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

• Autorzy: Senjanović I. , Ćatipović I. , Alujević N. , Čakmak D. , Vladimir N.
• Języki publikacji: EN

Abstrakty

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.

Słowa kluczowe

EN

rotating ring; in-plane vibration; out-of-plane vibration; toroidal shell; analytical solution; bifurcations of natural frequencies

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Archives of Mechanics
• Rocznik: 2018
• Tom: Vol. 70, nr 5
• Strony: 429--455
• Opis fizyczny: Bibliogr. 30 poz., rys.

Twórcy

autor

Senjanović I.

• Faculty of Mechanical Engineering and Naval Architecture University of Zagreb Ivana Lučića 5 Zagreb, Croatia

autor

Ćatipović I.

• Faculty of Mechanical Engineering and Naval Architecture University of Zagreb Ivana Lučića 5 Zagreb, Croatia

autor

Alujević N.

• Faculty of Mechanical Engineering and Naval Architecture University of Zagreb Ivana Lučića 5 Zagreb, Croatia

autor

Čakmak D.

• Faculty of Mechanical Engineering and Naval Architecture University of Zagreb Ivana Lučića 5 Zagreb, Croatia

autor

Vladimir N.

• Faculty of Mechanical Engineering and Naval Architecture University of Zagreb Ivana Lučića 5 Zagreb, Croatia

Bibliografia

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Uwagi

PL

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