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    Wyświetlanie 1-4 z 4
    Tytuł:
    Vibrations of microstructured beams with axial force
    Autorzy:
    Jędrysiak, Jarosław
    Powiązania:
    https://bibliotekanauki.pl/articles/2146554.pdf
    Data publikacji:
    2020
    Wydawca:
    Politechnika Poznańska. Instytut Mechaniki Stosowanej
    Tematy:
    microstructured periodic beams
    slender beams
    effect of microstructure
    tolerance modelling
    belka o strukturze periodycznej
    belka smukła
    efekt mikrostruktury
    modelowanie tolerancyjne
    Opis:
    In this contribution there are considered vibrations of microstructured periodic slender beams, with axial force. In order to analyse the effect of the microstructure size of the beams on their vibrations the tolerance modelling method is applied. Using this method there are derived governing equations of two tolerance models - general and standard, base on two various concepts - weakly-slowly-varying functions and slowly-varying functions. These models are applied to obtain formulas of lower order and higher order frequencies with influence of the axial force. To evaluate these results of the modelling the formula of lower order frequencies in the framework of the asymptotic model (neglecting the effect of the microstructure size) is also derived.
    Źródło:
    Vibrations in Physical Systems; 2020, 31, 2; art. no. 2020208
    0860-6897
    Pojawia się w:
    Vibrations in Physical Systems
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    An analytical-numerical approach to analysis of large amplitude vibrations of slender periodic beams
    Autorzy:
    Domagalski, Ł.
    Powiązania:
    https://bibliotekanauki.pl/articles/127691.pdf
    Data publikacji:
    2016
    Wydawca:
    Politechnika Poznańska. Instytut Mechaniki Stosowanej
    Tematy:
    nonlinear vibrations
    periodic beams
    averaging
    tolerance modelling
    drgania nieliniowe
    belka o strukturze periodycznej
    uśrednianie
    modelowanie tolerancyjne
    Opis:
    The paper is devoted to analysis of geometrically nonlinear vibrations of beams with geometric and material properties periodically varying along the axis. The 1-D Euler-Bernoulli theory of beams with von Kármán nonlinearity is applied. An analytical-numerical model based on non-asymptotic tolerance modelling approach and Galerkin method is applied. The linear natural frequencies and mode shapes are determined and the results are confirmed by comparison with a finite element model. Forced damped vibrations analysis in the large deflection range is performed to illustrate complex behaviour of the system.
    Źródło:
    Vibrations in Physical Systems; 2016, 27; 99-106
    0860-6897
    Pojawia się w:
    Vibrations in Physical Systems
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The use of the surface location approach in the modeling of periodically nonhomogeneous slender visco-elastic beams
    Wykorzystanie metody lokalizacji powierzchniowej w modelowaniu cienkich belek lepkosprężystych
    Autorzy:
    Kula, D.
    Powiązania:
    https://bibliotekanauki.pl/articles/2084055.pdf
    Data publikacji:
    2021
    Wydawca:
    Szkoła Główna Gospodarstwa Wiejskiego w Warszawie. Wydawnictwo Szkoły Głównej Gospodarstwa Wiejskiego w Warszawie
    Tematy:
    periodically nonhomogeneous beams
    tolerance modeling
    Fourier expansion
    Opis:
    The aim of the study is to develop an analytical reformulation the known theory for thin periodically nonhomogeneous viscoelastic beams, which should to form the basis for the planned research of the full beam dispersion relation. The methodology applied in the paper is similar to that described in paper Tolerance Modelling of Vibrations and Stability for Periodic Slender Visco-Elastic Beams on a Foundation will Damping. Revisiting by Jarosław Jędrysiak, published in scientific journal “Materials” in 2020, but it differs in the way of the use of tolerance modeling in the beam theory. The mathematical tool of considerations is a special choice of the micro-macro decomposition of the beam deflection. It is based on a certain regularization of the displacement field (in the small neighborhood of discontinuity surfaces) and results a certain reformulations of the classical beams theory. Obtained model equations is an alternative proposal for model equations obtained in mentioned paper by Professor Jędrysiak as a certain approximation for periodically nonhomogeneous viscoelastic beams theory as a result of the original tolerance modeling developed. The standardization of the beam deflection field proposed in the presented paper allows us to use the infinite Fourier expansion for deflection field in any region occupied by a homogeneous periodic composite material, which can be modeled in a typical way using the virtual work principle for commonly used beam constrains. The deflection field of the beam is written in the form of an infinite Fourier series, using periodically distributed region of material homogeneity of the beam. Applied method can be viewed as an attempt to use an infinite number of shape functions in the tolerance modeling but at the same time as an equivalent reformulation of the equations of the beam vibration theory. The obtained system of equations is an infinite system of ordinary differential equations for infinitely many Fourier coefficients in the mentioned Fourier expansion of the beam deflection field with respect to the base described in the surface location method.
    Źródło:
    Acta Scientiarum Polonorum. Architectura; 2021, 20, 3; 19-25
    1644-0633
    Pojawia się w:
    Acta Scientiarum Polonorum. Architectura
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Nonlinear vibrations of a slender beam interacting with a periodic viscoelastic subsoil
    Autorzy:
    Świątek, M.
    Jędrysiak, J.
    Domagalski, Ł.
    Powiązania:
    https://bibliotekanauki.pl/articles/127930.pdf
    Data publikacji:
    2018
    Wydawca:
    Politechnika Poznańska. Instytut Mechaniki Stosowanej
    Tematy:
    periodic beams
    Euler-Bernoulli beam
    belka o strukturze periodycznej
    belka Bernoulliego-Eulera
    Opis:
    The paper describes nonlinear vibrations of Euler-Bernoulli beams interacting with a periodic viscoelastic foundation. The original model equations with highly oscillating periodic coefficients are transformed using the tolerance modelling technique. Newly delivered equations have constant coefficients and describe macro-dynamics of the beam including the effect of the microstructure size. The main purpose of this paper is to propose an equivalent approximate model describing the nonlinear vibrations of a beam interacting with a periodic viscoelastic subsoil.
    Źródło:
    Vibrations in Physical Systems; 2018, 29; 1-9
    0860-6897
    Pojawia się w:
    Vibrations in Physical Systems
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-4 z 4

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