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2 Vibrations in Physical Systems

2 Noga S.

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Free vibrations of an annular membrane attached to Winkler foundation

Noga S.

Vibrations in Physical Systems

2010

Vol. 24

295--300

In this study the free transverse vibration analysis of the annular membrane resting on elastic foundation with fixed boundary conditions at the inner and outer edges of the annular membrane is presented on the basis of the analytical method and numerical simulation. The elastic foundation is described by the Winkler model. At first the general solution of the free vibrations are derived by the Bernoulli – Fourier method. The natural frequencies and natural mode shapes of vibrations of system under consideration are determined. Then the model of the system formulated by using finite element representations is prepared and eigenvalue problem is solved. Obtained results of calculation are discussed and compared for these two models. It is important to note that the data presented in the paper is brought the practical advice to design engineers.

W pracy analizowane są drgania własne poprzeczne membrany pierścieniowej osadzonej na podłożu sprężystym typu Winklera. Prezentowane modele matematyczne układu opracowano w oparciu o klasyczną teorię drgań membran pierścieniowych oraz metodę elementów skończonych. Rozwiązanie ścisłe drgań własnych układu wyprowadzono stosując metodę Bernoulliego – Fouriera (metoda rozdzielenia zmiennych). Uzyskane z rozwiązania ścisłego wyniki (częstości własne i odpowiadające im formy własne) porównano z rezultatami otrzymanymi z metody elementów skończonych.

Free transverse vibration analysis of an annular membrane

Noga S.

Vibrations in Physical Systems

2008

Vol. 23

283--288

In the paper, transversal vibration of an annular membrane is studied using analytical methods and numerical simulation. The two mathematical models are analysed. The first model is treated as a continuous system. The general solution of the free vibrations are derived by the Bernoulli-Fourier method and the boundary problem is solved. The second model is formulated by using finite element representations. The natural frequencies and natural mode shapes of vibration of membrane are determined. The FE model is manually tuned to reduce the difference between the natural frequencies of the tuned and continuous models, respectively. It is important to note that the data presented in the paper is brought the practical advice to design engineers.