Application of the homotopy analysis method for determining the free vibrations of beam

• Autorzy: Gromysz, K. , Słota, D.
• Języki publikacji: EN

Abstrakty

EN

In this paper we present the application of the homotopy analysis method for determining the free vibrations of the simply supported beam. The linear and nonlinear cases are considered. The homotopy analysis gives the possibility to search for the solution of a wide range of problems described by means of the operator equations. The numerical examples are presented to confirm the exactness and fast convergence of the introduced method. The presented computational examples confirm the precision and the fast convergence of investigated method. In the linear case we knew the exact solutions, so we could compare with them the solutions obtained with the aid of homotopy analysis method. Differences between the obtained solutions were slight. However, the advantage of the examined method is that we receive here the approximate solution in the form of continuous function which can be used then in a further analysis or to perform various simulations.

PL

W artykule przedstawiono homotopijną metodę analizy równań opisujących drgania swobodne układu o jednym stopniu swobody opisane równaniami liniowymi oraz nieliniowymi. Homotopijna metoda analizy daje możliwość poszukiwania rozwiązania szerokiego zakresu problemów opisanych za pomocą równań operatorowych. W artykule przedstawiono przykłady liczbowe w celu potwierdzenia dokładności i szybkiej zbieżności metody. W przypadku liniowym znane było dokładne rozwiązanie, dzięki czemu można było porównać je z rozwiązaniami uzyskanymi za pomocą analizy homotopijnej. Różnice między otrzymanymi roztworami były niewielkie. Zaletą badanej metody jest jednak to, że otrzymano przybliżone rozwiązania w postaci ciągłych funkcji, które można wykorzystać w dalszych analizach, w tym do interpretacji wyników badań doświadczalnych.

Słowa kluczowe

PL

analiza homotopijna; drgania swobodne; obciążenie udarowe

EN

homotopy analysis; free vibrations; impact load

• Czasopismo: Architecture Civil Engineering Environment
• Rocznik: 2018
• Tom: Vol. 11, no. 1
• Strony: 61--71
• Opis fizyczny: Bibliogr. 31 poz.

Twórcy

autor

Gromysz, K.

• Faculty of Civil Engineering, The Silesian University of Technology, Akademicka 5, 44-100 Gliwice, Poland,

autor

Słota, D.

• Faculty of Applied Mathematics, The Silesian University of Technology, Kaszubska 23, 44-100 Gliwice, Poland,

Bibliografia

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Uwagi

PL

Opracowanie w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018)

Identyfikatory

DOI

10.21307/ACEE-2018-006