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    Wyświetlanie 1-5 z 5
    Tytuł:
    Green’s function in frequency analysis of circular thin plates of variable thickness
    Autorzy:
    Żur, K. K.
    Powiązania:
    https://bibliotekanauki.pl/articles/280832.pdf
    Data publikacji:
    2015
    Wydawca:
    Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
    Tematy:
    circular plates
    Green's functions
    Neumann series
    Opis:
    Free vibration analysis of homogeneous and isotropic circular thin plates with variable distribution of parameters by using Green’s functions (solution to homogeneous ordinary differential equations with variable coefficients) is considered. The formula of Green’s function (called the influence function) depends on the Poisson ratio and the coefficient of distribution of plate flexural rigidity, and the thickness is obtained in a closed-form. The limited independent solutions to differential Euler equations are expanded in the Neumann power series using the Volterra integral equations of the second kind. This approach allows one to obtain the analytical frequency equations as the power series rapidly convergens to exact eigenvalues for different values of the power index and different values of the Poisson ratio. The six lower natural dimensionless frequencies of axisymmetric vibration of circular plates of constant and variable thickness are calculated for different boundary conditions. The obtained results are compared with selected results presented in the literature.
    Źródło:
    Journal of Theoretical and Applied Mechanics; 2015, 53, 4; 873-884
    1429-2955
    Pojawia się w:
    Journal of Theoretical and Applied Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Mathematical modeling of random diffusion flows in two-phase multilayered stochastically nonhomogeneous bodies
    Autorzy:
    Chaplya, Y.
    Chernukha, O.
    Davydok, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/1938615.pdf
    Data publikacji:
    2015
    Wydawca:
    Politechnika Gdańska
    Tematy:
    diffusion process
    mass flow
    random structure
    Neumann series
    averaging over the ensemble of phase configurations
    Opis:
    An approach for studying stochastical diffusion flows of admixture particles in bodies of multiphase randomly nonhomogeneous structures is proposed, according to which initialboundary value problems of diffusion are formulated for flow functions and methods of solution construction are adapted for the formulated problems. By this approach the admixture diffusion flow is investigated in a two-phase multilayered strip for the uniform distribution of phases under conditions of constant flow on the upper surface and zero concentration of admixture on the lower surface. An integro-differential equation equivalent to the original initial-boundary value problem is constructed. Its solution is found in terms of the Neumann series. Calculation formulae are obtained for the diffusion flow averaged over the ensemble of phase configurations under both zero and constant nonzero initial concentrations. Software is developed, a dependence of averaged diffusion flows on the medium characteristics is studied and general regularities of this process are established.
    Źródło:
    TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk; 2015, 19, 3; 297-320
    1428-6394
    Pojawia się w:
    TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Simulation of diffusion flows in two-phase multilayered stochastically nonhomogeneous bodies with non-uniform distribution of inclusions
    Autorzy:
    Chaplya, Y.
    Chernukha, O.
    Davydok, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/1938616.pdf
    Data publikacji:
    2015
    Wydawca:
    Politechnika Gdańska
    Tematy:
    diffusion process
    mass flow
    random structure
    Neumann series
    averaging over the ensemble of phase configurations
    beta distribution
    Opis:
    Admixture diffusion flows are investigated in two-phase randomly nonhomogeneous multilayered strips with non-uniform distributions of inclusions. Cases where the most probable disposition of layered inclusions is located near the body boundary on which the mass source acts in the neighborhood of another boundary and in the middle of the body are considered. The initial-boundary value problem is formulated for the function of random mass flow under conditions of a constant flow on the upper surface and zero concentration of the admixture on the lower surface. Calculation formulae are obtained for the diffusion flow averaged over the ensemble of phase configurations in the particular cases of beta-distribution at zero and nonzero initial concentrations. The dependences of the averaged admixture flows on medium characteristics are established. It is shown that if the admixture diffusion coefficient in inclusions is greater than in the matrix, consolidation of inclusions in the middle of the body leads to an increasing diffusion flow. Simulation of the averaged diffusion flows of the admixture in the multilayered strip is performed for different model variants of a probable disposition of phases in the body and their comparative analysis is carried out.
    Źródło:
    TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk; 2015, 19, 3; 321-351
    1428-6394
    Pojawia się w:
    TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Mathematical modeling of random concentracion field and its second moments in semispace with Erlangian distributions of layerd inclusions
    Autorzy:
    Chernukha, O.
    Bilushchak, Y.
    Powiązania:
    https://bibliotekanauki.pl/articles/1938608.pdf
    Data publikacji:
    2016
    Wydawca:
    Politechnika Gdańska
    Tematy:
    diffusion process
    randomly inhomogeneous stratified structure
    Erlangian distribution
    field dispersion
    correlation function
    Neumann series
    averaging over the ensemble of phase configurations
    Opis:
    The processes of admixture diffusion in a two-phase stratified semispace with random disposition of syblayers are studied by the approach where internal random nonhomogeneities are considered as inner sources and the solution is found in the form of a Neumann series. The diffusion equations are formulated for one-connected regions of each phase and non-ideal contact conditions for the concentration on interphases are imposed. By the theory of generalized functions the contact problem is reduced to the equation of mass transfer in the whole body, which operator includes explicitly jump discontinuities of the concentration function and its derivatives. The obtained initial-boundary value problem of mass transfer is reduced to the equivalent integro-differentual equation. The solution is constructed in the form of a Neumann series and averaged over the ensemble of phase configurations with Erlangian and exponential distributions of inclusions. Dispersion and the two-point correlation function of the concentration field for diffusion are determined taking into account the probable distribution of inclusions, pair interaction of sublayers and the function of phase correlation. The dependence of the behavior of the averaged admixture concentration, field dispersion and the correlation function in the semispace with Erlangian and exponential distributions of inclusions on different medium characteristics is investigated and established.
    Źródło:
    TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk; 2016, 20, 3; 295-334
    1428-6394
    Pojawia się w:
    TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Recovering a part of potential by partial information on spectra of boundary problems
    Autorzy:
    Pivovarchik, V.
    Powiązania:
    https://bibliotekanauki.pl/articles/255115.pdf
    Data publikacji:
    2005
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    sine-type function
    Lagrange interpolation series
    Dirichlet boundary value problem
    Dirichlet-Neumann boundary value problem
    Opis:
    Under additional conditions uniqueness of the solution is proved for the following problem. Given 1) the spectrum of the Dirichlet problem for the Sturm-Liouville equation on [0, a] with real potential q(x) mem L2(0, a), 2) a certain part of the spectrum of the Dirichlet problem for the same equation on [a/3, a] and 3) the potential on [0, a/3]. The aim is to find the potential on [a/3 ,a].
    Źródło:
    Opuscula Mathematica; 2005, 25, 1; 131-137
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-5 z 5

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