15 research outputs found

    Finite difference approximation of eigenvibrations of a bar with oscillator

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    The second-order ordinary differential spectral problem governing eigenvibrations of a bar with attached harmonic oscillator is investigated. We study existence and properties of eigensolutions of formulated bar-oscillator spectral problem. The original second-order ordinary differential spectral problem is approximated by the finite difference mesh scheme. Theoretical error estimates for approximate eigenvalues and eigenfunctions of this mesh scheme are established. Obtained theoretical results are illustrated by computations for a model problem with constant coefficients. Theoretical and experimental results of this paper can be developed and generalized for the problems on eigenvibrations of complex mechanical constructions with systems of harmonic oscillators

    Eigenvibrations of a beam with two mechanical resonators attached to the ends

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    The fourth-order ordinary differential spectral problem describing vertical eigenvibrations of a beam with two mechanical resonators attached to the ends is studied. This problem has positive simple eigenvalues and corresponding eigenfunctions. We define limit differential spectral problem and establish the convergence of the eigenvalues and eigenfunctions of the original spectral problem to the eigenvalues and eigenfunctions of the limit spectral problem as parameters of the attached resonators tending to infinity. The initial fourth-order ordinary differential spectral problem is approximated by the finite difference method. Theoretical error estimates for approximate eigenvalues and eigenfunctions are derived. Obtained theoretical results are illustrated by computations for model problem with constant coefficients. Theoretical and experimental results of this paper can be developed for the problems on eigenvibrations of complex mechanical constructions with systems of resonators

    Eigenvibrations of a beam with two mechanical resonators attached to the ends

    No full text
    The fourth-order ordinary differential spectral problem describing vertical eigenvibrations of a beam with two mechanical resonators attached to the ends is studied. This problem has positive simple eigenvalues and corresponding eigenfunctions. We define limit differential spectral problem and establish the convergence of the eigenvalues and eigenfunctions of the original spectral problem to the eigenvalues and eigenfunctions of the limit spectral problem as parameters of the attached resonators tending to infinity. The initial fourth-order ordinary differential spectral problem is approximated by the finite difference method. Theoretical error estimates for approximate eigenvalues and eigenfunctions are derived. Obtained theoretical results are illustrated by computations for model problem with constant coefficients. Theoretical and experimental results of this paper can be developed for the problems on eigenvibrations of complex mechanical constructions with systems of resonators

    Finite difference approximation of eigenvibrations of a bar with oscillator

    Get PDF
    The second-order ordinary differential spectral problem governing eigenvibrations of a bar with attached harmonic oscillator is investigated. We study existence and properties of eigensolutions of formulated bar-oscillator spectral problem. The original second-order ordinary differential spectral problem is approximated by the finite difference mesh scheme. Theoretical error estimates for approximate eigenvalues and eigenfunctions of this mesh scheme are established. Obtained theoretical results are illustrated by computations for a model problem with constant coefficients. Theoretical and experimental results of this paper can be developed and generalized for the problems on eigenvibrations of complex mechanical constructions with systems of harmonic oscillators

    Фізіологічні властивості СО2 – обґрунтування унікальності карбокситерапії

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    CO2 due to the optimal mechanism of maintaining of its reserve is a universal condition for the existence of thebody. A physiological concentration of CO2 in the cells is an absolutely necessary condition for normal course ofbiochemical processes. CO2 is a natural regulator of respiration, blood circulation, metabolism, electrolyte balance,acid-base balance, the excitability of nerve cells, smooth muscle tone. Physiological properties provide CO2 diverselocal and resorptive effects, due to this carboxytherapy has become an effective and safe method of treatment inmany areas of medicine.СО 2, благодаря оптимальным механизмам поддержания его резерва, является универсальным усло-вием существования организма. Физиологическая концентрация CO2 в клетках – абсолютно необходимоеусловие нормального протекания всех биохимических процессов. CO2 является естественным регуля-тором дыхания, кровообращения, обмена веществ, электролитного баланса, кислотно-щелочногоравновесия, возбудимости нервных клеток, тонуса гладкой мускулатуры. Физиологические свойства СО 2обеспечивают многообразные локальные и резорбтивные эффекты, благодаря чему карбокситерапиястала эффективным и безопасным методом лечения во многих областях медицины.СО 2, завдяки оптимальним механізмам підтримки його резерву, є універсальною умовою існуванняорганізму. Фізіологічна концентрація CO2 в клітинах – абсолютно необхідна умова нормального перебігувсіх біохімічних процесів. CO2 є природним регулятором дихання, кровообігу, обміну речовин, електролітногобалансу, кислотно-лужної рівноваги, збудливості нервових клітин, тонусу гладкої мускулатури. Фізіологічнівластивості СО 2 забезпечують різноманітні локальні та резорбтивні ефекти, завдяки чому карбокситерапіястала ефективним і безпечним методом лікування в багатьох галузях медицини
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