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    Wyświetlanie 1-3 z 3
    Tytuł:
    Modified laplace based variational iteration method for the mechanical vibrations and its applications
    Autorzy:
    Rehman, Shahida
    Hussain, Akhtar
    Rahman, Jamshaid Ul
    Anjum, Naveed
    Munir, Taj
    Powiązania:
    https://bibliotekanauki.pl/articles/2106003.pdf
    Data publikacji:
    2022
    Wydawca:
    Politechnika Białostocka. Oficyna Wydawnicza Politechniki Białostockiej
    Tematy:
    variational iterative method
    nonlinear oscillator
    Laplace transform
    Opis:
    In this paper, we are putting forward the periodic solution of non-linear oscillators by means of variational iterative method (VIM) using Laplace transform. Here, we present a comparative study of the new technique based on Laplace transform and the previous tech-niques of maximum minimum approach (MMA) and amplitude frequency formulation (AFF) for the analytical results. For the non-linear oscillators, MMA, AFF and VIM by Laplace transform give the same analytical results. Comparison of analytical results of VIM by Laplace transform with numerical results by fourth-order Runge–Kutta (RK) method conforms the soundness of the method for solving non-linear oscillators as well as for the time and boundary conditions of the non-linear oscillators.
    Źródło:
    Acta Mechanica et Automatica; 2022, 16, 2; 98--102
    1898-4088
    2300-5319
    Pojawia się w:
    Acta Mechanica et Automatica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Numerical criterion for the duration of non-chaotic transients in ODEs
    Autorzy:
    Szczebiot, Ryszard
    Kaczyński, Roman
    Gołdyn, Leszek
    Powiązania:
    https://bibliotekanauki.pl/articles/2204683.pdf
    Data publikacji:
    2022
    Wydawca:
    Politechnika Białostocka. Oficyna Wydawnicza Politechniki Białostockiej
    Tematy:
    numerical criterion
    non-chaotic transients
    limit cycle
    ODEs systems
    Van der Pol oscillator
    Opis:
    The paper proposes an original numerical criterion for the duration analysis of non-chaotic transients based on the Euclidean norm of a properly defined vector. For this purpose, transient trajectories, prior to their entering a small neighbourhood of the limit cycle, are used. The vector has been defined with its components constituting the lengths of the sections, which connect the origin of the coordinate system with appropriately determined transient trajectory points. The norm of the vector for the analysis of non-chaotic transients has also been applied. As an assessment criterion of transients, the convergence of the norm to small neighbourhood of the limit cycle with the assumed accuracy is used. The paper also provides examples of the application of this criterion to the Van der Pol oscillators in the case of periodic oscillations.
    Źródło:
    Acta Mechanica et Automatica; 2022, 16, 4; 388--392
    1898-4088
    2300-5319
    Pojawia się w:
    Acta Mechanica et Automatica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Solutions of the nonlinear evolution problems and their applications
    Autorzy:
    Amir, Muhammad
    Haider, Jamil Abbas
    Rahman, Jamshaid Ul
    Ashraf, Asifa
    Powiązania:
    https://bibliotekanauki.pl/articles/2233663.pdf
    Data publikacji:
    2023
    Wydawca:
    Politechnika Białostocka. Oficyna Wydawnicza Politechniki Białostockiej
    Tematy:
    Laplace variational iteration method
    nonlinear problems
    duffing equation
    simple pendulum
    mass and spring oscillator
    Simulink
    Opis:
    In this article, a well-known technique, the variational iterative method with the Laplace transform, is used to solve nonlinear evolution problems of a simple pendulum and mass spring oscillator, which represents the duffing equation. In the variational iteration method (VIM), finding the Lagrange multiplier is an important step, and the variational theory is often used for this purpose. This paper shows how the Laplace transform can be used to find the multiplier in a simpler way. This method gives an easy approach for scientists and engineers who deal with a wide range of nonlinear problems. Duffing equation is solved by different analytic methods, but we tackle this for the first time to solve the duffing equation and the nonlinear oscillator by using the Laplace-based VIM. In the majority of cases, Laplace variational iteration method (LVIM) just needs one iteration to attain high accuracy of the answer for linearization anddiscretization, or intensive computational work is needed. The convergence criteria of this method are efficient as compared with the VIM. Comparing the analytical VIM by Laplace transform with MATLAB’s built-in command Simulink that confirms the method’s suitability for solving nonlinear evolution problems will be helpful. In future, we will be able to find the solution of highly nonlinear oscillators.
    Źródło:
    Acta Mechanica et Automatica; 2023, 17, 3; 357--363
    1898-4088
    2300-5319
    Pojawia się w:
    Acta Mechanica et Automatica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-3 z 3

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