title: ÐÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ ÑÐ°ÑÐ¿ÑÐ¾ÑÑÑÐ°Ð½ÐµÐ½Ð¸Ñ ÑÐ½ÐµÑÐ³Ð¸Ð¸ Ð² ÑÑÐµÐ´Ðµ Ñ Ð¼Ð¸ÐºÑÐ¾ÑÑÑÑÐºÑÑÑÐ¾Ð¹
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: Study of energy propagation of media with microstructure
Creators: name: ÐÑÑÐ·Ð´ÐµÐ², ÐÐ³Ð¾Ñ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: 2022
Subjects: Ð´Ð¸Ð½Ð°Ð¼Ð¸ÐºÐ°
ÑÐµÐ¿Ð¾ÑÐºÐ°
ÑÐ½ÐµÑÐ³Ð¸Ñ
Ð¿Ð¾ÑÐ¾Ðº
Ð´Ð¸ÑÐ¿ÐµÑÑÐ¸Ñ
dynamic
chain
energy
flux
dispersion

description: Ð Ð´Ð°Ð½Ð½Ð¾Ð¹ ÑÐ°Ð±Ð¾ÑÐµ Ð¿ÑÐ¾Ð²Ð¾Ð´Ð¸ÑÑÑ ÑÑÐ°Ð²Ð½Ð¸ÑÐµÐ»ÑÐ½ÑÐ¹ Ð°Ð½Ð°Ð»Ð¸Ð· Ð´Ð²Ð¸Ð¶ÐµÐ½Ð¸Ñ ÑÐ½ÐµÑÐ³ÐµÑÐ¸ÑÐµÑÐºÐ¾Ð³Ð¾ ÑÐµÐ½ÑÑÐ° Ð² Ð³Ð°ÑÐ¼Ð¾Ð½Ð¸ÑÐµÑÐºÐ¸Ñ Ð¾Ð´Ð½Ð¾Ð°ÑÐ¾Ð¼Ð½Ð¾Ð¼ Ð¸ Ð´Ð²ÑÑÐ°ÑÐ¾Ð¼Ð½Ð¾Ð¼ ÐºÑÐ¸ÑÑÐ°Ð»Ð»Ð°Ñ, Ð° ÑÐ°ÐºÐ¶Ðµ ÐºÑÐ¸ÑÑÐ°Ð»Ð»Ð° Ð½Ð° ÑÐ¿ÑÑÐ³Ð¾Ð¼ Ð¾ÑÐ½Ð¾Ð²Ð°Ð½Ð¸Ð¸. Ð ÐºÐ°Ð¶Ð´Ð¾Ð¼ ÑÐ»ÑÑÐ°Ðµ Ð¿Ð¾Ð»ÑÑÐµÐ½Ð¾ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ðµ Ð´Ð²Ð¸Ð¶ÐµÐ½Ð¸Ðµ ÑÐ½ÐµÑÐ³ÐµÑÐ¸ÑÐµÑÐºÐ¾Ð³Ð¾ ÑÐµÐ½ÑÑÐ° Ð´Ð»Ñ Ð¿ÑÐ¾Ð¸Ð·Ð²Ð¾Ð»ÑÐ½Ð¾Ð³Ð¾ Ð²Ð¾Ð·Ð¼ÑÑÐµÐ½Ð¸Ñ, Ð¾Ð±Ð»Ð°Ð´Ð°ÑÑÐµÐ³Ð¾ ÐºÐ¾Ð½ÐµÑÐ½Ð¾Ð¹ ÑÐ½ÐµÑÐ³Ð¸ÐµÐ¹. ÐÐ¾ÐºÐ°Ð·Ð°Ð½Ð¾, ÑÑÐ¾ Ð² ÑÐµÐ¿Ð¾ÑÐºÐµ ÐÑÐºÐ° Ð¸ ÐºÑÐ¸ÑÑÐ°Ð»Ð»Ð° Ð½Ð° ÑÐ¿ÑÑÐ³Ð¾Ð¼ Ð¾ÑÐ½Ð¾Ð²Ð°Ð½Ð¸Ð¸ ÑÐ½ÐµÑÐ³ÐµÑÐ¸ÑÐµÑÐºÐ¸Ð¹ ÑÐµÐ½ÑÑ Ð´Ð²Ð¸Ð¶ÐµÑÑÑ ÑÐ°Ð²Ð½Ð¾Ð¼ÐµÑÐ½Ð¾. ÐÑÐ¸ ÑÑÐ¾Ð¼ Ð¿ÑÐ¸ Ð·Ð°Ð´Ð°Ð½Ð¸Ð¸ Ð¿ÐµÑÐ²Ð¾Ð³Ð¾ Ð¼Ð¾Ð¼ÐµÐ½ÑÐ° ÑÐ½ÐµÑÐ³Ð¸Ð¸ Ð´Ð»Ñ Ð´Ð²ÑÑÐ°ÑÐ¾Ð¼Ð½Ð¾Ð¹ ÑÐµÐ¿Ð¾ÑÐºÐ¸ Ð´Ð¾ÑÑÐ°ÑÐ¾ÑÐ½Ð¾ ÑÑÑÐ´Ð½Ð¾ Ð¿Ð¾Ð»ÑÑÐ¸ÑÑ ÑÐ¾ÑÐ½Ð¾Ðµ ÑÐ¾ÑÑÐ°Ð½ÐµÐ½Ð¸Ðµ Ð¿Ð¾ÑÐ¾ÐºÐ° ÑÐ½ÐµÑÐ³Ð¸Ð¸. ÐÐ¾ÐºÐ°Ð·Ð°Ð½Ð¾, ÑÑÐ¾ Ð² ÐºÑÐ¸ÑÑÐ°Ð»Ð»Ðµ Ñ ÑÐµÑÐµÐ´Ð¾Ð²Ð°Ð½Ð¸ÐµÐ¼ Ð¼Ð°ÑÑ Ð¼Ð¾Ð¶Ð½Ð¾ Ð¿Ð¾Ð»ÑÑÐ¸ÑÑ Ð°Ð½Ð°Ð»Ð¾Ð³Ð¸ÑÐ½ÑÐ¹ ÑÐµÐ·ÑÐ»ÑÑÐ°Ñ Ð¿ÑÐ¸ Ð±Ð¾Ð»ÐµÐµ ÑÐ»Ð¾Ð¶Ð½Ð¾Ð¼ Ð·Ð°Ð´Ð°Ð½Ð¸Ð¸ Ð¿ÐµÑÐ²Ð¾Ð³Ð¾ Ð¼Ð¾Ð¼ÐµÐ½ÑÐ° ÑÐ½ÐµÑÐ³Ð¸Ð¸. Ð¢Ð°ÐºÐ¶Ðµ Ð´Ð»Ñ ÐºÑÐ¸ÑÑÐ°Ð»Ð»Ð° ÐÑÐºÐ° Ð¸ ÑÐµÐ¿Ð¾ÑÐºÐ¸ Ð½Ð° ÑÐ¿ÑÑÐ³Ð¾Ð¼ Ð¾ÑÐ½Ð¾Ð²Ð°Ð½Ð¸Ð¸ Ð±ÑÐ»Ð¸ Ð¿ÑÐ¸Ð²ÐµÐ´ÐµÐ½Ñ Ð²ÑÐºÐ»Ð°Ð´ÐºÐ¸, Ð¿Ð¾ÐºÐ°Ð·ÑÐ²Ð°ÑÑÐ¸Ðµ, ÑÑÐ¾ Ð²ÑÐ¾ÑÐ°Ñ Ð¿ÑÐ¾Ð¸Ð·Ð²Ð¾Ð´Ð½Ð°Ñ Ð²ÑÐ¾ÑÐ¾Ð³Ð¾ Ð¼Ð¾Ð¼ÐµÐ½ÑÐ° ÑÐ½ÐµÑÐ³Ð¸Ð¸ â Ð¿Ð¾ÑÑÐ¾ÑÐ½Ð½Ð°Ñ Ð²ÐµÐ»Ð¸ÑÐ¸Ð½Ð°. ÐÐ° Ð¾ÑÐ½Ð¾Ð²Ðµ ÑÑÐ¾Ð³Ð¾ Ð¼Ð¾Ð¶Ð½Ð¾ Ð²ÑÐ²ÐµÑÑÐ¸ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ñ ÑÐ²Ð¾Ð»ÑÑÐ¸Ð¸ ÑÐ½ÐµÑÐ³ÐµÑÐ¸ÑÐµÑÐºÐ¾Ð³Ð¾ ÑÐ°Ð´Ð¸ÑÑÐ°, ÐºÐ¾ÑÐ¾ÑÑÐ¹ Ð±ÑÐ´ÐµÑ Ð°Ð½Ð°Ð»Ð¾Ð³Ð¾Ð¼ ÑÐ°Ð´Ð¸ÑÑÐ° Ð¸Ð½ÐµÑÑÐ¸Ð¸ Ð² Ð´Ð¸Ð½Ð°Ð¼Ð¸ÐºÐµ Ð¼Ð°ÑÑÑ. ÐÐ° Ð¾ÑÐ½Ð¾Ð²Ðµ Ð¿ÑÐ¾Ð²ÐµÐ´ÑÐ½Ð½Ð¾Ð³Ð¾ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ ÑÑÑÐ¾Ð¸ÑÑÑ Ð°Ð½Ð°Ð»Ð¾Ð³Ð¸Ñ Ð¼ÐµÐ¶Ð´Ñ Ð´Ð¸Ð½Ð°Ð¼Ð¸ÐºÐ¾Ð¹ Ð¼Ð°ÑÑÑ Ð¸ Ð´Ð¸Ð½Ð°Ð¼Ð¸ÐºÐ¾Ð¹ ÑÐ½ÐµÑÐ³Ð¸Ð¸.
description: In this work a comparative analysis of the movement of an energy center in harmonic monatomic and diatomic crystals, as well as a crystal on an elastic foundation, is carried out. In each case, the equation of motion of the energy center for an arbitrary perturbation with a finite energy is obtained. It is shown that in the chain of Hookâs and a crystal on an elastic foundation, the energy center moves uniformly. In this case, when specifying the first moment of energy for a diatomic chain, it is rather difficult to obtain an exact conservation of the energy flux. It is proved that in a crystal with mass alternation, a similar result can be obtained with a more complex setting of the first moment of energy. Also, for a Hookâs crystal and a chain on an elastic foundation, calculations were made showing that the second derivative of the second moment of energy is a constant. Based on this, one can derive the equations of evolution of the energy radius, which will be an analogue of the radius of gyration in mass dynamics.Based on this research, an analogy is built between the dynamics of mass and the dynamics of energy.