title: ÐÐ°ÑÐ°Ð¼ÐµÑÑÐ¸ÑÐµÑÐºÐ¾Ðµ Ð²Ð¾Ð·Ð±ÑÐ¶Ð´ÐµÐ½Ð¸Ðµ ÐºÐ¾Ð»ÐµÐ±Ð°Ð½Ð¸Ð¹ Ð² Ð¼Ð½Ð¾Ð³Ð¾Ð¼Ð°ÑÑÐ¾Ð²Ð¾Ð¼ ÑÐµÐ·Ð¾Ð½Ð°ÑÐ¾ÑÐµ Ñ ÐºÑÑÐ³Ð¾Ð²ÑÐ¼ ÑÐ°ÑÐ¿Ð¾Ð»Ð¾Ð¶ÐµÐ½Ð¸ÐµÐ¼ ÑÐ¿ÑÑÐ³Ð¸Ñ ÑÐ»ÐµÐ¼ÐµÐ½Ñ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: Parametric excitation of oscillations in a multi-mass resonator with a circular arrangement of elastic elements
Creators: name: ÐÐµÑÐ¼Ð°Ð½, Ð®ÑÐ¸Ð¹
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: 2024
Subjects: Ð¼Ð¸ÐºÑÐ¾ÑÐ»ÐµÐºÑÑÐ¾Ð¼ÐµÑ Ð°Ð½Ð¸ÑÐµÑÐºÐ¸Ðµ ÑÐµÐ·Ð¾Ð½Ð°ÑÐ¾ÑÑ
Ð¼ÐµÑÐ¾Ð´ ÐÐ°Ð»ÐµÑÐºÐ¸Ð½Ð°
Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÐ¸ÑÐµÑÐºÐ¸Ðµ ÐºÐ¾Ð»ÐµÐ±Ð°Ð½Ð¸Ñ
Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÐ¸ÑÐµÑÐºÐ¸Ð¹ ÑÐµÐ·Ð¾Ð½Ð°Ð½Ñ
ÑÐ¾Ð±ÑÑÐ²ÐµÐ½Ð½ÑÐµ ÑÐ¾ÑÐ¼Ñ
mems
Galerkin method
parametric oscillations
parametric resonance
eigen forms

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description: This work is devoted to the study of a mechanical resonator with a circular arrangement of elastic elements, which represents a relevant and significant task in the context of increasing the efficiency and reliability of such systems. 1. Drawing up an equation of motion taking into account the influence of longitudinal force. These equations take into account the influence of the longitudinal force that appears during heating by periodically acting electrical pulses. 2. Development of a model of a multi-mass resonator with a circular arrangement of elastic elements like strings on an elastic base. 3. Carrying out an analytical calculation of the natural frequencies of a string on an elastic foundation. 4. Carrying out an analytical calculation of the zones of possible buildup of parametric oscillations when heated by periodically acting electrical pulses. An analytical determination of the zones of possible buildup of parametric oscillations during heating by periodically acting electrical pulses was carried out. There are as many of these swing zones as there are natural frequencies of the system. At sufficiently large amplitudes of external influence, these zones intersect. This means that at certain frequencies of external influence, simultaneous excitation of several forms of oscillations is possible.