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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Modal Analyses of a Thin Shell with Constrained Layer Damping (CLD) Based on Rayleigh-Ritz Method

Journal of Applied Nonlinear Dynamics 4(3) (2015) 313--327 | DOI:10.5890/JAND.2015.09.011

Xu-Yuan Song; Hong-Jun Ren; Jing-Yu Zhai; Qing-Kai Han

School of Mechanical Engineering, Dalian University of Technology, Liaoning, 116024, PR China

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Abstract

Foreign Object Debris (FOD) is debris or article alien, which may This paper presents analytical results of natural frequencies and loss factors of node-diameter and node-circumferential modes of a thin shell treated with constrained layer damping (CLD) based on Rayleigh-Ritz method. General differential equations of motion of the thin CLD shell are derived firstly by following the Donnell-Mushtari shell theory. By taking the beam characteristic functions as the admissible functions, the Rayleigh-Ritz method is employed to deduce the higher degree equations of natural frequencies of the thin CLD shell under different boundary conditions. It is confirmed that the present method is accurate and convenient so that it is applicable to the thin CLD shell compared with classic analytic method or transfer matrix method. Several examples are achieved and compared to illustrate the effects of the viscoelastic material (VEM) and constrain layer’s thickness ratios on the natural frequencies and modal loss factors, besides the effect of boundary conditions. The results show that the thickness ratio of VEM affects sensitively the modal frequencies and the total damping capacity of the thin CLD shell.

Acknowledgments

This work is supported by Natural Science Foundation of China (Grant No. 51175070, 11472068), and National Basic Research Program of China (No. 2012CB026000-05, 2013CB035402-2), and the Fundamental Research Funds for the Central Universities (DUT14RC(3)095).

References

  1. [1]  Teng, T.-L. and Hu, N.-K. (2001), Analysis of Damping Characteristics for Viscoelastic Laminated Beams, Computer Methods in Applied Mechanics and Engineering, 190, 3881-3892.
  2. [2]  Hu, Y.-C. and Huang, S.-C. (2000), The Frequency Response and Damping Effect of Three-Layer Thin Shell With Viscoelastic Core, Computers & Structures, 76(5), 577-591.
  3. [3]  Leissa, A.W. (1973), Vibration of shells (NASA SP-288), US Government Printing Office, Washington, DC.
  4. [4]  Soedel, W. (1992), Vibrations of shells and plates, Marcell Dekker, New York.
  5. [5]  Love, A.E.H. (1888), the Small Free Vibrations and Deformation of a Thin Elastic Shell, Phil. Trans. Roy. Soc. A, 179.
  6. [6]  Donnell, L.H. (1933), Stability of thin-walled tubes under torsion. Pasadena (USA), California.
  7. [7]  Naghdi, P.M. (1957), On the Theory of Thin Elastic Shells, Quart.
  8. [8]  Sanders, J.L. (1959), An Improved First-Approximation Theory For Thin Shells, NASA-TR-R24.
  9. [9]  Fluegge, S. (1973), Stresses in Shells. 2nd ed, Springer, Berlin.
  10. [10]  Oh, I.K. (2008), Dynamic Characteristics of Cylindrical Hybrid Panels Containing Viscoelastic Layer Based on Layerwise Mechanics, Composites, Part B, 38(2), 159-171.
  11. [11]  Sainsburya, M.G. and Mastib, R.S. (2007), Vibration Damping of Cylindrical Shells Using Strain-Energy- Based Distribution of An Add-On Viscoelastic Treatment, Finite Elements in Analysis and Design, 43(3), 175-192.
  12. [12]  Ramesh, T.C. and Ganesan, N. (1993), Vibration and Damping Analysis of Cylindrical Shells With a Constrained Damping Layer, Computers & Structures, 46(4), 751-758.
  13. [13]  Ramesh, T.C. and Ganesan, N. (1994), Finite Element Analysis of Cylindrical Shells With a Constrained Viscoelastic Layer, Journal of Sound and Vibration, 172(3), 359-370.
  14. [14]  Ramesh, T.C. and Ganesan, N. (1993), Vibration and Damping Analysis of Cylindrical Shells With a Constrained Damping Layer, Computers & Structures, 46(4), 751-758.
  15. [15]  Wang, H.-J. and Chen, L.-W. (2004), Finite Element Dynamic Analysis of Orthotropic Cylindrical Shells With a Constrained Damping Layer, Finite Elements in Analysis and Design, 40(7), 737-755.
  16. [16]  Li, E.-Q., Li, D.-K., Tang, G.-J. and Lei, Y.-J. (2008), Dynamic Analysis of Constrained Layered Damping Cylindrical Shell, Engineering Mechanics (in Chinese), 25, 6-11.
  17. [17]  Leissa, A.W., Lee, J.K. and Wang, A.J. (1981), Vibrations of cantilevered shallow cylindrical shells of rectangular planform, Journal of Sound and Vibration, 78(3), 311-328.
  18. [18]  Liew, K.M. and Wang, C.M. (1993), Rayleigh-Ritz method for general plate analysis, Engineering Structures, 15(1), 55-60.
  19. [19]  Liew, K. and Lim, A. C. W. (1994), Vibratory characteristics of cantilevered rectangular shallow shells of variable thickness, AIAA Journal, 32, 387-396.
  20. [20]  Lam, K.Y. and Loy, C.T. (1995), Analysis of rotating laminated cylindrical shells by different thin shell theories, Journal of Sound and Vibration, 186(1), 23-35.
  21. [21]  Lam, K.Y. and Loy, C.T. (1995), Free vibrations of a rotating multi-layered cylindrical shell, International Journal of Solids and Structures, 32(5), 647-663.
  22. [22]  Pradhana, S.C., Loya, C.T., Lama, K.Y. and Reddyb, J.N. (2000), Vibration characteristics of functionally graded cylindrical shells under various boundary conditions. Applied Acoustics, 61(1), 111-129.
  23. [23]  Han, Q.-K., Wang, Y. and Li, X.-J. (2013), High nodal diameter vibration characteristics of rotating shell and the effects of its Sealing teeth, Scientia Sinica Physica, Mechanica & Astronomica, 43(4), 436-458.

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