title: ÐÐ¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ Ð¸ Ð°Ð½Ð°Ð»Ð¸Ð· Ð¿ÑÐ¾ÑÐµÑÑÐ¾Ð² Ð´Ð¸ÑÑÐ¸Ð¿Ð°ÑÐ¸Ð¸ ÑÐ½ÐµÑÐ³Ð¸Ð¸ Ð¼Ð¸ÐºÑÐ¾Ð¼ÐµÑ Ð°Ð½Ð¸ÑÐµÑÐºÐ¸Ñ Ð±Ð°Ð»Ð¾ÑÐ½ÑÑ ÑÐµÐ·Ð¾Ð½Ð°ÑÐ¾ÑÐ¾Ð²
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: Modeling and analysis of the dissipation processes of micromechanical beam resonators
Creators: name: Ð¨ÐµÑÑÐ°ÐºÐ¾Ð², ÐÐ»ÐµÐºÑÐ°Ð½Ð´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´Ð¾Ð±ÑÐ¾ÑÐ½Ð¾ÑÑÑ
ÑÐµÐ·Ð¾Ð½Ð°ÑÐ¾Ñ
ÐÐ­ÐÐ¡
Ð´Ð¸ÑÑÐ¸Ð¿Ð°ÑÐ¸Ñ
PML
Ð°Ð½ÐºÐµÑÐ½Ð°Ñ Ð´Ð¸ÑÑÐ¸Ð¿Ð°ÑÐ¸Ñ
ÑÐµÑÐ¼Ð¾ÑÐ¿ÑÑÐ³Ð°Ñ Ð´Ð¸ÑÑÐ¸Ð¿Ð°ÑÐ¸Ñ
quality factor
resonator
MEMS
dissipation
anchor losses
thermoelastic dissipation

description: ÐÐ°Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð° Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ Ð¿ÑÐ¾ÑÐµÑÑÐ¾Ð² Ð´Ð¸ÑÑÐ¸Ð¿Ð°ÑÐ¸Ð¸, Ð¿ÑÐ¾ÑÐµÐºÐ°ÑÑÐ¸Ñ Ð² Ð¼Ð¸ÐºÑÐ¾Ð¼ÐµÑÐ°Ð½Ð¸ÑÐµÑÐºÐ¸Ñ Ð±Ð°Ð»Ð¾ÑÐ½ÑÑ ÑÐµÐ·Ð¾Ð½Ð°ÑÐ¾ÑÐ°Ñ. ÐÐ°Ð´Ð°ÑÐ¸, ÐºÐ¾ÑÐ¾ÑÑÐµ ÑÐµÑÐ°Ð»Ð¸ÑÑ Ð² ÑÐ¾Ð´Ðµ ÑÐ°Ð±Ð¾ÑÑ: 1. ÐÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ Ð¸ Ð°Ð½Ð°Ð»Ð¸Ð· Ð°Ð½Ð°Ð»Ð¸ÑÐ¸ÑÐµÑÐºÐ¸Ñ Ð¼Ð¾Ð´ÐµÐ»ÐµÐ¹ Ð°Ð½ÐºÐµÑÐ½Ð¾Ð¹ Ð¸ ÑÐµÑÐ¼Ð¾ÑÐ¿ÑÑÐ³Ð¾Ð¹ Ð´Ð¸ÑÑÐ¸Ð¿Ð°ÑÐ¸Ð¸. 2. Ð§Ð¸ÑÐ»ÐµÐ½Ð½Ð¾Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ Ð¿ÑÐ¾ÑÐµÑÑÐ¾Ð² Ð´Ð¸ÑÑÐ¸Ð¿Ð°ÑÐ¸Ð¸. 3. ÐÐ±ÑÐ°Ð±Ð¾ÑÐºÐ° ÑÐ¸ÑÐ»ÐµÐ½Ð½ÑÑ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐ¾Ð² Ð¸ Ð¸Ñ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ðµ Ñ Ð°Ð½Ð°Ð»Ð¸ÑÐ¸ÑÐµÑÐºÐ¸Ð¼Ð¸ ÑÐµÑÐµÐ½Ð¸ÑÐ¼Ð¸. 4. ÐÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ ÑÐ²Ð¾Ð¹ÑÑÐ² PML Ð´Ð»Ñ Ð·Ð°Ð´Ð°Ñ Ñ Ð±ÐµÑÐºÐ¾Ð½ÐµÑÐ½ÑÐ¼Ð¸ Ð¾Ð±Ð»Ð°ÑÑÑÐ¼Ð¸. 5. ÐÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ Ð·Ð½Ð°ÑÐµÐ½Ð¸Ð¹ Ð¿Ð¾Ð»Ð½Ð¾Ð¹ Ð´Ð¾Ð±ÑÐ¾ÑÐ½Ð¾ÑÑÐ¸ Ð² Ð·Ð°Ð²Ð¸ÑÐ¸Ð¼Ð¾ÑÑÐ¸ Ð¾Ñ Ð¿Ð°ÑÐ°-Ð¼ÐµÑÑÐ¾Ð² ÑÐ¸ÑÑÐµÐ¼Ñ. Ð ÑÐ¾Ð´Ðµ ÑÐ°Ð±Ð¾ÑÑ Ð±ÑÐ»Ð¸ Ð½Ð°Ð³Ð»ÑÐ´Ð½Ð¾ Ð¿ÑÐ¾Ð´ÐµÐ¼Ð¾Ð½ÑÑÑÐ¸ÑÐ¾Ð²Ð°Ð½Ñ ÑÐ²Ð¾Ð¹ÑÑÐ²Ð° Ð´Ð¾Ð±ÑÐ¾ÑÐ½Ð¾ÑÑÐ¸ ÐºÐ¾Ð»ÐµÐ±Ð°Ð½Ð¸Ð¹ Ð±Ð°Ð»Ð¾ÑÐ½ÑÑ ÑÐµÐ·Ð¾Ð½Ð°ÑÐ¾ÑÐ¾Ð² Ð² Ð·Ð°Ð²Ð¸ÑÐ¸Ð¼Ð¾ÑÑÐ¸ Ð¾Ñ Ð³ÐµÐ¾Ð¼ÐµÑÑÐ¸ÑÐµÑÐºÐ¸Ñ Ð¸ ÑÐµÐ¼Ð¿ÐµÑÐ°ÑÑÑÐ½ÑÑ Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÐ¾Ð² ÑÐ¸ÑÑÐµÐ¼Ñ. ÐÑÐ¸Ð²ÐµÐ´ÐµÐ½Ñ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ñ Ð°Ð½Ð°Ð»Ð¸ÑÐ¸ÑÐµÑÐºÐ¸Ñ Ð¸ ÑÐ¸ÑÐ»ÐµÐ½Ð½ÑÑ Ð²ÑÑÐ¸ÑÐ»ÐµÐ½Ð¸Ð¹ Ð´Ð¾Ð±ÑÐ¾ÑÐ½Ð¾ÑÑÐ¸ Ð½Ð° Ð¿ÑÐ¸Ð¼ÐµÑÐµ ÑÐµÐ·Ð¾Ð½Ð°ÑÐ¾ÑÐ¾Ð² Ð´Ð²ÑÑ ÑÐ¸Ð¿Ð¾Ð² Ð·Ð°ÐºÑÐµÐ¿Ð»ÐµÐ½Ð¸Ð¹ Ð² Ð·Ð°Ð²Ð¸ÑÐ¸Ð¼Ð¾ÑÑÐ¸ Ð¾Ñ Ð¸Ñ Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÐ¾Ð². Ð§Ð¸ÑÐ»ÐµÐ½Ð½ÑÐµ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ Ð¿ÑÐ¾Ð²Ð¾Ð´Ð¸Ð»Ð¸ÑÑ Ð² Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ðµ ÐºÐ¾Ð½ÐµÑÐ½Ð¾-ÑÐ»ÐµÐ¼ÐµÐ½ÑÐ½Ð¾Ð³Ð¾ Ð°Ð½Ð°Ð»Ð¸Ð·Ð° Comsol Multiphysics. ÐÐ¾Ð»ÑÑÐµÐ½Ñ Ð³ÑÐ°ÑÐ¸ÐºÐ¸ Ð´Ð¾Ð±ÑÐ¾ÑÐ½Ð¾ÑÑÐ¸ Ð¿ÑÐ¸ Ð²Ð°ÑÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð¸Ð¸ ÑÐ°Ð·Ð»Ð¸ÑÐ½ÑÑ Ð³ÐµÐ¾Ð¼ÐµÑÑÐ¸ÑÐµÑÐºÐ¸Ñ Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÐ¾Ð² ÑÐµÐ·Ð¾Ð½Ð°ÑÐ¾ÑÐ¾Ð² Ð¿ÑÐ¸ ÑÐ¾Ð²Ð¼ÐµÑÑÐ½Ð¾Ð¼ ÑÑÐµÑÐµ Ð°Ð½ÐºÐµÑÐ½Ð¾Ð¹ Ð¸ ÑÐµÑÐ¼Ð¾ÑÐ¿ÑÑÐ³Ð¾Ð¹ Ð´Ð¸ÑÑÐ¸Ð¿Ð°ÑÐ¸Ð¸.
description: This work is devoted to the study of the dissipation processes occurring in micromechanical beam resonators. The research set the following goals: 1. Research and analysis of analytical models of anchor and thermoelastic dissipation. 2. Numerical simulation of dissipation processes. 3. Processing of numerical results and their comparison with analytical solutions. 4. Exploring the properties of PML for problems with infinite domains. 5. Investigation of the total Q-factor values depending on the system parameters. In the course of the work, the properties of the Q-factor of vibrations of beam resonators were clearly demonstrated, depending on the geometric and temperature parameters of the system. Comparisons of analytical and numerical calculations of the Q-factor on the example of resonators of two types of bonds, depending on their parameters, are given. Numerical studies were carried out in the Comsol Multiphysics finite element analysis program. The Q-factor graphs are obtained for varying the various geometric parameters of the resonators with the joint account of the anchor and thermo-elastic dissipation.