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    Wyświetlanie 1-4 z 4
    Tytuł:
    Exact Analytical Solutions of Nonlinear Differential Equation of a Large Amplitude Simple Pendulum
    Autorzy:
    Sobamowo, M. G.
    Powiązania:
    https://bibliotekanauki.pl/articles/1030465.pdf
    Data publikacji:
    2020
    Wydawca:
    Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
    Tematy:
    Exact Analytical solution
    Large amplitude
    Oscillation system
    Strong nonlinearity
    Opis:
    The governing equation of large amplitude simple pendulum is a nonlinear equation which is very difficult to be solved exactly and analytically. However, the classical way for finding analytical solution is obviously still very much important. This is because an exact analytical solution serves as an accurate benchmark for numerical solution and provides a better insight into the significance of various system parameters affecting the phenomena than the numerical solution. Therefore, in this present work, exact analytical solutions for nonlinear differential equation of large amplitude simple pendulum is presented. Also, with the aid of the exact analytical solutions, parametric studies are carried out to study the effects of the model parameters on the dynamic behavior of the large-amplitude nonlinear oscillation system. The solutions can serve as benchmarks for the numerical solution or approximate analytical solution.
    Źródło:
    World Scientific News; 2020, 144; 70-88
    2392-2192
    Pojawia się w:
    World Scientific News
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Nonlinear Analysis of a Large-Amplitude Forced Harmonic Oscillation System using Differential Transformation Method-Padé Approximant Technique
    Autorzy:
    Sobamowo, M. G.
    Yinusa, A. A.
    Oyekeye, M. O.
    Folorunsho, S. S.
    Powiązania:
    https://bibliotekanauki.pl/articles/1031931.pdf
    Data publikacji:
    2020
    Wydawca:
    Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
    Tematy:
    Large amplitude; Oscillation system; Strong nonlinearity; Forced vibration; Differential transformation method-Padé approximant techniques
    Opis:
    This work presents the nonlinear analysis of forced harmonic oscillation system using differential transformation method-Padé approximant techniques. Without any series expansion of the included sine and cosine of the angular displacement in the nonlinear model of the system, an improved analytical solution of the dynamic model is presented. The high level of accuracy and validity of the analytical solutions obtained by the differential transformation method are shown through comparison of the results of the solution with the corresponding numerical solutions obtained by fourth-fifth-order Runge-Kutta method, homotopy perturbation method and energy balance methods. Also, with the aid of the analytical solutions, parametric studies are carried to study the impacts of the model parameters on the dynamic behavior of the large-amplitude nonlinear oscillation system. The method avoids any numerical complexity and it is very simple, suitable and useful as a mathematical tool for dealing the nonlinear problems.
    Źródło:
    World Scientific News; 2020, 140; 139-155
    2392-2192
    Pojawia się w:
    World Scientific News
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the Efficiency of Differential Transformation Method to the Solutions of Large Amplitude Nonlinear Oscillation Systems
    Autorzy:
    Sobamowo, M. G.
    Yinusa, A. A.
    Adeleye, O. A.
    Alozie, S. I.
    Salawu, S. A.
    Salami, M. O.
    Powiązania:
    https://bibliotekanauki.pl/articles/1031949.pdf
    Data publikacji:
    2020
    Wydawca:
    Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
    Tematy:
    Analytical solution
    Differential transformation method
    Large amplitude
    Oscillation system
    Strong nonlinearity
    Opis:
    In this work, the efficiency of differential transformation method to the solutions of large amplitude nonlinear oscillatory systems is further established. Two cases of oscillation systems, nonlinear plane pendulum and pendulum in a rotating plane are considered. Without any linearization, discretization or series expansion of the sine and cosine of the angular displacement in the nonlinear models of the systems, the differential transformation method with Padé approximant is used to provide analytical solutions to the nonlinear problems. Also, the increased predictive power and the high level of accuracy of the differential transformation method over the previous methods are presented. The extreme accuracy and validity of the analytical solutions obtained by the differential transformation method are shown through comparison of the results of the solution with the corresponding numerical solutions obtained by fourth-fifth-order Runge-Kutta method. Also, with the aid of the analytical solutions, parametric studies were carried to study the impacts of the model parameters on the dynamic behavior of the large-amplitude nonlinear oscillation system. The method avoids any numerical complexity and it is very simple, suitable and useful as a mathematical tool for dealing the nonlinear problems.
    Źródło:
    World Scientific News; 2020, 139, 1; 1-60
    2392-2192
    Pojawia się w:
    World Scientific News
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Thermoelastic strongly nonlinear vibration of rotating functionally graded ring plate
    Autorzy:
    Hu, Yu Da
    Bao, Hai Jun
    XU, Hao Ran
    Powiązania:
    https://bibliotekanauki.pl/articles/1839696.pdf
    Data publikacji:
    2021
    Wydawca:
    Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
    Tematy:
    functionally graded ring plate
    natural vibration
    rotational motion
    strong nonlinearity
    improved L-P method
    Opis:
    For a metal ceramic functionally graded (FGM) ring plate, considering variations in physical properties with temperature and a power-law distribution of material components along the thickness direction, thermoelastic coupled nonlinear vibration equation in thermal environment is derived by means of Kirchhoff’s thin plate theory and the Hamiltonian principle. The transverse nonlinear vibration differential equation of the inner and outside-clamped ring plate under static load is obtained by using the Galerkin method; moreover, perturbation solution of static deflection is carried out. An improved L-P method is employed to solve the strongly nonlinear vibration equation. The vibration response and nonlinear natural frequency expression are developed. Through numerical examples, natural frequency characteristic curves of the rotating FGM ring plate are plotted. The Runge Kutta method is applied to obtain vibration response, phase and power spectrum diagrams. The influence of different parameters on natural vibration characteristics is analyzed. The results show that analytical solutions are consistent with numerical solutions, and the natural frequency decreases with an increase in the metal content and surface temperature, but grows with an increase in the rotational speed.
    Źródło:
    Journal of Theoretical and Applied Mechanics; 2021, 59, 1; 157-171
    1429-2955
    Pojawia się w:
    Journal of Theoretical and Applied Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-4 z 4

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