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Известия РАН. Механика твердого тела, 2023, № 3, стр. 135-151

МОДЕЛЬ МИКРОМЕХАНИЧЕСКОГО МОДАЛЬНО-ЛОКАЛИЗОВАННОГО АКСЕЛЕРОМЕТРА С ЧУВСТВИТЕЛЬНЫМ ЭЛЕМЕНТОМ В ВИДЕ БАЛКИ С НАЧАЛЬНОЙ ПОГИБЬЮ

Д. А. Индейцев a, b, Н. В. Можгова b, *, А. В. Лукин b, **, И. А. Попов b, ***

a Институт проблем машиноведения Российской академии наук
Санкт-Петербург, Россия

b Санкт-Петербургский политехнический университет Петра Великого
Санкт-Петербург, Россия

* E-mail: nmojgova@yandex.ru
** E-mail: lukin_av@spbstu.ru
*** E-mail: popov_ia@spbstu.ru

Поступила в редакцию 19.08.2022
После доработки 07.09.2022
Принята к публикации 08.09.2022

Аннотация

Настоящее исследование посвящено математическому моделированию предложенной новой архитектуры микроэлектромеханического модально-локализованного датчика ускорений (МЭМС-акселерометра/гравиметра) с чувствительным элементом в виде защемленной с двух концов микробалки с начальной погибью, выполненной по форме первой несимметричной моды свободных колебаний. В работе показано, что при несимметричной форме начальной погиби в области положительных осевых усилий существуют зоны близости частотных ветвей, соответствующих второй симметричной и первой несимметричной формам колебаний. При конструкционном обеспечении требуемого значения осевого растягивающего усилия в микробалке этот эффект может быть использован, в частности, для измерения осевой компоненты переносного ускорения по принципу амплитудной модальной локализации. Предусмотренная в компоновке датчика возможность нагрева чувствительного элемента с помощью протекающего по микробалке электрического тока позволяет управлять рабочей точкой режима колебаний и, таким образом, в весьма широких пределах варьировать диапазон измеряемых ускорений и степень чувствительности датчика. Предложенная в статье конфигурация электродов возбуждения колебаний и съема выходного сигнала позволяет, с помощью контура обратной связи, стабилизировать на требуемом уровне амплитуду колебаний по рабочей (третьей) симметричной форме и, при этом, измерять связанную с изменением величины измеряемой компоненты переносного ускорения амплитуду колебаний по несимметричной форме. Таким образом, в работе предложена и исследована математическая модель оригинального модально-локализованного акселерометра (гравиметра), содержащего единственный чувствительный микробалочный элемент и задействующего эффект обмена энергией между различными его формами колебаний.

Ключевые слова: МЭМС, балка с начальной погибью, бистабильность, акселерометр, модальная локализация колебаний, близость частот

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