Free harmonic oscillations in systems with homogeneous elements

Popov, I. P.

doi:10.1016/j.jappmathmech.2012.09.005

Cited by 7 publications

(2 citation statements)

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“…Полученные результаты отличаются от описанных в [2] повышением строгости и достоверности определения фазы свободных гармо-нических колебаний грузов за счет составления и решения соответствующего дифференциального уравнения (8), а также существенным развитием представления о пространственной конфигурации осциллирующей системы за счет представления соответствующего графического материала. Отличие от работы [5] состоит в теоретическом обосновании возможности построения осциллирующей системы с произвольным числом колеблющихся грузов, что значительно расширяет область возможных технических приложений.…”

Section: для рассматриваемой плоской многомерной системы координат сп...unclassified

“…звестны двухмерные [1][2][3] и трехмерные [4,5] плоские монореактивные осцилляторы, в которых могут возникать свободные гармонические колебания [6][7][8]. Недостатком двухмерных является несбалансированность по силам, что может приводить к вредным побочным вибрационным эффектам.…”

Section: Introductionunclassified

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Modeling and Analysis of a Multidimensional Planar Monoreactive Oscillator

Popov,

Filkin,

Kharin

et al. 2023

Vestnik IzhGTU imeni M.T. Kalashnikova

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The work belongs to the field of mechanical engineering, namely: to oscillating mechanical systems. The relevance of the study is determined by the fact that fluctuations of inertial masses are found everywhere. In the field of construction and use of aviation and rocket technology, this topic is of particular importance. Like a three-dimensional plane coordinate system in the coordinate plane Z, a multidimensional system with n axes shifted relative to each other by angles can be considered. There is an arbitrary vector emanating from the origin. It is proved that the points which are the coordinates of the end of the vector in the coordinate system are the vertices of a regular polygon. The shape and dimensions of the polygon are not related to the coordinates of the vector i.e. are unchanged. The center of a regular polygon in all cases coincides with the middle of the vector. In the considered (idealized) case, the polygon, at the vertices of which there are oscillating weights of masses m, lies in the Z plane multi-piston mechanism. In the considered multidimensional plane monoreactive oscillator, free harmonic linear oscillations of loads can occur. In this case, only kinetic energy is involved in the energy exchange. There is no need for elastic elements. The oscillator does not have a fixed natural oscillation frequency. The frequency depends on the initial speeds and positions of the weights. A regular polygon makes a double rotation - around the point 0 and around the point r. At the same time, the loads carry out linear harmonic oscillations with amplitude R. The use of a crank-slider or crank-and-rod mechanism will allow organizing the parallel movement of goods.

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Section: для рассматриваемой плоской многомерной системы координат сп...unclassified

Section: Introductionunclassified

Modeling and Analysis of a Multidimensional Planar Monoreactive Oscillator

Popov,

Filkin,

Kharin

et al. 2023

Vestnik IzhGTU imeni M.T. Kalashnikova

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Calculation of Parameters of Mechanical Systems With Harmonic Vibration

Popov¹

2021

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Parallel and series connections of mechanical power consumers are considered. According to the known parameters of systems and the disturbing harmonic effect, the velocities of the elements of mechanical systems and the forces applied to them are algebraically determined. Attention is paid to resonant modes, incl. resonance of forces and resonance of speeds. The use of a symbolic (complex) description of mechanical systems with forced harmonic vibrations (in a steady state) made it possible to abandon the extremely cumbersome and laborious calculation algorithm associated with solving differential equations and replace it with simple and visual algebraic operations. Due to this, the calculation time is reduced significantly. Vector diagrams, not being a necessary component of the study of mechanical systems, are of significant methodological importance, since they show quantitative and phase relationships between the parameters of systems.

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CALCULATION OF PARAMETERS OF BRANCHED MECHANICAL SYSTEMS WITH HARMONIC VIBRATIONS. Continuation

Popov¹

2021

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Parallel-series and series-parallel connections of mechanical power consumers are considered. According to the known parameters of systems and the disturbing harmonic effect, the velocities of the elements of mechanical systems and the forces applied to them are algebraically determined. For the considered branched mechanical schemes, the classical methods based on solving second-order differential equations become many times more complicated and require solving systems of equations that reduce to higher-order differential equations. The use of a symbolic (complex) description of mechanical processes and systems makes it possible to use instead simple and compact algebraic methods, the complexity of which is ten times less. Vector diagrams, not being a necessary component of the study of mechanical systems, are of significant methodological importance, since they show quantitative and phase relationships between the parameters of systems.

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Free harmonic oscillations in systems with homogeneous elements

Cited by 7 publications

References 0 publications

Modeling and Analysis of a Multidimensional Planar Monoreactive Oscillator

Modeling and Analysis of a Multidimensional Planar Monoreactive Oscillator

Calculation of Parameters of Mechanical Systems With Harmonic Vibration

CALCULATION OF PARAMETERS OF BRANCHED MECHANICAL SYSTEMS WITH HARMONIC VIBRATIONS. Continuation

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