title: Ð£ÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾ÑÑÑ ÑÐ°Ð²Ð½Ð¾Ð²ÐµÑÐ¸Ñ ÑÐµÐ¿Ð¾ÑÐµÐº Ð¿Ð¾Ð»ÑÑÐ¸Ð»Ð¸Ð½Ð´ÑÐ¾Ð², ÑÑÑÐ½ÑÑÑÑ ÑÐ¿ÑÑÐ³Ð¾Ð¹ Ð½Ð¸ÑÑÑ
title: Equilibrium stability of chains of semi-cylinders stretched by an elastic thread
Creators: name: Ð¡Ð¼Ð¸ÑÐ½Ð¾Ð², ÐÐ»ÐµÐºÑÐµÐ¹
name: Ð¥Ð°ÑÐ±Ð°, Ð¢Ð¸Ð¼ÑÑ
name: Ð¡Ð¼Ð¾Ð»ÑÐ½Ð¸ÐºÐ¾Ð², ÐÐ¾ÑÐ¸Ñ
name: "Ð¡Ð¸ÑÑÐµÐ¼Ð½ÑÐ¹ Ð°Ð½Ð°Ð»Ð¸Ð· Ð² Ð¿ÑÐ¾ÐµÐºÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð¸Ð¸ Ð¸ ÑÐ¿ÑÐ°Ð²Ð»ÐµÐ½Ð¸Ð¸", Ð¼ÐµÐ¶Ð´ÑÐ½Ð°ÑÐ¾Ð´Ð½Ð°Ñ Ð½Ð°ÑÑÐ½Ð¾-Ð¿ÑÐ°ÐºÑÐ¸ÑÐµÑÐºÐ°Ñ ÐºÐ¾Ð½ÑÐµÑÐµÐ½ÑÐ¸Ñ (26; 2022; 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: 2023
Subjects: Ð¡ÑÐ°ÑÐ¸ÐºÐ°
Ð¿Ð¾Ð»ÑÑÐ¸Ð»Ð¸Ð½Ð´Ñ
ÑÐµÐ¿Ð¾ÑÐºÐ°
ÑÐ¿ÑÑÐ³Ð°Ñ Ð½Ð¸ÑÑ
Ð¿Ð¾ÑÐµÐ½ÑÐ¸Ð°Ð»ÑÐ½Ð°Ñ ÑÐ½ÐµÑÐ³Ð¸Ñ
Ð¼Ð°ÑÑÐ¸ÑÐ° ÐºÐ²Ð°Ð·Ð¸ÑÐ¿ÑÑÐ³Ð¸Ñ ÐºÐ¾ÑÑÑÐ¸ÑÐ¸ÐµÐ½ÑÐ¾Ð²
ÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾ÑÑÑ ÑÐ°Ð²Ð½Ð¾Ð²ÐµÑÐ¸Ñ
ÐºÑÐ¸ÑÐµÑÐ¸Ð¹ Ð¡Ð¸Ð»ÑÐ²ÐµÑÑÑÐ°
Ð±ÐµÐ·ÑÐ°Ð·Ð¼ÐµÑÐ½ÑÐ¹ Ð¿Ð°ÑÐ°Ð¼ÐµÑÑ
ÑÑÐ»Ð¾Ð²Ð¸Ñ ÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾ÑÑÐ¸
semi-cylinder
chain
elastic thread
potential energy
matrix of quasi-elastic coefficients
equilibrium stability
Sylvester criterion
dimensionless parameter
stability conditions

description: Ð ÑÐ°Ð±Ð¾ÑÐµ ÑÐ°ÑÑÐ¼Ð°ÑÑÐ¸Ð²Ð°ÑÑÑÑ Ð´Ð²Ðµ Ð·Ð°Ð´Ð°ÑÐ¸ Ð¾Ð± ÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾ÑÑÐ¸ ÑÐ°Ð²Ð½Ð¾Ð²ÐµÑÐ¸Ñ ÑÐµÐ¿Ð¾ÑÐµÐº ÑÑÐ¶ÐµÐ»ÑÑ Ð¿Ð¾Ð»ÑÑÐ¸Ð»Ð¸Ð½Ð´ÑÐ¸ÑÐµÑÐºÐ¸Ñ Ð±ÑÑÑÑÐµÐ², ÐºÐ¾ÑÐ¾ÑÑÐµ ÑÑÑÐ½ÑÑÑ ÑÐ¿ÑÑÐ³Ð¾Ð¹ Ð½Ð¸ÑÑÑ, Ð¿ÑÐ¾ÑÐ¾Ð´ÑÑÐµÐ¹ ÑÐµÑÐµÐ· Ð¿ÑÐ¾ÑÐ²ÐµÑÐ»ÐµÐ½Ð½ÑÐµ Ð¿Ð¾ ÑÐ°Ð´Ð¸ÑÑÑ Ð¾ÑÐ²ÐµÑÑÑÐ¸Ñ. Ð¢Ð°ÐºÐ¸Ðµ ÑÐ¸ÑÑÐµÐ¼Ñ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÑÑÑ ÑÐ°Ð·Ð»Ð¸ÑÐ½ÑÐµ Ð½ÐµÑÑÑÐ¸Ðµ ÐºÐ¾Ð½ÑÑÑÑÐºÑÐ¸Ð¸, Ð¿ÑÐµÐ´Ð½Ð°Ð·Ð½Ð°ÑÐµÐ½Ð½ÑÐµ Ð´Ð»Ñ Ð²ÑÑÐ¾ÑÐ½ÑÑ ÑÐ¾Ð¾ÑÑÐ¶ÐµÐ½Ð¸Ð¹. ÐÐ»Ñ ÐºÐ°Ð¶Ð´Ð¾Ð¹ Ð¸Ð· Ð·Ð°Ð´Ð°Ñ Ð¿ÑÐ¸Ð²Ð¾Ð´Ð¸ÑÑÑ Ð¿Ð¾ÑÑÑÐ¾ÐµÐ½Ð¸Ðµ Ð¿Ð¾ÑÐµÐ½ÑÐ¸Ð°Ð»ÑÐ½Ð¾Ð¹ ÑÐ½ÐµÑÐ³Ð¸Ð¸ ÑÐ¸ÑÑÐµÐ¼Ñ Ð² ÐºÐ²Ð°Ð´ÑÐ°ÑÐ¸ÑÐ½Ð¾Ð¹ Ð°Ð¿Ð¿ÑÐ¾ÐºÑÐ¸Ð¼Ð°ÑÐ¸Ð¸ Ð¸ Ð½Ð° ÐµÐµ Ð¾ÑÐ½Ð¾Ð²Ðµ ÑÐ¾ÑÐ¼Ð¸ÑÑÐµÑÑÑ Ð¼Ð°ÑÑÐ¸ÑÐ° ÐºÐ²Ð°Ð·Ð¸ÑÐ¿ÑÑÐ³Ð¸Ñ ÐºÐ¾ÑÑÑÐ¸ÑÐ¸ÐµÐ½ÑÐ¾Ð². ÐÑÐ¸ Ð¿Ð¾Ð¼Ð¾ÑÐ¸ ÐºÑÐ¸ÑÐµÑÐ¸Ñ Ð¡Ð¸Ð»ÑÐ²ÐµÑÑÑÐ° Ð²ÑÑÐ²Ð»ÑÑÑÑÑ ÑÑÐ»Ð¾Ð²Ð¸Ñ ÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾ÑÑÐ¸ ÑÑÐ¸Ð²Ð¸Ð°Ð»ÑÐ½Ð¾Ð³Ð¾ Ð¿Ð¾Ð»Ð¾Ð¶ÐµÐ½Ð¸Ñ ÑÐ°Ð²Ð½Ð¾Ð²ÐµÑÐ¸Ñ ÑÐµÐ¿Ð¾ÑÐµÐº Ð¿Ð¾Ð»ÑÑÐ¸Ð»Ð¸Ð½Ð´ÑÐ¾Ð² Ð² Ð·Ð°Ð²Ð¸ÑÐ¸Ð¼Ð¾ÑÑÐ¸ Ð¾Ñ Ð¸Ñ ÑÐ¸ÑÐ»Ð°, ÐºÐ¾ÑÐ¾ÑÑÐµ Ð¾Ð¿ÑÐµÐ´ÐµÐ»ÑÑÑ ÑÑÐµÐ±Ð¾Ð²Ð°Ð½Ð¸Ñ Ðº ÑÐ¸Ð»Ðµ Ð½Ð°ÑÑÐ¶ÐµÐ½Ð¸Ñ Ð½Ð¸ÑÐ¸. Ð­ÑÐ¸ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÑ Ð¿ÑÐ¸Ð²ÐµÐ´ÐµÐ½Ñ Ð² ÑÐ°Ð±Ð»Ð¸ÑÐ½Ð¾Ð¼ Ð²Ð¸Ð´Ðµ, Ð¿Ð¾Ð·Ð²Ð¾Ð»ÑÑÑÐµÐ¼ Ð¾ÑÑÑÐµÑÑÐ²Ð¸ÑÑ ÑÐ¾Ð¿Ð¾ÑÑÐ°Ð²Ð»ÐµÐ½Ð¸Ðµ ÑÑÐ»Ð¾Ð²Ð¸Ð¹ ÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾ÑÑÐ¸ Ð´Ð»Ñ Ð¾Ð±ÐµÐ¸Ñ Ð·Ð°Ð´Ð°Ñ. Ð¡Ð´ÐµÐ»Ð°Ð½Ð½ÑÐµ Ð²ÑÐ²Ð¾Ð´Ñ Ð¿ÑÐµÐ´ÑÑÐ°Ð²Ð»ÑÑÑ Ð½Ðµ ÑÐ¾Ð»ÑÐºÐ¾ ÑÐµÐ¾ÑÐµÑÐ¸ÑÐµÑÐºÐ¸Ð¹ Ð¸Ð½ÑÐµÑÐµÑ, Ð½Ð¾ ÑÐ°ÐºÐ¶Ðµ Ð¼Ð¾Ð³ÑÑ Ð¾ÐºÐ°Ð·Ð°ÑÑÑÑ Ð¿Ð¾Ð»ÐµÐ·Ð½ÑÐ¼Ð¸ Ð¸ Ð² Ð¿ÑÐ°ÐºÑÐ¸ÑÐµÑÐºÐ¾Ð¼ Ð¾ÑÐ½Ð¾ÑÐµÐ½Ð¸Ð¸ Ð¿ÑÐ¸ ÑÐµÑÐµÐ½Ð¸Ð¸ Ð·Ð°Ð´Ð°Ñ Ð¿ÑÐ¸ÐºÐ»Ð°Ð´Ð½Ð¾Ð¹ Ð¼ÐµÑÐ°Ð½Ð¸ÐºÐ¸.
description: The paper considers two problems of the stability of the equilibrium ofchains of heavy semi-cylindrical bars, which are pulled together by an elastic thread passing through holes drilled along the radius. Such systems model various load-bearing structures intended for high-rise buildings. For each of the problems the construction of the potential energy of the system in a quadratic approximation is given, and on its basis a matrix of quasi-elastic coefficients is formed. Using the Sylvester criterion, stability conditions of the trivial equilibrium position of chains of semi-cylinders depending on their number are revealed, which determine requirements for the thread tension force. These results are presented in tabular form, which makes it possible to compare stability conditions for both problems. The conclusions drawn are not only of theoretical interest, but can also be useful in practical terms for solving problems of applied mechanics.