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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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References

Teng, T. L., and Hu, N. K., 2001, “Analysis of Damping Characteristics for Viscoelastic Laminated Beams,” Comput. Methods Appl. Mech. Eng., 190, pp. 3881–3892. [CrossRef]
Oh, I. K., 2007, “Dynamic Characteristics of Cylindrical Hybrid Panels Containing Viscoelastic Layer Based on Layerwise Mechanics,” Composites, Part B, 38, pp. 159–171. [CrossRef]
Mead, D. J., 2007, “The Measurement of the Loss Factors of Beams and Plates With Constrained and Unconstrained Damping Layers: A Critical Assessment,” J. Sound Vib., 300, pp. 744–762. [CrossRef]
Liu, X. D., Zhang, Y. R., He, T., and ShanY. Ch., 2008, “Application of Damping Materials in Oil-Pan's Vibration and Noise Control,” Noise Vib. Control, 28, pp. 132–137 (in Chinese).
Pan, H. H., 1969, “Axisymmetrical Vibrations of a Circular Sandwich Shell With a Viscoelastic Core Layer,” J. Sound Vib., 9, pp. 338–348. [CrossRef]
Bogdanovich, A. E., 1975, “Parametric Vibrations of Cylindrical Shells With a Viscoelastic Core,” Polym. Mech., 11, pp. 718–725 [CrossRef].
Ramesh, T. C., and Ganesan, N., 1993, “Vibration and Damping Analysis of Cylindrical Shells With a Constrained Damping Layer,” Comput. Struct., 46, pp. 751–758. [CrossRef]
Ramesh, T. C., and Ganesan, N., 1994, “Finite Element Analysis of Cylindrical Shells With a Constrained Viscoelastic Layer,” J. Sound Vib., 172, pp. 359–370. [CrossRef]
Ramesh, T. C., and Ganesan, N., 1995, “Influence of Constrained Damping Layer on the Resonant Response of Orthotropic Cylindrical Shells,” J. Sound Vib., 185, pp. 483–500. [CrossRef]
Hu, Y. C., and Huang, S. C., 2000, “The Frequency Response and Damping Effect of Three-Layer Thin Shell With Viscoelastic Core,” Comput. Struct., 76, pp. 577–591. [CrossRef]
Wang, H. J., and Chen, L. W., 2004, “Finite Element Dynamic Analysis of Orthotropic Cylindrical Shells With a Constrained Damping Layer,” Finite Elem. Anal. Design, 40, pp. 737–755. [CrossRef]
Li, E. Q., Li, D. K., Tang, G. J., and Lei, Y. J., 2008, “Dynamic Analysis of Constrained Layered Damping Cylindrical Shell,” Eng. Mech., 25, pp. 6–11 (in Chinese).
Cao, X. T., Zhang, Z. Y., and Hua, H. X., 2011, “Free Vibration of Circular Cylindrical Shell With Constrained Layer Damping,” Appl. Math. Mech., 32, pp. 495–506. [CrossRef]
Farough, M., and Ramin, S., 2012, “Linear and Nonlinear Vibration Analysis of Sandwich Cylindrical Shell With Constrained Viscoelastic Core Layer,” Int. J. Mech. Sci., 54, pp. 156–171. [CrossRef]
Chen, L. H., and Huang, S. C., 1999, “Vibrations of a Cylindrical Shell With Partially Constrained Layer Damping (CLD) Treatment,” Int. J. Mech. Sci., 41, pp. 1485–1498. [CrossRef]
Li, E. Q., Li, D. K., Tang, G. J., and Lei, Y. J., 2007, “Dynamic Analysis of Cylindrical Shell With Partially Covered Ring-Shape Constrained Layer Damping by the Transfer Function Method,” Chin. J. Aeronaut., 28, pp. 1487–1493 (in Chinese).
Sainsbury, M. G., and Masti, R. S., 2007, “Vibration Damping of Cylindrical Shells Using Strain-Energy-Based Distribution of an Add-On Viscoelastic Treatment,” Finite Elem. Anal. Design, 43, pp. 175–192. [CrossRef]
Fuller, C. R., and Fahy, F. J., 1982, “Characteristics of Wave Propagation and Energy Distributions in Cylindrical Elastic Shells Filled With Fluid,” J. Sound Vib., 81, pp. 501–518. [CrossRef]
Fuller, C. R., 1983, “The Input Mobility of an Infinite Circular Cylindrical Elastic Shell Filled With Fluid,” J. Sound Vib., 87, pp. 409–427. [CrossRef]
Brevart, B. J., and Fuller, C. R., 1993, “Effect of an Internal Flow on the Distribution of Vibrational Energy in an Infinite Fluid-Filled Thin Cylindrical Elastic Shell,” J. Sound Vib., 167, pp. 149–163. [CrossRef]
Xu, M. B., Zhang, X. M., and Zhang, W. H., 1997, “Characteristics of Wave Propagation and Vibrational Power Flow in a Fluid-Filled Cylindrical Shell,” J. Vibr. Eng.,10, pp. 230–235 (in Chinese).
Xu, M. B., Zhang, X. M., and Zhang, W. H., 1997, “The Vibrational Energy Flow in a Cylindrical Shell Filled With Fluid,” J. Huazhong Univ. Sci. Technol., 24, pp. 85–87 (in Chinese).
Xu, M. B., and Zhang, X. M., 1998, “Vibration Power Flow in a Fluid-Filled Cylindrical Shell,” J. Sound Vib., 218, pp. 587–598. [CrossRef]
Xu, M. B., Zhang, X. M., and Zhang, W. H., 1999, “Input Vibrational Power Flow and Its Transmission in a Fluid-Filled Shell,” Chin. J. Acoust., 24, pp. 391–399 (in Chinese).
Xu, M. B., and Zhang, W. H., 2000, “Vibrational Power Flow Input and Transmission in a Circular Cylindrical Shell Filled With Fluid,” J. Sound Vib., 234, pp. 387–403. [CrossRef]
Sorokin, S. V., Nielsen, J. B., and Olhlff, N., 2004, “Green's Matrix and the Boundary Integral Equation Method for the Analysis of Vibration and Energy Flow in Cylindrical Shells With and Without Internal Fluid Loading,” J. Sound Vib., 271, pp. 815–847. [CrossRef]
Yan, J., Li, T. Y., Liu, T. G., and Liu, J. X., 2006, “Characteristics of the Vibrational Power Flow Propagation in a Submerged Periodic Ring-Stiffened Cylindrical Shell,” Appl. Acoust., 67, pp. 550–569. [CrossRef]
Yan, J., Li, T. Y., Liu, J. X., and Zhu, X., 2008, “Input Power Flow in a Submerged Infinite Cylindrical Shell With Doubly Periodic Supports,” Appl. Acoust., 69, pp. 681–690. [CrossRef]
Yan, J., Li, T. Y., Liu, J. X., and Zhu, X., 2007, “Power Flow Analysis of a Submerged Cylindrical Shell Coated by Viscoelastic Materials With Wave Propagation Approach,” J. Ship Mech., 11, pp. 780–787 (in Chinese).
Yan, J., Li, F. C., and Li, T. Y., 2007, “Vibrational Power Flow Analysis of a Submerged Viscoelastic Cylindrical Shell With Wave Propagation Approach,” J. Sound Vib., 303, pp. 264–276. [CrossRef]
Yan, J., 2006, “Characteristics of Power Flow and Sound Radiation in Submerged Complex Cylindrical Shells,” Ph.D. thesis, Huazhong University of Science and Technology, Wu Han, China (in Chinese).
Zhang, J. J., 2010, “Vibrational Power Flow and Radiated Sound Power of Cylindrical Shell in Fluid With Different Theories,” Ph.D. thesis, Huazhong University of Science and Technology, Wu Han, China (in Chinese).
Wilhelm, F., 1973, Stresses in Shells, Springer-Verlag, New York, pp. 204–215.
Stefan, M., 1998, The Mechanics of Vibrations of Cylindrical Shells, Elsevier Science, Amsterdam, pp. 1–100.
Chen, L. H., and Huang, S. C., 2001, “Vibration Attenuation of a Cylindrical Shell With Constrained Layer Damping Strips Treatment,” Comput. Struct., 79, pp. 1355–1362. [CrossRef]
He, Z. Y., and Zhao, Y. F., 1981, Basic Theory of Acoustic, National Defense Industry, Beijing, China, pp. 96–105 (in Chinese).
He, Z. Y., 2001, Structural Vibration and Acoustic, Harbin Engineering University, Harbin, China, pp. 67–144 (in Chinese).
Zhang, X. M., Liu, G. R., and Lam, K. Y., 2001, “Coupled Vibration Analysis of Fluid-Filled Cylindrical Shells Using the Wave Propagation Approach,” Appl. Acoust., 62, pp. 229–243. [CrossRef]
Zhang, X. M., 2002, “Frequency Analysis of Submerged Cylindrical Shells With the Wave Propagation Approach,” Int. J. Mech. Sci., 44, pp. 1259–1273. [CrossRef]
Zhang, X. M., 2002, “Parametric Studies of Coupled Vibration of Cylindrical Pipes Conveying Fluid With the Wave Propagation Approach,” Comput. Struct., 80, pp. 287–295. [CrossRef]
Brazier-Smith, P. R., and Scott, J. F. M., 1991, “On the Determination of the Roots of Dispersion Equations by Use of Winding Number Integrals,” J. Sound Vib., 145, pp. 503–510. [CrossRef]
Ivansson, S., and Karasalo, I., 1993, “Computation of Modal Wavenumbers Using an Adaptive Wingding-Number Integral Method With Error Control,” J. Sound Vib., 161, pp. 173–180. [CrossRef]
Scott, J. F. M., 1988, “The Free Modes of Propagation of an Infinite Fluid-Loaded Thin Cylindrical Shell,” J. Sound Vib., 125, pp. 241–280. [CrossRef]

Figures

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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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