Ð´Ð½Ð¾ÑÐ¾Ð´Ð½ÑÐ¼Ð¸ ÑÐ¸Ð»Ð¸Ð½Ð´ÑÐ¸ÑÐµÑÐºÐ¸Ð¼Ð¸ Ð¾Ð±Ð¾Ð»Ð¾ÑÐºÐ°Ð¼Ð¸. ÐÐµÐ¾Ð´Ð½Ð¾ÑÐ¾Ð´Ð½Ð¾ÑÑÑ ÑÐ¿ÑÑÐ³Ð¸Ñ ÑÐ²Ð¾Ð¹ÑÑÐ² Ð¼Ð¾Ð¶ÐµÑ Ð±ÑÑÑ Ð·Ð°Ð»Ð¾Ð¶ÐµÐ½Ð° ÐºÐ°Ðº Ð¸Ð·Ð½Ð°ÑÐ°Ð»ÑÐ½Ð¾, ÑÐ°Ðº Ð²Ð¾Ð·Ð½Ð¸ÐºÐ½ÑÑÑ Ð¸ Ð² ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐµ ÑÐºÑÐ¿Ð»ÑÐ°ÑÐ°ÑÐ¸Ð¸. Ð ÑÑÐ°ÑÑÐµ Ð½ÐµÐ¾Ð´Ð½Ð¾ÑÐ¾Ð´Ð½Ð°Ñ Ð¾Ð±Ð¾Ð»Ð¾ÑÐºÐ° Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÑÐµÑÑÑ ÑÐ»Ð¾Ð¸ÑÑÐ¾Ð¹ Ð¾Ð±Ð¾Ð»Ð¾ÑÐºÐ¾Ð¹ (Ð¿Ð¾ ÐºÐ»Ð°ÑÑÐ¸ÑÐµÑÐºÐ¾Ð¹ ÑÐµÐ¾ÑÐ¸Ð¸ ÐÐ¸ÑÑÐ³Ð¾ÑÐ°-ÐÑÐ²Ð°), Ð½ÐµÐ¾Ð´Ð½Ð¾ÑÐ¾Ð´Ð½ÑÐµ ÑÐ²Ð¾Ð¹ÑÑÐ²Ð° ÐºÐ¾ÑÐ¾ÑÐ¾Ð¹ Ð·Ð°Ð²Ð¸ÑÑÑ ÑÐ¾Ð»ÑÐºÐ¾ Ð¾Ñ ÑÐ°Ð´Ð¸Ð°Ð»ÑÐ½Ð¾Ð¹ Ð¿ÐµÑÐµÐ¼ÐµÐ½Ð½Ð¾Ð¹. Ð Ð°ÑÑÐ¼Ð°ÑÑÐ¸Ð²Ð°ÑÑÑÑ ÑÐ²Ð¾Ð±Ð¾Ð´Ð½ÑÐµ Ð³Ð°ÑÐ¼Ð¾Ð½Ð¸ÑÐµÑÐºÐ¸Ðµ
ÐºÐ¾Ð»ÐµÐ±Ð°Ð½Ð¸Ñ Ð¾Ð±Ð¾Ð»Ð¾ÑÐºÐ¸. ÐÑÐ¾Ð°Ð½Ð°Ð»Ð¸Ð·Ð¸ÑÐ¾Ð²Ð°Ð½Ð° Ð¾Ð±Ð»Ð°ÑÑÑ Ð¿ÑÐ¸Ð¼ÐµÐ½Ð¸Ð¼Ð¾ÑÑÐ¸ ÑÐ°Ð·Ð»Ð¸ÑÐ½ÑÑ Ð¼Ð¾Ð´ÐµÐ»ÐµÐ¹ ÑÑÑÐµÐ´Ð½ÐµÐ½Ð¸Ñ Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÐ¾Ð² Ð½ÐµÐ¾Ð´Ð½Ð¾ÑÐ¾Ð´Ð½Ð¾Ð¹ Ð¾Ð±Ð¾Ð»Ð¾ÑÐºÐ¸ Ð½Ð° Ð¿ÑÐ¸Ð¼ÐµÑÐµ Ð´Ð²ÑÑÐ»Ð¾Ð¹Ð½Ð¾Ð¹ Ð¾Ð±Ð¾Ð»Ð¾ÑÐºÐ¸ Ñ Ð½ÐµÐ¾Ð´Ð½Ð¾ÑÐ¾Ð´Ð½Ð¾ÑÑÑÑ Ð¿Ð»Ð¾ÑÐ½Ð¾ÑÑÐ¸ Ð¼Ð°ÑÐµÑÐ¸Ð°Ð»Ð°. ÐÐ° Ð¾ÑÐ½Ð¾Ð²Ðµ ÑÐ¾ÑÐ½Ð¾Ð³Ð¾ Ð°Ð½Ð°Ð»Ð¸ÑÐ¸ÑÐµÑÐºÐ¾Ð³Ð¾ ÑÐµÑÐµÐ½Ð¸Ñ, Ð¸ÑÑÐ»ÐµÐ´ÑÐµÑÑÑ Ð²Ð»Ð¸ÑÐ½Ð¸Ðµ Ð½ÐµÐ¾Ð´Ð½Ð¾ÑÐ¾Ð´Ð½Ð¾ÑÑÐ¸ Ð½Ð° ÑÐ¾Ð±ÑÑÐ²ÐµÐ½Ð½ÑÐµ ÑÐ°ÑÑÐ¾ÑÑ Ð¾Ð±Ð¾Ð»Ð¾ÑÐºÐ¸ Ð´Ð»Ñ Ð¾Ð±Ð¾Ð»Ð¾ÑÐµÑÐ½ÑÑ Ð¼Ð¾Ð´.
description: Actual for modern industry are problems in the design and operation of various pipelines, which are modelled by inhomogeneous cylindrical shells. The inhomogeneity of elastic properties can be inherent from the beginning, or it can arise as a result of operation. In the paper such a shell is modelled by a layered shell according to the classical Kirchhoff-Love theory, the inhomogeneous properties of which depend only on the radial variable. Free harmonic vibrations of the shell are considered. The area of applicability of different models of averaging of inhomogeneous shell parameters is analysed on the example of a two-layer shell with inhomogeneity of material density. On the basis of the exact analytical solution, the influence of inhomogeneity on the shell natural frequencies for the shell modes is investigated.