Analytical solutions for free oscillations of beams on nonlinear elastic foundations using the Variational Iteration Method

• Autorzy: Younesian D. , Saadatnia Z. , Askari H.

Warianty tytułu

PL

Analityczne rozwiązania problemu drgań swobodnych belek umieszczonych na sprężystym podłożu wyznaczone za pomocą iteracyjnej metody wariacyjnej

• Języki publikacji: EN

Abstrakty

EN

Closed form expressions are obtained for the dynamic response of an elastic beam rested on a nonlinear foundation in this paper. The nonlinear governing equation is solved using the Variational Iteration Method (VIM). An iteration formulation is constructed based on the VIM and the dynamic responses are then obtained. Frequency responses are presented in a closed form and their sensitivity with respect to the initial amplitudes are investigated. A number of numerical simulations are then carried out and performance and validity of the solution procedure is evaluated in the time domain. It is proved that the VIM is quite a reliable and straightforward technique to solve the corresponding set of coupled nonlinear differential equations.

PL

W pracy przedstawiono zamknięte formy rozwiązań opisujących odpowiedź dynamiczną elastycznej belki spoczywającej na nieliniowo sprężystym podłożu. Równanie ruchu rozwiązano przy pomocy iteracyjnej metody wariacyjnej (VIM). Sformułowanie iteracyjne skonstruowane w oparciu o tę metodę pozwoliło na wyznaczenie odpowiedzi dynamicznej belki. Charakterystyki częstościowe przedstawiono w zamkniętej formie i podkreślono ich wrażliwość na wartość amplitud początkowych. Następnie zaprezentowano wyniki kilku symulacji numerycznych w celu oszacowania wydajności i dokładności zastosowanej procedury rozwiązywania równań ruchu w dziedzinie czasu. Wykazano, że metoda VIM jest wystarczająco prosta i wiarygodna w rozwiązywaniu układu sprzężonych, nieliniowych równań różniczkowych.

Słowa kluczowe

EN

beam; nonlinear oscillation; variational iteration method; elastic foundation

• Wydawca: Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
• Czasopismo: Journal of Theoretical and Applied Mechanics
• Rocznik: 2012
• Tom: Vol. 50 nr 2
• Strony: 639--652
• Opis fizyczny: Bibliogr. 27 poz., rys., tab.

Twórcy

autor

Younesian D.

autor

Saadatnia Z.

autor

Askari H.

• Center of Excellence in Railway Transportation, School of Railway Engineering, Iran University of Science and Technology, Narmak, Tehran, Iran,

Bibliografia

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