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title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¼Ð°Ð³Ð¸ÑÑÑÐ°
titleType: Subtitle
title: Accounting for rotational inertia in calculating structures for seismic impact
Creators: name: ÐÐµÑÐµÑÑÐºÐ¸Ñ, ÐÐ°ÑÐ¸Ñ
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2021
Subjects: Ð¡ÐµÐ¹ÑÐ¼Ð¾ÑÑÐ¾Ð¹ÐºÐ¸Ðµ Ð·Ð´Ð°Ð½Ð¸Ñ Ð¸ ÑÐ¾Ð¾ÑÑÐ¶ÐµÐ½Ð¸Ñ
ÑÐ¾Ð±ÑÑÐ²ÐµÐ½Ð½Ð°Ñ ÑÐ°ÑÑÐ¾ÑÐ°
Ð¼Ð¾Ð¼ÐµÐ½Ñ Ð¸Ð½ÐµÑÑÐ¸Ð¸ Ð¼Ð°ÑÑÑ
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ÑÑÐµÐ¿ÐµÐ½Ñ ÑÐ²Ð¾Ð±Ð¾Ð´Ñ
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description: Ð Ð°Ð±Ð¾ÑÐ° Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð° ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐºÐµ ÑÐ¿Ð¾ÑÐ¾Ð±Ð° ÑÐ°ÑÑÐµÑÐ° ÑÑÐµÑÐ¶Ð½ÐµÐ²ÑÑ ÑÐ¸ÑÑÐµÐ¼ Ñ ÑÑÐµÑÐ¾Ð¼ Ð¿Ð¾Ð²Ð¾ÑÐ¾ÑÐ½Ð¾Ð¹ ÑÑÐµÐ¿ÐµÐ½Ð¸ ÑÐ²Ð¾Ð±Ð¾Ð´Ñ Ð¸ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ Ð²Ð»Ð¸ÑÐ½Ð¸Ñ Ð¸Ð½ÐµÑÑÐ¸Ð¸ Ð²ÑÐ°ÑÐµÐ½Ð¸Ñ Ð½Ð° ÑÑÐµÑÐ¶Ð½ÐµÐ²ÑÐµ ÑÐ¸ÑÑÐµÐ¼Ñ Ð¿ÑÐ¸ Ð¸Ñ ÑÐ°ÑÑÐµÑÐµ Ð½Ð° ÑÐµÐ¹ÑÐ¼Ð¸ÑÐµÑÐºÐ¾Ðµ Ð²Ð¾Ð·Ð´ÐµÐ¹ÑÑÐ²Ð¸Ðµ. ÐÐ°Ð´Ð°ÑÐ¸, ÐºÐ¾ÑÐ¾ÑÑÐµ ÑÐµÑÐ°Ð»Ð¸ÑÑ Ð² ÑÐ¾Ð´Ðµ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ: 1. Ð Ð°Ð·ÑÐ°Ð±Ð¾ÑÐºÐ° ÑÐ¿Ð¾ÑÐ¾Ð±Ð° ÑÑÐµÑÐ° Ð¸Ð½ÐµÑÑÐ¸Ð¸ Ð²ÑÐ°ÑÐµÐ½Ð¸Ñ Ð¿ÑÐ¸ Ð²ÑÐ¿Ð¾Ð»Ð½ÐµÐ½Ð¸Ð¸ Ð¼Ð¾Ð´Ð°Ð»ÑÐ½Ð¾Ð³Ð¾ Ð°Ð½Ð°Ð»Ð¸Ð·Ð°; 2. ÐÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ Ð²Ð»Ð¸ÑÐ½Ð¸Ðµ ÑÑÐµÑÐ° Ð¼Ð¾Ð¼ÐµÐ½ÑÐ° Ð¸Ð½ÐµÑÑÐ¸Ð¸ Ð¼Ð°ÑÑÑ Ð½Ð° ÑÐ¾Ð±ÑÑÐ²ÐµÐ½Ð½ÑÐµ ÑÐ°ÑÑÐ¾ÑÑ Ð±Ð°Ð»Ð¾Ðº Ð¿ÑÐ¸ Ð¸Ñ ÑÐ°Ð·Ð»Ð¸ÑÐ½Ð¾Ð¼ Ð·Ð°ÐºÑÐµÐ¿Ð»ÐµÐ½Ð¸Ð¸; 3. ÐÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ Ð²Ð»Ð¸ÑÐ½Ð¸Ðµ ÑÑÐµÑÐ° Ð¼Ð¾Ð¼ÐµÐ½ÑÐ° Ð¸Ð½ÐµÑÑÐ¸Ð¸ Ð¼Ð°ÑÑÑ Ð½Ð° Ð²Ð½ÑÑÑÐµÐ½Ð½Ð¸Ðµ ÑÑÐ¸Ð»Ð¸Ñ Ð±Ð°Ð»Ð¾Ðº Ð¿ÑÐ¸ Ð¸Ñ ÑÐ°Ð·Ð»Ð¸ÑÐ½Ð¾Ð¼ Ð·Ð°ÐºÑÐµÐ¿Ð»ÐµÐ½Ð¸Ð¸; 4. ÐÑÐ¸Ð¼ÐµÐ½ÐµÐ½Ð¸Ðµ ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐ°Ð½Ð½Ð¾Ð³Ð¾ ÑÐ¿Ð¾ÑÐ¾Ð±Ð° ÑÑÐµÑÐ° Ð¸Ð½ÐµÑÑÐ¸Ð¸ Ð²ÑÐ°ÑÐµÐ½Ð¸Ñ Ð¿ÑÐ¸ ÑÐ°ÑÑÐµÑÐ°Ñ ÑÐ¾Ð¾ÑÑÐ¶ÐµÐ½Ð¸Ð¹ Ð½Ð° ÑÐµÐ¹ÑÐ¼Ð¸ÑÐµÑÐºÐ¾Ðµ Ð²Ð¾Ð·Ð´ÐµÐ¹ÑÑÐ²Ð¸Ðµ. ÐÑÐµÐ´Ð»Ð°Ð³Ð°ÐµÑÑÑ ÑÐ¿Ð¾ÑÐ¾Ð± ÑÑÐµÑÐ° Ð¸Ð½ÐµÑÑÐ¸Ð¸ Ð²ÑÐ°ÑÐµÐ½Ð¸Ñ Ð¿ÑÐ¸ Ð²ÑÐ¿Ð¾Ð»Ð½ÐµÐ½Ð¸Ð¸ Ð¼Ð¾Ð´Ð°Ð»ÑÐ½Ð¾Ð³Ð¾ Ð°Ð½Ð°Ð»Ð¸Ð·Ð°. ÐÐ½Ð°Ð»Ð¸Ð·Ð¸ÑÑÑÑÑÑ ÑÐ¾Ð±ÑÑÐ²ÐµÐ½Ð½ÑÐµ ÑÐ°ÑÑÐ¾ÑÑ ÐºÐ¾Ð»ÐµÐ±Ð°Ð½Ð¸Ð¹ Ð±Ð°Ð»Ð¾Ðº, ÐºÐ¾ÑÐ¾ÑÑÐµ ÑÑÐ°Ð²Ð½Ð¸Ð²Ð°ÑÑÑÑ Ñ ÑÐ¾ÑÐ½ÑÐ¼ ÑÐµÑÐµÐ½Ð¸ÐµÐ¼. ÐÑÐ¾Ð¸Ð·Ð²Ð¾Ð´Ð¸ÑÑÑ ÑÐ°ÑÑÐµÑ Ð½Ð° ÑÐµÐ¹ÑÐ¼Ð¸ÑÐµÑÐºÐ¾Ðµ Ð²Ð¾Ð·Ð´ÐµÐ¹ÑÑÐ²Ð¸Ðµ Ð±Ð°Ð»Ð¾Ðº Ð¸ ÑÐ°Ð·Ð»Ð¸ÑÐ½ÑÑ ÑÐ¾Ð¾ÑÑÐ¶ÐµÐ½Ð¸Ð¹ Ñ Ð¿ÑÐ¸Ð¼ÐµÐ½ÐµÐ½Ð¸ÐµÐ¼ ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐ°Ð½Ð½Ð¾Ð³Ð¾ ÑÐ¿Ð¾ÑÐ¾Ð±Ð° ÑÑÐµÑÐ° Ð¸Ð½ÐµÑÑÐ¸Ð¸ Ð²ÑÐ°ÑÐµÐ½Ð¸Ñ. ÐÐ°Ð´Ð°ÑÐ¸ ÑÐµÑÐ°Ð»Ð¸ÑÑ Ñ Ð¿Ð¾Ð¼Ð¾ÑÑÑ ÐÐ SCAD Office, ÐÐ¸ÑÐ° ÑÐ¾ÑÑ Ð¸ Ð°Ð½Ð°Ð»Ð¸ÑÐ¸ÑÐµÑÐºÐ¸Ð¼ Ð¿ÑÑÐµÐ¼. ÐÑÐµÐ½ÐºÐ° ÑÐ¾ÑÐ½Ð¾ÑÑÐ¸ Ð¿ÑÐ¸Ð±Ð»Ð¸Ð¶ÐµÐ½Ð½ÑÑ ÑÐµÑÐµÐ½Ð¸Ð¹ Ð¾ÑÑÑÐµÑÑÐ²Ð»ÑÐµÑÑÑ Ñ Ð¿ÑÐ¸Ð¼ÐµÐ½ÐµÐ½Ð¸ÐµÐ¼ Ð¼ÐµÑÐ¾Ð´Ð° Ð. Ð¡. Ð¨Ð²Ð°ÑÑÐ¼Ð°Ð½Ð°. ÐÑÐµÐ´Ð»Ð¾Ð¶ÐµÐ½ Ð¼ÐµÑÐ¾Ð´ ÑÑÐµÑÐ° Ð¼Ð¾Ð¼ÐµÐ½ÑÐ° Ð¸Ð½ÐµÑÑÐ¸Ð¸ Ð¼Ð°ÑÑÑ Ð¿ÑÐ¸ Ð²ÑÐ¿Ð¾Ð»Ð½ÐµÐ½Ð¸Ð¸ Ð¼Ð¾Ð´Ð°Ð»ÑÐ½Ð¾Ð³Ð¾ Ð°Ð½Ð°Ð»Ð¸Ð·Ð°, Ð¿ÑÑÐµÐ¼ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸Ñ Ð´Ð¸Ð°Ð³Ð¾Ð½Ð°Ð»ÑÐ½Ð¾Ð¹ Ð¼Ð°ÑÑÐ¸ÑÑ Ð¼Ð°ÑÑ, ÑÑÐ¸ÑÑÐ²Ð°ÑÑÐµÐ¹ Ð²ÑÐ°ÑÐµÐ½Ð¸Ðµ. ÐÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¾ Ð²Ð»Ð¸ÑÐ½Ð¸Ðµ Ð¸Ð½ÐµÑÑÐ¸Ð¸ Ð²ÑÐ°ÑÐµÐ½Ð¸Ñ Ð½Ð° ÑÐ¾Ð±ÑÑÐ²ÐµÐ½Ð½ÑÐµ Ð´Ð¸Ð½Ð°Ð¼Ð¸ÑÐµÑÐºÐ¸Ðµ ÑÐ°ÑÐ°ÐºÑÐµÑÐ¸ÑÑÐ¸ÐºÐ¸ Ð¸ Ð½Ð°Ð¿ÑÑÐ¶ÐµÐ½Ð½Ð¾-Ð´ÐµÑÐ¾ÑÐ¼Ð¸ÑÑÐµÐ¼Ð¾Ðµ ÑÐ¾ÑÑÐ¾ÑÐ½Ð¸Ðµ ÑÑÐµÑÐ¶Ð½ÐµÐ²ÑÑ ÑÐ¸ÑÑÐµÐ¼ Ð¿ÑÐ¸ Ð¸Ñ ÑÐ°ÑÑÐµÑÐ°Ñ Ð½Ð° ÑÐµÐ¹ÑÐ¼Ð¸ÑÐµÑÐºÐ¾Ðµ Ð²Ð¾Ð·Ð´ÐµÐ¹ÑÑÐ²Ð¸Ðµ.
description: The work is devoted to the development of a method for calculating rod systems considering the rotational degree of freedom and the study of the influence of the inertia of rotation on rod systems when calculating them for seismic impact. The research set the following goals: 1. Development of a method for taking into account the inertia of rotation when performing modal analysis; 2. Study of the effect of taking into account the moment of inertia of the mass on the natural frequencies of beams when they are fixed differently; 3. Study of the effect of taking into account the moment of inertia of the mass on the internal forces of the beams when they are fixed differently; 4. Application of the developed method of accounting for the inertia of rotation in the calculations of structures for seismic impact. A method for taking into account the inertia of rotation when performing modal analysis is proposed. The natural vibration frequencies of the beams are analyzed and compared with the exact solution. The calculation is made for the seismic impact of beams and various structures using the developed method of accounting for the inertia of rotation. The tasks were solved using the SCAD Office PC, Lira Soft, and analytical methods. The accuracy of the approximate solutions is estimated using the B. S. Shvartsman method. A method is proposed for considering the mass moment of inertia when performing a modal analysis, by using a diagonal mass matrix that considers rotation. The influence of the inertia of rotation on the native dynamic characteristics and the stress-strain state of rod systems in their calculations on the seismic impact is investigated.