title: ÐÐ°Ð»Ð°Ð½Ñ Ð¿Ð¾ÑÐ¾ÐºÐ° ÑÐ½ÐµÑÐ³Ð¸Ð¸ Ð² Ð´Ð¸ÑÐºÑÐµÑÐ½ÑÑ Ð¸ ÐºÐ¾Ð½ÑÐ¸Ð½ÑÐ°Ð»ÑÐ½ÑÑ ÑÑÐµÐ´Ð°Ñ
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð±Ð°ÐºÐ°Ð»Ð°Ð²ÑÐ°
titleType: Subtitle
title: Balance of energy flow in discrete and continuum media
Creators: name: ÐÑÐ¾Ð·Ð´Ð¾Ð², Ð¡Ð²ÑÑÐ¾ÑÐ»Ð°Ð²
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: 2023
Subjects: ÑÐ½ÐµÑÐ³ÐµÑÐ¸ÑÐµÑÐºÐ¸Ð¹ ÑÐµÐ½ÑÑ
ÑÐ°ÑÐ¿ÑÐ¾ÑÑÑÐ°Ð½ÐµÐ½Ð¸Ðµ ÑÐ½ÐµÑÐ³Ð¸Ð¸
Ð´Ð¸Ð½Ð°Ð¼Ð¸ÐºÐ° Ð¼Ð°ÑÑÑ Ð¸ ÑÐ½ÐµÑÐ³Ð¸Ð¸
Ð±Ð°Ð»Ð°Ð½Ñ Ð¿Ð¾ÑÐ¾ÐºÐ° ÑÐ½ÐµÑÐ³Ð¸Ð¸
ÑÐ¸ÑÐ»ÐµÐ½Ð½Ð¾Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ
energy center
energy propagation
mass and energy dynamics
energy flow balance
numerical simulation

description: Ð Ð´Ð°Ð½Ð½Ð¾Ð¹ ÑÐ°Ð±Ð¾ÑÐµ Ð¸ÑÑÐ»ÐµÐ´ÑÐµÑÑÑ Ð²Ð»Ð¸ÑÐ½Ð¸Ðµ ÑÐ¼ÐµÑÐµÐ½Ð¸Ñ ÑÐ¾ÑÐµÐº ÑÑÐµÐ´Ñ Ð½Ð° ÑÐ°ÑÐ¿ÑÐ¾ÑÑÑÐ°Ð½ÐµÐ½Ð¸Ðµ ÑÐ½ÐµÑÐ³Ð¸Ð¸ Ð² Ð½ÐµÐ¹. Ð ÑÐ°Ð¼ÐºÐ°Ñ ÑÑÐ¾Ð³Ð¾ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ Ð±ÑÐ»Ð¸ ÑÐ°ÑÑÐ¼Ð¾ÑÑÐµÐ½Ñ ÑÐ»ÐµÐ´ÑÑÑÐ¸Ðµ Ð¾Ð´Ð½Ð¾Ð¼ÐµÑÐ½ÑÐµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ ÑÑÐµÐ´: 1) ÐÐ¾Ð½ÑÐ¸Ð½ÑÐ°Ð»ÑÐ½Ð°Ñ Ð¼Ð¾Ð´ÐµÐ»Ñ. 2) ÐÐ¸ÑÐºÑÐµÑÐ½Ð°Ñ Ð¼Ð¾Ð´ÐµÐ»Ñ Ñ Ð»Ð¸Ð½ÐµÐ¹Ð½Ð¾Ð¹ ÑÐ¸Ð»Ð¾Ð¹ Ð²Ð·Ð°Ð¸Ð¼Ð¾Ð´ÐµÐ¹ÑÑÐ²Ð¸Ñ ÑÐ°ÑÑÐ¸Ñ. 3) ÐÐ¸ÑÐºÑÐµÑÐ½Ð°Ñ Ð¼Ð¾Ð´ÐµÐ»Ñ Ñ Ð½ÐµÐ»Ð¸Ð½ÐµÐ¹Ð½Ð¾Ð¹ ÑÐ¸Ð»Ð¾Ð¹ Ð²Ð·Ð°Ð¸Ð¼Ð¾Ð´ÐµÐ¹ÑÑÐ²Ð¸Ñ ÑÐ°ÑÑÐ¸Ñ. Ð ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐµ Ð±ÑÐ»Ð¸ Ð¿Ð¾Ð»ÑÑÐµÐ½Ñ ÑÐ¾Ð¾ÑÐ½Ð¾ÑÐµÐ½Ð¸Ñ, Ð¾Ð¿Ð¸ÑÑÐ²Ð°ÑÑÐ¸Ðµ Ð´Ð²Ð¸Ð¶ÐµÐ½Ð¸Ñ ÑÐ½ÐµÑÐ³ÐµÑÐ¸ÑÐµÑÐºÐ¸Ñ ÑÐµÐ½ÑÑÐ¾Ð² Ð²Ð¾Ð·Ð¼ÑÑÐµÐ½Ð¸Ð¹ Ð² ÑÑÐ¸Ñ ÑÑÐµÐ´Ð°Ñ. ÐÐ¾ÐºÐ°Ð·Ð°Ð½Ð¾, ÑÑÐ¾ ÐµÑÐ»Ð¸ Ð¿ÐµÑÐµÐ¼ÐµÑÐµÐ½Ð¸Ñ ÑÐ°ÑÑÐ¸Ñ ÑÑÐµÐ´Ñ Ð·Ð½Ð°ÑÐ¸ÑÐµÐ»ÑÐ½Ñ, ÑÐ¾ Ð½ÐµÐ¾Ð±ÑÐ¾Ð´Ð¸Ð¼Ð¾ ÑÑÐ¸ÑÑÐ²Ð°ÑÑ Ð¿ÐµÑÐµÐ½Ð¾Ñ ÑÐ½ÐµÑÐ³Ð¸Ð¸, Ð²ÑÐ·Ð²Ð°Ð½Ð½ÑÐ¹ Ð¼ÐµÑÐ°Ð½Ð¸ÑÐµÑÐºÐ¸Ð¼ ÑÐ¼ÐµÑÐµÐ½Ð¸ÐµÐ¼ ÑÐ°ÑÑÐ¸Ñ ÑÑÐµÐ´Ñ. ÐÐ²ÐµÐ´ÐµÐ½Ñ Ð¿Ð¾Ð½ÑÑÐ¸Ñ Ð¸Ð¼Ð¿ÑÐ»ÑÑÐ½Ð¾Ð³Ð¾ Ð¼Ð¾Ð¼ÐµÐ½ÑÐ° Ð¸ Ð¸Ð¼Ð¿ÑÐ»ÑÑÐ½Ð¾Ð³Ð¾ ÑÐµÐ½ÑÑÐ° Ð²Ð¾Ð·Ð¼ÑÑÐµÐ½Ð¸Ñ, Ñ Ð¿Ð¾Ð¼Ð¾ÑÑÑ ÐºÐ¾ÑÐ¾ÑÑÑ Ð½Ð° Ð¾ÑÐ½Ð¾Ð²Ð°Ð½Ð¸Ð¸ ÑÐ¸ÑÐ»ÐµÐ½Ð½Ð¾Ð³Ð¾ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Ð¿ÑÐµÐ´Ð»Ð¾Ð¶ÐµÐ½ ÑÐ¿Ð¾ÑÐ¾Ð± Ð¿ÑÐ¸Ð±Ð»Ð¸Ð·Ð¸ÑÐµÐ»ÑÐ½Ð¾Ð³Ð¾ Ð¾Ð¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð¸Ñ ÑÐºÐ¾ÑÐ¾ÑÑÐ¸ ÑÐ½ÐµÑÐ³ÐµÑÐ¸ÑÐµÑÐºÐ¾Ð³Ð¾ ÑÐµÐ½ÑÑÐ° Ð²Ð¾Ð·Ð¼ÑÑÐµÐ½Ð¸Ñ Ð² ÑÐ»ÑÑÐ°Ðµ ÑÐ´Ð°ÑÐ½Ð¾Ð³Ð¾ Ð½Ð°Ð³ÑÑÐ¶ÐµÐ½Ð¸Ñ. ÐÐ¾ÐºÐ°Ð·Ð°Ð½Ð¾, ÑÑÐ¾ ÑÐ°ÐºÐ¾Ð¹ ÑÐ¿Ð¾ÑÐ¾Ð± Ð¼Ð¾Ð¶ÐµÑ Ð±ÑÑÑ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½ ÐºÐ°Ðº Ð´Ð»Ñ ÑÑÐµÐ´ Ñ Ð»Ð¸Ð½ÐµÐ¹Ð½Ð¾Ð¹ ÑÐ¸Ð»Ð¾Ð¹ Ð²Ð·Ð°Ð¸Ð¼Ð¾Ð´ÐµÐ¹ÑÑÐ²Ð¸Ñ ÑÐ°ÑÑÐ¸Ñ, ÑÐ°Ðº Ð¸ Ð´Ð»Ñ ÑÑÐµÐ´ Ñ Ð½ÐµÐ»Ð¸Ð½ÐµÐ¹Ð½Ð¾Ð¹ ÑÐ¸Ð»Ð¾Ð¹ Ð²Ð·Ð°Ð¸Ð¼Ð¾Ð´ÐµÐ¹ÑÑÐ²Ð¸Ñ ÑÐ°ÑÑÐ¸Ñ.
description: In this work we investigate the effect of displacement of points in the medium on the propagation of energy in it. As part of this study, the following one-dimensional models of media were considered: 1) Continuous elastic model. 2) Discrete model with linear force of interaction of particles. 3) Discrete model with nonlinear force of interaction of particles. As a result, the relations describing movements of energy centers of disturbances in these media have been obtained. It is shown that if displacements of particles of the medium are significant, it is necessary to take into account the energy transfer caused by mechanical displacement of particles of the medium. The concepts of impulse moment and impulse center of perturbation are introduced, with the help of which, based on numerical modeling, the method of approximate determination of the energy center of perturbation, in the case of shock loading is proposed. It is shown that this method can be used both for media with linear particle interaction force and for media with nonlinear particle interaction force.