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Вычисление характеристик гистерезисного трения в закритически сжатом элементе переменного поперечного сечения

Вычисление характеристик гистерезисного трения в закритически сжатом элементе переменного поперечного сечения

Abstract

Предложен метод вычисления коэффициента потерь в корректоре жесткости виброизолятора квазинулевой жесткости, предназначенного для виброизоляции высокоточного оборудования от низкочастотных колебаний основания. Корректор жесткости представляет собой балку переменного поперечного сечения с начальной кривизной, нагруженной в середине поперечной нагрузкой. Начальная кривизна балки определяется из решения задачи осевого деформирования балки переменного поперечного сечения при нагрузке, превышающей критическую эйлерову силу. Коэффициент потерь в материале корректора жесткости определяется в соответствии с энергетической теорией, разработанной Я.Г. Пановко. Для этих целей определяется форма упругой оси корректора жесткости, нагруженного поперечной силой, а также потенциальная энергия изгиба балки корректора, соответствующая этому состоянию. Путем деления приведенного коэффициента поглощения материала корректора жесткости на потенциальную энергию его изгиба определяется величина коэффициента потерь для различных типов поперечных сечений балок корректора. Для определения приведенного коэффициента потерь материала корректора жесткости проводятся опытные эксперименты, в которых путем аппроксимации виброграммы затухающих колебаний определяются коэффициенты аппроксимирующей функции.

The article focuses on calculating the loss factor in the stiffness corrector of quasi-zero stiffness vibration isolator, designed for precision equipment vibration isolation from low-frequency base vibrations. Stiffness corrector is a beam with a variable cross-section and an initial curvature loaded in the middle with the transverse load. The initial curvature of the beam is determined by solving the problem of the axial deformation of the beam of variable cross-section with an axial load exceeding the critical Euler force. The loss factor of the stiffness corrector’s material is determined in accordance with Panovko energy theory. For these purposes, the elastic shape of the stiffness corrector loaded with transverse force is calculated and potential energy of the corrector, which corresponds to the prescribed elastic shape, is obtained. Loss factor is calculated by dividing the absorption coefficient of the stiffness corrector material by its potential energy for various types of cross-sections of corrector’s beams. Determination of stiffness corrector’s material loss factor is performed through several experimental investigations, in which the coefficients of the approximating function are obtained via approximation of specimen of damped oscillations.

Keywords

ВИБРОИЗОЛЯЦИЯ,VIBRATION ISOLATION,КОЭФФИЦИЕНТ ПОТЕРЬ,LOSS FACTOR,СЖАТО-ИЗОГНУТЫЙ СТЕРЖЕНЬ,БОЛЬШИЕ ДЕФОРМАЦИИ,LARGE DEFORMATIONS,ГИСТЕРЕЗИСНОЕ ТРЕНИЕ,INTERNAL FRICTION,ВНУТРЕННИЕ ПОТЕРИ,РЕССОРНО-ПРУЖИННАЯ СТАЛЬ,SPRING STEEL,КОРРЕКТОР ЖЕСТКОСТИ,STIFFNESS CORRECTOR,ЭНЕРГЕТИЧЕСКАЯ ТЕОРИЯ,ENERGY THEORY,BEAM COLUMN,HYSTERESIS DAMPING

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
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