title: ÐÐ¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð¸Ðµ Ð²Ð¾Ð·Ð¼Ð¾Ð¶Ð½ÑÑ Ð¿Ð¾Ð»Ð¾Ð¶ÐµÐ½Ð¸Ð¹ ÑÐ°Ð²Ð½Ð¾Ð²ÐµÑÐ¸Ñ Ð´Ð¸ÑÑÐµÑÐµÐ½ÑÐ¸Ð°Ð»ÑÐ½Ð¾Ð³Ð¾ Ð¼Ð¸ÐºÑÐ¾ÑÐµÐ·Ð¾Ð½Ð°ÑÐ¾ÑÐ° Ð¸ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ Ð¸Ñ ÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾ÑÑÐ¸
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: Determination of the equilibrium conditions of a differential microresonator and study of their stability
Creators: name: Ð®Ð³Ð¾Ð², Ð¡ÐµÑÐ³ÐµÐ¹
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: 2020
Subjects: Ð¼ÑÐ¼Ñ
Ð½ÑÐ¼Ñ
ÑÐµÐ·Ð¾Ð½Ð°ÑÐ¾Ñ
Ð´Ð¸ÑÑÐµÑÐµÐ½ÑÐ¸Ð°Ð»ÑÐ½ÑÐ¹ ÑÐµÐ·Ð¾Ð½Ð°ÑÐ¾Ñ
Ð¿Ð¾ÑÐµÐ½ÑÐ¸Ð°Ð»ÑÐ½Ð°Ñ ÑÐ½ÐµÑÐ³Ð¸Ñ
ÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾ÑÑÑ
Ð¾Ð±Ð»Ð°ÑÑÑ ÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾ÑÑÐ¸
Ð°Ð¼Ð¿Ð»Ð¸ÑÑÐ´Ð° ÐºÐ¾Ð»ÐµÐ±Ð°Ð½Ð¸Ð¹
mems
nems
resonator
differential resonator
potential energy
stability
sustainability area
amplitude of vibrations

description: Ð¢ÐµÐ¼Ð° Ð²ÑÐ¿ÑÑÐºÐ½Ð¾Ð¹ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð¾Ð¹ ÑÐ°Ð±Ð¾ÑÑ: Â«ÐÐ¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð¸Ðµ Ð²Ð¾Ð·Ð¼Ð¾Ð¶Ð½ÑÑ Ð¿Ð¾Ð»Ð¾Ð¶ÐµÐ½Ð¸Ð¹ ÑÐ°Ð²Ð½Ð¾Ð²ÐµÑÐ¸Ñ Ð´Ð¸ÑÑÐµÑÐµÐ½ÑÐ¸Ð°Ð»ÑÐ½Ð¾Ð³Ð¾ Ð¼Ð¸ÐºÑÐ¾ÑÐµÐ·Ð¾Ð½Ð°ÑÐ¾ÑÐ° Ð¸ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ Ð¸Ñ ÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾ÑÑÐ¸Â». ÐÐ°Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð° Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ Ð¾Ð±Ð»Ð°ÑÑÐ¸ Ð´Ð¾Ð¿ÑÑÑÐ¸Ð¼ÑÑ Ð°Ð¼Ð¿Ð»Ð¸ÑÑÐ´ ÐºÐ¾Ð»ÐµÐ±Ð°Ð½Ð¸Ð¹ Ð´Ð¸ÑÑÐµÑÐµÐ½ÑÐ¸Ð°Ð»ÑÐ½Ð¾Ð³Ð¾ ÑÐµÐ·Ð¾Ð½Ð°ÑÐ¾ÑÐ° Ð¿ÑÐ¸ Ð¸ÑÑÐ¾Ð´Ð½ÑÑ Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÐ°Ñ ÑÐ¸ÑÑÐµÐ¼Ñ Ð¸ Ñ Ð½ÐµÐ±Ð¾Ð»ÑÑÐ¸Ð¼Ð¸ Ð¾ÑÐºÐ»Ð¾Ð½ÐµÐ½Ð¸ÑÐ¼Ð¸. 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·Ð¾Ñ Ð¿ÑÐ¾Ð±Ð»ÐµÐ¼Ñ ÑÐ¾Ð·Ð´Ð°Ð½Ð¸Ñ ÐÐ­ÐÐ¡, ÑÐ¾Ð´ÐµÑÐ¶Ð°ÑÐ¸Ñ ÑÐµÐ·Ð¾Ð½Ð°ÑÐ¾ÑÑ. 2. ÐÐ·Ð½Ð°ÐºÐ¾Ð¼Ð»ÐµÐ½Ð¸Ðµ Ñ Ð¿ÑÐµÐ´Ð»Ð°Ð³Ð°ÐµÐ¼ÑÐ¼Ð¸ Ð² Ð»Ð¸ÑÐµÑÐ°ÑÑÑÐµ ÑÐ»ÐµÐºÑÑÐ¾Ð¼ÐµÑÐ°Ð½Ð¸ÑÐµÑÐºÐ¸Ð¼Ð¸ Ð¼Ð¾Ð´ÐµÐ»ÑÐ¼Ð¸ ÑÐµÐ·Ð¾Ð½Ð°ÑÐ¾ÑÐ¾Ð² Ð² Ð²Ð¸Ð´Ðµ ÑÐ¿ÑÑÐ³Ð¸Ñ ÑÐ»ÐµÐ¼ÐµÐ½ÑÐ¾Ð². 3. Ð¡Ð¾ÑÑÐ°Ð²Ð»ÐµÐ½Ð¸Ðµ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ð¹ Ð´Ð²Ð¸Ð¶ÐµÐ½Ð¸Ñ Ð´Ð¸ÑÑÐµÑÐµÐ½ÑÐ¸Ð°Ð»ÑÐ½Ð¾Ð³Ð¾ ÑÐµÐ·Ð¾Ð½Ð°ÑÐ¾ÑÐ°. 4. ÐÐ°ÑÐ¾Ð¶Ð´ÐµÐ½Ð¸Ðµ Ð²Ð¾Ð·Ð¼Ð¾Ð¶Ð½ÑÑ Ð¿Ð¾Ð»Ð¾Ð¶ÐµÐ½Ð¸Ð¹ ÑÐ°Ð²Ð½Ð¾Ð²ÐµÑÐ¸Ñ Ð¸ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ Ð¸Ñ ÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾ÑÑÐ¸ Ð¿ÑÐ¸ Ð¾ÑÐºÐ»Ð¾Ð½ÐµÐ½Ð¸ÑÑ Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÐ¾Ð² ÑÐ¸ÑÑÐµÐ¼Ñ Ð¾Ñ Ð½Ð¾Ð¼Ð¸Ð½Ð°Ð»ÑÐ½ÑÑ Ð·Ð½Ð°ÑÐµÐ½Ð¸Ð¹. ÐÑÐ»Ð¸ Ð¿ÑÐ¾Ð²ÐµÐ´ÐµÐ½Ñ Ð°Ð½Ð°Ð»Ð¸ÑÐ¸ÑÐµÑÐºÐ¸Ðµ Ð²ÑÐ²Ð¾Ð´Ñ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ð¹ ÑÐ°Ð²Ð½Ð¾Ð²ÐµÑÐ¸Ñ Ð¸ Ð¿Ð¾ÑÐµÐ½ÑÐ¸Ð°Ð»ÑÐ½Ð¾Ð¹ ÑÐ½ÐµÑÐ³Ð¸Ð¸. Ð Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð½Ð¾Ð¼ Ð¿Ð°ÐºÐµÑÐµ MATLAB Ð±ÑÐ»Ð° Ð¿Ð¾Ð»ÑÑÐµÐ½Ð° ÑÐ°ÑÐ¿ÑÐµÐ´ÐµÐ»Ð¸ÑÐµÐ»ÑÐ½Ð°Ñ Ð¿Ð¾Ð²ÐµÑÑÐ½Ð¾ÑÑÑ Ð¿Ð¾ÑÐµÐ½ÑÐ¸Ð°Ð»ÑÐ½Ð¾Ð¹ ÑÐ½ÐµÑÐ³Ð¸Ð¸. ÐÐ¾Ð»ÑÑÐµÐ½Ð½ÑÐµ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÑ Ð¼Ð¾Ð³ÑÑ Ð¿ÑÐ¸Ð¼ÐµÐ½ÑÑÑÑÑ Ð¿ÑÐ¸ Ð¿ÑÐ¾ÐµÐºÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð¸Ð¸ Ð´Ð¸ÑÑÐµÑÐµÐ½ÑÐ¸Ð°Ð»ÑÐ½ÑÑ ÑÐµÐ·Ð¾Ð½Ð°ÑÐ¾ÑÐ¾Ð².
description: The subject of the graduate qualification work is âDetermination of possible equilibrium positions of a differential microresonator and study of their stabilityâ. This work is devoted to the study of the range of allowable oscillation amplitudes of a differential resonator with initial parameters of the system and with small deviations. Tasks that were solved during the study: 1. Overview of the problem of creating MEMS containing resonators. 2. Familiarization with the proposed in the literature electromechanical models of resonators in the form of elastic elements. 3. Compilation of the equations of motion of the differential resonator. 4. Finding possible equilibrium positions and study their stability when the system parameters deviate from the nominal values. Analytical conclusions of the equations of equilibrium and potential energy were carried out. The distribution surface of potential energy was obtained in the MATLAB software package. The results can be applied in the design of differential resonators.