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Research Papers

Vibration Analysis for Rotating Ring-Stiffened Cylindrical Shells With Arbitrary Boundary Conditions

[+] Author and Article Information
Lun Liu

e-mail: lnhgdht@sina.com

Dengqing Cao

e-mail: dqcao@hit.edu.cn

Shupeng Sun

School of Astronautics,
Harbin Institute of Technology,
PO Box 137,
Harbin 150001, China

1Corresopnding author.

Contributed by the Design Engineering Division of ASME for publication in the Journal of Vibration and Acoustics. Manuscript received November 22, 2012; final manuscript received April 10, 2013; published online June 19, 2013. Assoc. Editor: Marco Amabili.

J. Vib. Acoust. 135(6), 061010 (Jun 19, 2013) (12 pages) Paper No: VIB-12-1325; doi: 10.1115/1.4024220 History: Received November 22, 2012; Revised April 10, 2013

The free vibration analysis of rotating ring-stiffened cylindrical shells with arbitrary boundary conditions is investigated by employing the Rayleigh–Ritz method. Six sets of characteristic orthogonal polynomials satisfying six classical boundary conditions are constructed directly by employing Gram–Schmidt procedure and then are employed to represent the general formulations for the displacements in any axial mode of free vibrations for shells. Employing those formulations during the Rayleigh–Ritz procedure and based on Sanders' shell theory, the eigenvalue equations related to rotating ring-stiffened cylindrical shells with various classical boundary conditions have been derived. To simulate more general boundaries, the concept of artificial springs is employed and the eigenvalue equations related to free vibration of shells under elastic boundary conditions are derived. By adjusting the stiffness of artificial springs, those equations can be used to investigate the vibrational characteristics of shells with arbitrary boundaries. By comparing with the available analytical results for the ring-stiffened cylindrical shells and the rotating shell without stiffeners, the method proposed in this paper is verified. Strong convergence is also observed from convergence study. Further, the effects of parameters, such as the stiffness of artificial springs, the rotating speed of the ring-stiffened shell, the number of ring stiffeners and the depth to width ratio of ring stiffeners, on the natural frequencies are studied.

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Figures

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Fig. 1

Geometry of the rotating ring-stiffened cylindrical shell

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Fig. 2

Artificial springs distributed on the two ends of the rotating ring-stiffened shell

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Fig. 3

Variation of the natural frequencies (Hz) with the circumferential wavenumber n

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Fig. 4

Effect of the nondimensional artificial stiffness on the natural frequencies (m = 1, n = 3): (a) and (b), backward wave; (c) and (d), forward wave; (a) and (c), k¯u=k¯ϑ=0; (b) and (d), k¯v=k¯w=100

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Fig. 5

Effect of the nondimensional artificial stiffness on the natural frequencies (m = 1, n = 6): (a) and (b), backward wave; (c) and (d), forward wave; (a) and (c), k¯u = k¯ϑ = 0; (b) and (d), k¯v = k¯w = 100

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Fig. 6

Variation of fundamental frequencies of the ring-stiffened cylindrical shell with the rotating speed for various boundary conditions

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Fig. 7

Variation of fundamental frequencies of the ring-stiffened cylindrical shell with the rotating speed for various ring stiffener depth to width ratio dr/br

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Fig. 8

Variation of fundamental frequencies of the ring-stiffened cylindrical shell with the rotating speed for various ring stiffener numbers Nr

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