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Research Papers

Free Vibration of a Fluid Loaded Ring-Stiffened Conical Shell With Variable Thickness

[+] Author and Article Information
Ming Liu

School of Naval Architecture
and Ocean Engineering,
Huazhong University of Science and Technology,
Wuhan 430074, China
e-mail: liu_ming_1@163.com

Jun Liu

School of Naval Architecture
and Ocean Engineering,
Huazhong University of Science and Technology,
Wuhan 430074, China
e-mail: hustlj@hust.edu.cn

Yuansheng Cheng

School of Naval Architecture
and Ocean Engineering,
Huazhong University of Science and Technology,
Wuhan 430074, China
e-mail: yscheng@hust.edu.cn

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received May 27, 2013; final manuscript received June 2, 2014; published online July 25, 2014. Assoc. Editor: Marco Amabili.

J. Vib. Acoust 136(5), 051003 (Jul 25, 2014) (10 pages) Paper No: VIB-13-1179; doi: 10.1115/1.4027804 History: Received May 27, 2013; Revised June 02, 2014

An analytical method is presented for the free vibration of a fluid loaded (submerged) ring-stiffened conical shell with variable thickness in the low frequency range. Based on the Flügge theory and equivalent method of ring-stiffeners, the governing equations of vibration of a ring-stiffened conical shell are developed in the form of a coupled set of the first order differential equations. Fluid loading is taken into account by dividing the shell into narrow strips which are considered to be locally cylindrical. Analytical solutions are presented by using the transfer matrix method, which is suitable for structures broken into a sequence of subsystems that interact only with adjacent subsystems. By comparing the results from the present method and the finite element model, good agreement are obtained. The effects of the spacing of the stiffeners, the shell thickness, the shell thickness ratio, the ring's height, and the boundary conditions on the natural frequencies of the fluid loaded ring-stiffened conical shell with variable thickness are discussed.

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Figures

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Fig. 3

Local cylindrical approximation of the conical shell

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Fig. 1

Conical shell and coordinate system

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Fig. 2

Section of the ring-stiffened conical shell with variable thickness

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Fig. 5

The Ansys model of the stiffened conical shell

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Fig. 6

The Ansys model of the water

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Fig. 4

Real solutions of the characteristic equation (h/R0 = 0.015, n = 1)

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Fig. 7

Effect of the fluid loading and the ring-stiffeners on the frequencies

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Fig. 8

Natural frequencies of fluid loaded ring-stiffened conical shell with variable thickness versus different shell thickness

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Fig. 9

Natural frequencies of fluid loaded ring-stiffened conical shell with variable thickness at different boundary conditions

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