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Research Papers

Analysis of Dispersion Characteristics of an Infinite Cylindrical Shell Submerged in Viscous Fluids Considering Hydrostatic Pressure

[+] Author and Article Information
H. S. Chen

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

T. Y. Li

School of Naval Architecture
and Ocean Engineering,
Huazhong University of Science and Technology,
Wuhan 430074, China
e-mail: LTYZ801@mail.hust.edu.cn

X. Zhu

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

J. Yang

Department of Aerospace Engineering,
University of Bristol,
University Walk,
Bristol BS8 1TH, UK
e-mail: j.yang@bristol.ac.uk

J. J. Zhang

National Key Laboratory on Ship Vibration & Noise,
Wuhan 430064, China
e-mail: zhangjunjie0103@163.com

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received December 21, 2013; final manuscript received November 10, 2014; published online January 27, 2015. Assoc. Editor: Marco Amabili.

J. Vib. Acoust 137(2), 021018 (Apr 01, 2015) (14 pages) Paper No: VIB-13-1437; doi: 10.1115/1.4029114 History: Received December 21, 2013; Revised November 10, 2014; Online January 27, 2015

In previous investigations of the vibro-acoustic characteristics of a submerged cylindrical shell in a flow field, the fluid viscosity was usually ignored. In this paper, the effect of fluid viscosity on the vibrational dispersion characteristics of an infinite circular cylindrical shell immersed in a viscous acoustic medium and subject to hydrostatic pressure is studied. The Flügge's thin shell theory for an isotropic, elastic, and thin cylindrical shell is employed to obtain the equations of motion of the structure. Together with the wave equations for the viscous flow field as well as continuity conditions at the interface, the dispersion equation of the coupled system is derived. Numerical analysis based on a winding-number integral method is conducted to solve the dispersion equation for the shell loaded with viscous fluids with varying levels of viscosity. Then the variations of the dispersion characteristic, the amplitude ratio of complex waves and the relative difference parameter against the nondimensional axial wave number in the coupled system with different circumferential mode numbers are discussed in detail. It is found that the influence of fluid viscosity on dispersion characteristics of the propagating waves is more significant in the low-frequency range than at high frequencies. As for the complex waves, the amount of the waves in the coupled system and the cut-off frequency is dependant on the fluid viscosity coefficients.

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Figures

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Fig. 1

(a) Coordinate system and (b) circumferential mode shapes

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Fig. 2

Comparison between the calculation results and the literature values (n = 0, p0 = 0)

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Fig. 3

Dispersion characteristic curves with case 1: (a) n = 0, (b) n = 1, and (c) n = 5

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Fig. 4

Dispersion characteristic curves with case 2: (a) n = 0, (b) n = 1, and (c) n = 5

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Fig. 5

Dispersion characteristic curves with case 3: (a) n = 0, (b) n = 1, and (c) n = 5

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Fig. 6

Amplitude ratio curves of the complex waves with case 1: (a) n = 0, s = 4, (b) n = 1, s = 4, and s = 5, (c) n = 1, s = 6, (d) n = 5, s = 4, and s = 5, and (e) n = 5, s = 6, and s = 7

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Fig. 7

Amplitude ratio curves of the complex waves with case 2: (a) n = 0, s = 4, and s = 5, (b) n = 1, s = 4, and s = 5, (c) n = 1, s = 6, (d) n = 5, s = 4, and s = 5, and (e) n = 5, s = 6, and s = 7

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Fig. 8

Amplitude ratio curves of the complex waves with case 3: (a) n = 0, s = 4, and s = 5, (b) n = 0, s = 6, (c) n = 1, s = 4, and s = 5, (d) n = 1, s = 6, and s = 7, (e) n = 5, s = 4, and s = 5, and (f) n = 5, s = 6, and s = 7

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Fig. 9

Comparison of the dispersion characteristics in the coupled systems of ideal and viscous fluid: (a) n = 0 and (b) n = 1

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Fig. 10

The relative difference parameter curves between case 1 and case 2: (a) propagating waves, n = 0, (b) propagating waves, n = 1, s = 1, (c) propagating waves, n = 1, s = 2, and s = 3, (d) propagating waves, n = 5, (e) complex waves, n = 0, (f) complex waves, n = 1, and (g) complex waves, n = 5

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Fig. 11

The relative difference parameter curves between case 2 and case 3: (a) propagating waves, n = 0, (b) propagating waves, n = 1, s = 1, (c) propagating waves, n = 1, s = 2, and s = 3, (d) propagating waves, n = 5, s = 1, (e) propagating waves, n = 5, s = 2, and s = 3, (f) complex waves, n = 0, (g) complex waves, n = 1, s = 4, and s = 5, (h) complex waves, n = 1, s = 6, (i) complex waves, n = 5, s = 4, and s = 5, and (j) complex waves, n = 5, s = 6

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