title: ÐÐµÐ»Ð¸Ð½ÐµÐ¹Ð½Ð°Ñ Ð´Ð¸Ð½Ð°Ð¼Ð¸ÐºÐ° Ð¼Ð¾Ð´Ð°Ð»ÑÐ½Ð¾-Ð»Ð¾ÐºÐ°Ð»Ð¸Ð·Ð¾Ð²Ð°Ð½Ð½Ð¾Ð³Ð¾ ÐÐ­ÐÐ¡-Ð°ÐºÑÐµÐ»ÐµÑÐ¾Ð¼ÐµÑÑÐ° Ñ Ð´Ð²ÑÐ¼Ñ ÑÐ»ÐµÐºÑÑÐ¾ÑÑÐ°ÑÐ¸ÑÐµÑÐºÐ¸ ÑÐ²ÑÐ·Ð°Ð½Ð½ÑÐ¼Ð¸ Ð±Ð°Ð»Ð¾ÑÐ½ÑÐ¼Ð¸ ÑÑÐ²ÑÑÐ²Ð¸ÑÐµÐ»ÑÐ½ÑÐ¼Ð¸ ÑÐ»ÐµÐ¼ÐµÐ½ÑÐ°Ð¼Ð¸
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¼Ð°Ð³Ð¸ÑÑÑÐ°
titleType: Subtitle
title: Nonlinear dynamics of mode-localized MEMS accelerometer with two electrostatically coupled microbeam sensing elements
Creators: name: ÐÐ³ÑÐ¼Ð½Ð¾Ð²Ð°, ÐÐ°ÑÐ¸Ð»Ð¸ÑÐ°
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 ÐµÐ·Ð¾Ð½Ð°ÑÐ¾ÑÑ
ÐÐµÐ½ÐµÑÐ°ÑÐ¾ÑÑ
ÐÐ°ÑÑÐ¸ÐºÐ¸
ÐÐ­ÐÐ¡-Ð°ÐºÑÐµÐ»ÐµÑÐ¾Ð¼ÐµÑÑÑ
Ð¼Ð¾Ð´Ð°Ð»ÑÐ½Ð°Ñ Ð»Ð¾ÐºÐ°Ð»Ð¸Ð·Ð°ÑÐ¸Ñ
Ð½ÐµÐ»Ð¸Ð½ÐµÐ¹Ð½Ð°Ñ Ð´Ð¸Ð½Ð°Ð¼Ð¸ÐºÐ°
Ð±Ð¸ÑÑÑÐºÐ°ÑÐ¸Ð¾Ð½Ð½ÑÐµ Ð´Ð¸Ð³ÑÐ°Ð¼Ð¼Ñ
Ð´Ð¸Ð½Ð°Ð¼Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐµÐ¶Ð¸Ð¼ ÑÐ°Ð±Ð¾ÑÑ Ð² Ð¾ÑÐºÑÑÑÐ¾Ð¼ ÐºÐ¾Ð½ÑÑÑÐµ
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Ð°Ð¼Ð¿Ð»Ð¸ÑÑÐ´Ð¾-ÑÐ°ÑÑÐ¾ÑÐ½ÑÐµ Ñ Ð°ÑÐ°ÐºÑÐµÑÐ¸ÑÑÐ¸ÐºÐ¸
MEMS-accelerometers
modal localization
nonlinear dynamics
bifurcation diagrams
dynamic mode of operation in an open loop
multi-scale method
amplitude-frequency characteristics

description: ÐÐ°Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð° Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ ÑÐ²Ð»ÐµÐ½Ð¸Ñ Ð¼Ð¾Ð´Ð°Ð»ÑÐ½Ð¾Ð¹ Ð»Ð¾ÐºÐ°Ð»Ð¸Ð·Ð°ÑÐ¸Ð¸, ÐºÐ¾ÑÐ¾ÑÐ°Ñ Ð²Ð¾Ð·Ð½Ð¸ÐºÐ°ÐµÑ Ð² ÑÐ¸ÑÑÐµÐ¼Ð°Ñ Ñ ÑÐ»Ð°Ð±Ð¾Ð¹ ÑÐ²ÑÐ·ÑÑ Ð¼ÐµÐ¶Ð´Ñ ÑÑÐ²ÑÑÐ²Ð¸ÑÐµÐ»ÑÐ½ÑÐ¼Ð¸ ÑÐ»ÐµÐ¼ÐµÐ½ÑÐ°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ÑÐ²Ð¾Ð´ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ð¹ Ð´Ð²Ð¸Ð¶ÐµÐ½Ð¸Ñ Ð¼Ð¸ÐºÑÐ¾Ð±Ð°Ð»Ð¾ÑÐ½ÑÑ ÑÑÐ²ÑÑÐ²Ð¸ÑÐµÐ»ÑÐ½ÑÑ ÑÐ»ÐµÐ¼ÐµÐ½ÑÐ¾Ð². 2. ÐÐ¾Ð»ÑÑÐµÐ½Ñ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ñ ÑÑÐ°ÑÐ¸ÐºÐ¸ Ð¸ Ð¿Ð¾ÑÑÑÐ¾ÐµÐ½Ñ Ð±Ð¸ÑÑÑÐºÐ°ÑÐ¸Ð¾Ð½Ð½ÑÐµ Ð´Ð¸Ð°Ð³ÑÐ°Ð¼Ð¼Ñ. 3. Ð Ð¿Ð¾ÑÑÐ°Ð½Ð¾Ð²ÐºÐµ ÑÐ²Ð¾Ð±Ð¾Ð´Ð½ÑÑ ÐºÐ¾Ð»ÐµÐ±Ð°Ð½Ð¸Ð¹ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ñ ÑÐ¿ÐµÐºÑÑÐ°Ð»ÑÐ½ÑÐµ ÑÐ²Ð¾Ð¹ÑÑÐ²Ð° ÑÐ¸ÑÑÐµÐ¼Ñ, Ð° ÑÐ°ÐºÐ¶Ðµ Ð¾ÑÐµÐ½ÐµÐ½Ð° ÑÑÐ²ÑÑÐ²Ð¸ÑÐµÐ»ÑÐ½Ð¾ÑÑÑ Ð´Ð°ÑÑÐ¸ÐºÐ° ÑÑÐºÐ¾ÑÐµÐ½Ð¸Ñ. 4. Ð Ð°ÑÑÐ¼Ð¾ÑÑÐµÐ½Ñ Ð²ÑÐ½ÑÐ¶Ð´ÐµÐ½Ð½ÑÐµ ÐºÐ¾Ð»ÐµÐ±Ð°Ð½Ð¸Ñ ÑÐµÐ·Ð¾Ð½Ð°ÑÐ¾ÑÐ¾Ð², Ð²Ð¾Ð·Ð±ÑÐ¶Ð´ÑÐ½Ð½ÑÐµ Ð¾Ñ Ð²Ð½ÐµÑÐ½ÐµÐ³Ð¾ Ð³ÐµÐ½ÐµÑÐ°ÑÐ¾ÑÐ°, Ð¿Ð¾Ð»ÑÑÐµÐ½Ñ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ñ Ð´Ð²Ð¸Ð¶ÐµÐ½Ð¸Ñ Ð² Ð¼ÐµÐ´Ð»ÐµÐ½Ð½ÑÑ Ð¿ÐµÑÐµÐ¼ÐµÐ½Ð½ÑÑ Ñ Ð¿Ð¾Ð¼Ð¾ÑÑÑ Ð¼ÐµÑÐ¾Ð´Ð° Ð¼Ð½Ð¾Ð³Ð¸Ñ Ð¼Ð°ÑÑÑÐ°Ð±Ð¾Ð². 5. ÐÐ¾ÑÑÑÐ¾ÐµÐ½Ñ Ð°Ð¼Ð¿Ð»Ð¸ÑÑÐ´Ð½Ð¾-ÑÐ°ÑÑÐ¾ÑÐ½ÑÐµ ÑÐ°ÑÐ°ÐºÑÐµÑÐ¸ÑÑÐ¸ÐºÐ¸ Ð´Ð°ÑÑÐ¸ÐºÐ° Ð¿ÑÐ¸ Ð²Ð°ÑÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð¸Ð¸ Ð¾ÑÐ½Ð¾Ð²Ð½ÑÑ Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÐ¾Ð² ÑÐ¸ÑÑÐµÐ¼Ñ. 6. ÐÑÐ¾Ð²ÐµÐ´ÐµÐ½Ð¾ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ðµ Ð¾ÑÐ½Ð¾ÑÐµÐ½Ð¸Ñ Ð°Ð¼Ð¿Ð»Ð¸ÑÑÐ´ Ð´Ð²ÑÑ ÑÐµÐ·Ð¾Ð½Ð°ÑÐ¾ÑÐ¾Ð² Ð´Ð»Ñ Ð¼Ð¾Ð´ÐµÐ»Ð¸, Ð¾Ð¿Ð¸ÑÑÐ²Ð°ÑÑÐµÐ¹ Ð¼Ð¾Ð´Ð°Ð»ÑÐ½ÑÐµ ÑÐ°ÑÐ°ÐºÑÐµÑÐ¸ÑÑÐ¸ÐºÐ¸ ÑÐ¸ÑÑÐµÐ¼Ñ, Ð¸ Ð¼Ð¾Ð´ÐµÐ»Ð¸, Ð¾Ð¿Ð¸ÑÑÐ²Ð°ÑÑÐµÐ¹ ÑÐµÐ°Ð»ÑÐ½ÑÐ¹ Ð´Ð¸Ð½Ð°Ð¼Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐµÐ¶Ð¸Ð¼ ÑÐ°Ð±Ð¾ÑÑ Ñ ÑÑÐµÑÐ¾Ð¼ Ð½ÐµÐ»Ð¸Ð½ÐµÐ¹Ð½ÑÑ ÑÐ°ÐºÑÐ¾ÑÐ¾Ð² Ð¾Ñ Ð²ÐµÐ»Ð¸ÑÐ¸Ð½Ñ Ð¾ÑÐµÐ²Ð¾Ð¹ Ð¸Ð½ÐµÑÑÐ¸Ð¾Ð½Ð½Ð¾Ð¹ ÑÐ¸Ð»Ñ.
description: This work is devoted to the study of the phenomenon of modal localization, which occurs in systems with weak coupling between sensitive elements. The research set the following goals: 1. Derivation of equations of motion of microbeam sensing elements. 2. Equations of statics are obtained and bifurcation diagrams are constructed. 3. In the formulation of free vibrations, the spectral properties of the system are investigated, and the sensitivity of the acceleration sensor is estimated. 4. Forced oscillations of resonators excited by an external generator are considered, equations of motion in slow variables are obtained using the method of many scales. 5. Amplitude-frequency characteristics of the sensor are constructed when the main parameters of the system are varied. 6. A comparison is made of the ratio of the amplitudes of the two resonators for the model describing the modal characteristics of the system and the model describing the real dynamic mode of operation, taking into account nonlinear factors from the value of the axial inertial force.