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Free in-plane and out-of-plane vibrations of rotating thin ring based on the toroidal shell theory

Senjanović I., Ćatipović I., Alujević N., Čakmak D., Vladimir N.

Archives of Mechanics

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2018

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Vol. 70, nr 5

429--455

EN

In this paper rigorous formulae for natural frequencies of in-plane and out-of-plane free vibrations of a rotating ring are derived. An in-plane vibration mode of the ring is characterised by coupled flexural and extensional deformations, whereas an out-of-plane mode is distinguished by coupled flexural and torsional deformations. The expressions for natural frequencies are derived from a generalised toroidal shell theory. For the in-plane vibrations, the ring is considered to be a short top segment of a toroidal shell. For the out-of-plane vibrations, the ring is considered to be a side segment of the shell. Natural vibrations are analysed by the energy approach. The expressions for the ring strain and kinetic energies are deduced from the corresponding expressions for the torus. It is shown that the ring rotation causes bifurcation of natural frequencies of the in-plane vibrations only. Bifurcation of natural frequencies of the out-of-plane vibrations does not occur. Otherwise, for non-rotating rings, the derived formulae for the natural frequencies of the in-plane and the out-of-plane flexural vibrations are very similar. The derived analytical results are validated by a comparison with FEM and FSM (Finite Strip Method) results, as well as with experimental results available in the literature.

2

Vibration analysis of a thick ring interacting with the disk treated as an elastic foundation

Noga S., Markowski T.

Vibrations in Physical Systems

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2014

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Vol. 26

217--222

EN

In this study the in plane flexural vibration of a thick ring interacting with Winkler foundation is analysed on the basis of the analytical and numerical method. The effect of rotary inertia and shear deformation is included. The normal frequencies and natural mode shapes of the system vibration are determined. Achieved results are discussed and compared with an experimental data. FE models are formulated by using ANSYS code.

3

Natural frequencies of flexural vibration of a ring with wheel–plate as the Winkler elastic foundation

Noga S, Markowski T, Bogacz R

Symulacja w Badaniach i Rozwoju

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2012

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Vol. 3, nr 1

39--46

EN

In this work the in plane flexural vibration of a circular ring with wheel–plate as a foundation of the Winkler type is studied on the basis of the analytical method and numerical simulation. To begin with the free vibration of the system is described by partial differential equations. The effect of rotary inertia and shear deformation is taken into account. The general solution of the analyzed problem is derived by the separation of variable method. Then the solution by using finite element method is received. The obtained results of calculation are discussed and compared for these solutions. FE models are formulated by using ANSYS software.

PL

W pracy analizowane są drgania własne giętne pierścienia kołowego współpracującego z tarczą modelowaną warstwą sprężystą typu Winklera. Prezentowane modele matematyczne układu opracowano na podstawie klasycznej teorii drgań giętnych pierścieni oraz metody elementów skończonych. W modelu ścisłym uwzględniono wpływ bezwładności obrotowej i odkształcenia postaciowego. Analityczne rozwiązanie drgań własnych układu otrzymano stosując metodę rozdzielenia zmiennych. Otrzymane rezultaty (częstości własne i odpowiadające im formy własne) porównano z rezultatami otrzymanymi z metody elementów skończonych. Obliczenia MES wykonano w programie ANSYS.