Research Papers

Vibration Power Flow Analysis of a Submerged Constrained Layer Damping Cylindrical Shell

[+] Author and Article Information
Yun Wang

e-mail: wangyun07@mails.tsinghua.edu.cn

Gangtie Zheng

e-mail: gtzheng@mail.tsinghua.edu.cn
School of Aerospace,
Tsinghua University,
Beijing 100084, China

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received March 2, 2013; final manuscript received July 20, 2013; published online October 3, 2013. Assoc. Editor: Marco Amabili.

J. Vib. Acoust 136(1), 011005 (Oct 03, 2013) (14 pages) Paper No: VIB-13-1067; doi: 10.1115/1.4025443 History: Received March 02, 2013; Revised July 20, 2013

The vibration power flow in a submerged infinite constrained layer damping (CLD) cylindrical shell is studied in the present paper using the wave propagation approach. Dynamic equations of the shell are derived with the Hamilton principle in conjunction with the Donnell shell assumptions. Besides, the pressure field in the fluid is described by the Helmholtz equation and the damping characteristics are considered with the complex modulus method. Then, the shell-fluid coupling dynamic equations are obtained by using the coupling between the shell and the fluid. Vibration power flows inputted to the coupled system and transmitted along the shell axial direction are both studied. Results show that input power flow varies with driving frequency and circumferential mode order, and the constrained damping layer will restrict the exciting force inputting power flow into the shell, especially for a thicker viscoelastic layer, a thicker or stiffer constraining layer (CL), and a higher circumferential mode order. Cut-off frequencies do not exist in the CLD cylindrical shell, so that the exciting force can input power flow into the shell at any frequency and for any circumferential mode order. The power flow transmitted in the CLD cylindrical shell exhibits an exponential decay form along its axial direction, which indicates that the constrained damping layer has a good damping effect, especially at middle or high frequencies.

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Fig. 1

Configuration of viscoelastic damping structures

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Fig. 2

Cylindrical shell treated with constrained layer damping (CLD)

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Fig. 3

Integration contour

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Fig. 4

Nondimensional input power flow into a shell of different circumferential mode order n, constrained layer damping shell, bare shell

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Fig. 5

Influences of the viscoelastic layer thickness on the input power flow of different circumferential mode order n, hv = 0.25hs, hv = 0.5hs, hv = 0.75hs, hv = 1.0hs

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Fig. 6

Influences of the constraining layer (CL) thickness on the input power flow of differentcircumferential mode order n, hc = 0.125hs, hc = 0.25hs, hc = 0.375hs, hc = 0.5hs

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Fig. 7

Influences of the constraining layer (CL) stiffness on the input power flow of different circumferential mode order n, Ec = 50.0 GPa, Ec = 70.0 GPa, Ec = 100.0 GPa, Ec = 150.0 GPa

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Fig. 8

Power transmitted by the shell for n = 5. (a1)–(a3) bare shell; (b1)–(b3) constrained layer damping (CLD) shell, P¯xs, P¯Mxs, P¯Nxs, P¯Qxs, P¯Txs

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Fig. 9

Nondimensional input power flow into a shell of different circumferential mode order n, submerged in the water, in vacuo

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Fig. 10

Power transmitted by the shell for n = 5, (a1)–(a3) CLD shell submerged in the water; (b1)–(b3) CLD shell in vacuo, P¯xs, P¯Mxs, P¯Nxs, P¯Qxs, P¯Txs




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