Simple approximate formulas for the natural frequencies of circular cylindrical shells are presented for modes in which transverse deflection dominates. Based on the Donnell-Mushtari thin shell theory the equations of motion of the circular cylindrical shell are introduced, using Vlasov assumptions and Fourier series for the circumferential direction, an exact solution in the axial direction is obtained. To improve the results assumptions of Vlasov’s semimomentless theory are enhanced, i.e. we have used only the hypothesis of middle surface inextensibility to obtain a solution in axial direction. Nonlinear characteristic equations and natural mode shapes, are derived for all type of boundary conditions. Good agreement with experimental data and FEM is shown and advantage over the existing formulas for a variety of boundary conditions is presented.
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ASME 2018 Pressure Vessels and Piping Conference
July 15–20, 2018
Prague, Czech Republic
Conference Sponsors:
- Pressure Vessels and Piping Division
ISBN:
978-0-7918-5171-5
PROCEEDINGS PAPER
Approximate Formulas for Cylindrical Shell Free Vibration Based on Vlasov’s and Enhanced Vlasov’s Semi-Momentless Theory Available to Purchase
Igor Orynyak,
Igor Orynyak
National Academy of Sciences of Ukraine, Kiev, Ukraine
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Yaroslav Dubyk
Yaroslav Dubyk
“IPP-CENTRE” Ltd., Kiev, Ukraine
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Igor Orynyak
National Academy of Sciences of Ukraine, Kiev, Ukraine
Yaroslav Dubyk
“IPP-CENTRE” Ltd., Kiev, Ukraine
Paper No:
PVP2018-84932, V008T08A050; 10 pages
Published Online:
October 26, 2018
Citation
Orynyak, I, & Dubyk, Y. "Approximate Formulas for Cylindrical Shell Free Vibration Based on Vlasov’s and Enhanced Vlasov’s Semi-Momentless Theory." Proceedings of the ASME 2018 Pressure Vessels and Piping Conference. Volume 8: Seismic Engineering. Prague, Czech Republic. July 15–20, 2018. V008T08A050. ASME. https://doi.org/10.1115/PVP2018-84932
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