title: ÐÑÐ¾Ð´Ð¾Ð»ÑÐ½ÑÐµ ÐºÐ¾Ð»ÐµÐ±Ð°Ð½Ð¸Ñ ÑÑÐµÑÐ¶Ð½ÐµÐ¹
title: ÑÑÐµÐ±Ð½Ð¾Ðµ Ð¿Ð¾ÑÐ¾Ð±Ð¸Ðµ
titleType: Subtitle
title: Longitudinal oscillations of rods
Creators: name: Ð¡Ð¼Ð¸ÑÐ½Ð¾Ð², ÐÐ»ÐµÐºÑÐµÐ¹
Publisher: name: ÐÐÐÐÐ¢ÐÐ¥-ÐÐ ÐÐ¡Ð¡
Year: 2023
Subjects: Ð¡ÑÐµÑÐ¶Ð½Ð¸

description: Ð£ÑÐµÐ±Ð½Ð¾Ðµ Ð¿Ð¾ÑÐ¾Ð±Ð¸Ðµ Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð¾ Ð¸Ð·ÑÑÐµÐ½Ð¸Ñ Ð¿ÑÐ¾Ð´Ð¾Ð»ÑÐ½ÑÑ ÐºÐ¾Ð»ÐµÐ±Ð°Ð½Ð¸Ð¹ ÑÐ¿ÑÑÐ³Ð¸Ñ ÑÑÐµÑÐ¶Ð½ÐµÐ¹, Ð¿ÑÐ¸ ÑÑÐ¾Ð¼ Ð¸Ð·Ð»Ð°Ð³Ð°ÑÑÑÑ ÐºÐ°Ðº ÐºÐ»Ð°ÑÑÐ¸ÑÐµÑÐºÐ¸Ðµ, ÑÐ°Ðº Ð¸ Ð½Ð¾Ð²ÑÐµ Ð·Ð°Ð´Ð°ÑÐ¸. ÐÐ° Ð¾ÑÐ½Ð¾Ð²Ðµ ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¾Ð¹ ÑÐµÐ¾ÑÐ¸Ð¸ Ð¸ÑÑÐ»ÐµÐ´ÑÑÑÑÑ ÑÐ²Ð¾Ð±Ð¾Ð´Ð½ÑÐµ Ð¸ Ð²ÑÐ½ÑÐ¶Ð´ÐµÐ½Ð½ÑÐµ ÐºÐ¾Ð»ÐµÐ±Ð°Ð½Ð¸Ñ ÑÑÐµÑÐ¶Ð½ÐµÐ¹ Ð¿Ð¾ÑÑÐ¾ÑÐ½Ð½Ð¾Ð³Ð¾ ÑÐµÑÐµÐ½Ð¸Ñ Ñ ÑÐ°Ð·Ð»Ð¸ÑÐ½ÑÐ¼Ð¸ Ð³ÑÐ°Ð½Ð¸ÑÐ½ÑÐ¼Ð¸ ÑÑÐ»Ð¾Ð²Ð¸ÑÐ¼Ð¸ Ð¸ Ð´ÐµÐ¹ÑÑÐ²ÑÑÑÐ¸Ð¼Ð¸ Ð½Ð°Ð³ÑÑÐ·ÐºÐ°Ð¼Ð¸. Ð Ð°ÑÑÐ¼Ð°ÑÑÐ¸Ð²Ð°ÑÑÑÑ ÐºÐ¾Ð»ÐµÐ±Ð°Ð½Ð¸Ñ ÑÑÐµÑÐ¶Ð½ÐµÐ²ÑÑ ÐºÐ¾Ð½ÑÑÑÑÐºÑÐ¸Ð¹ Ñ Ð¿ÐµÑÐµÐ¼ÐµÐ½Ð½ÑÐ¼ ÑÐµÑÐµÐ½Ð¸ÐµÐ¼ Ð¸ Ð·Ð°ÑÑÐ°Ð³Ð¸Ð²Ð°ÑÑÑÑ Ð²Ð¾Ð¿ÑÐ¾ÑÑ Ð¸Ñ Ð¾Ð¿ÑÐ¸Ð¼Ð¸Ð·Ð°ÑÐ¸Ð¸. ÐÑÐ´ÐµÐ»ÑÐ½Ð¾Ðµ Ð²Ð½Ð¸Ð¼Ð°Ð½Ð¸Ðµ ÑÐ´ÐµÐ»ÑÐµÑÑÑ Ð¸Ð·Ð»Ð¾Ð¶ÐµÐ½Ð¸Ñ Ð¿ÑÐ¸Ð±Ð»Ð¸Ð¶ÐµÐ½Ð½ÑÑ Ð¼ÐµÑÐ¾Ð´Ð¾Ð² Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ ÐºÐ¾Ð»ÐµÐ±Ð°Ð½Ð¸Ð¹ ÑÑÐµÑÐ¶Ð½ÐµÐ²ÑÑ ÑÐ¸ÑÑÐµÐ¼ Ð¿Ð¾ÑÑÐµÐ´ÑÑÐ²Ð¾Ð¼ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸Ñ ÐºÐ°Ðº ÑÐ¸Ð·Ð¸ÑÐµÑÐºÐ¾Ð³Ð¾, ÑÐ°Ðº Ð¸ Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ð³Ð¾ Ð¿Ð¾Ð´ÑÐ¾Ð´Ð°. ÐÐ¾Ð¼Ð¸Ð¼Ð¾ ÑÑÐ¾Ð³Ð¾ Ð¿ÑÐ¸Ð²Ð¾Ð´ÑÑÑÑ ÑÑÐ¾ÑÐ½ÐµÐ½Ð½ÑÐµ ÑÐµÐ¾ÑÐ¸Ð¸ Ð¿ÑÐ¾Ð´Ð¾Ð»ÑÐ½ÑÑ ÐºÐ¾Ð»ÐµÐ±Ð°Ð½Ð¸Ð¹ ÑÑÐµÑÐ¶Ð½ÐµÐ¹. ÐÐ¾Ð»ÑÑÐµÐ½Ð½ÑÐµ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÑ ÑÐ¾Ð¿ÑÐ¾Ð²Ð¾Ð¶Ð´Ð°ÑÑÑÑ Ð½Ð°Ð³Ð»ÑÐ´Ð½ÑÐ¼ Ð¸Ð»Ð»ÑÑÑÑÐ°ÑÐ¸Ð²Ð½ÑÐ¼ Ð¼Ð°ÑÐµÑÐ¸Ð°Ð»Ð¾Ð¼. Ð ÑÑÐµÐ±Ð½Ð¾Ð¼ Ð¿Ð¾ÑÐ¾Ð±Ð¸Ð¸ ÑÐ°ÐºÐ¶Ðµ Ð´Ð°ÑÑÑÑ ÑÐ²ÐµÐ´ÐµÐ½Ð¸Ñ Ð¾ Ð²ÑÐ´Ð°ÑÑÐ¸ÑÑÑ ÑÑÐµÐ½ÑÑ, Ð²Ð½ÐµÑÑÐ¸Ñ Ð±Ð¾Ð»ÑÑÐ¾Ð¹ Ð²ÐºÐ»Ð°Ð´ Ð² ÑÐ°Ð·Ð²Ð¸ÑÐ¸Ðµ Ð¿ÑÐµÐ´ÑÑÐ°Ð²Ð»ÐµÐ½Ð½Ð¾Ð¹ ÑÐµÐ¼Ð°ÑÐ¸ÐºÐ¸. ÐÑÐµÐ´Ð½Ð°Ð·Ð½Ð°ÑÐµÐ½Ð¾ Ð´Ð»Ñ ÑÑÑÐ´ÐµÐ½ÑÐ¾Ð² ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ñ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑÐ¾Ð², Ð°ÑÐ¿Ð¸ÑÐ°Ð½ÑÐ¾Ð², Ð¿ÑÐµÐ¿Ð¾Ð´Ð°Ð²Ð°ÑÐµÐ»ÐµÐ¹, Ð¸Ð½Ð¶ÐµÐ½ÐµÑÐ¾Ð² Ð¸ Ð½Ð°ÑÑÐ½ÑÑ ÑÐ¾ÑÑÑÐ´Ð½Ð¸ÐºÐ¾Ð², ÑÐ°Ð±Ð¾ÑÐ°ÑÑÐ¸Ñ Ð² Ð¾Ð±Ð»Ð°ÑÑÐ¸ ÑÐµÐ¾ÑÐ¸Ð¸ Ð¼ÐµÑÐ°Ð½Ð¸ÑÐµÑÐºÐ¸Ñ ÐºÐ¾Ð»ÐµÐ±Ð°Ð½Ð¸Ð¹.
description: The tutorial is devoted to the study of longitudinal oscillations of elastic rods, while both classical and new problems are presented. Based on the technical theory, free and forced oscillations of rods of constant section with various boundary conditions and acting loads are investigated. Oscillations of rod structures with variable section are considered and questions of their optimization are discussed. Special attention is paid to the presentation of approximate methods for studying oscillations of rod systems by using both physical and mathematical approach. In addition, refined theories of longitudinal oscillations of rods are given. The obtained results are accompanied by visual illustrative material. The book also provides information about outstanding scientists who have made significant contributions to the development of the presented topics. The book is intended for students of technical universities, graduate students, teachers, engineers and scientists working in the field of theory of mechanical oscillations.