Skip to main content
SpringerLink
Log in

Investigation of the Thickness Variability and Material Heterogeneity Effects on Free Vibration of the Viscoelastic Circular Plates

  • Published:
Acta Mechanica Solida Sinica Aims and scope Submit manuscript

Abstract

The present study deals with free vibration analysis of variable thickness viscoelastic circular plates made of heterogeneous materials and resting on two-parameter elastic foundations in addition to their edge conditions. It is assumed that the viscoelastic material properties vary in the transverse and radial directions simultaneously. The complex modulus approach is employed in conjunction with the elastic-viscoelastic correspondence principle to obtain the solution. The governing equations are solved by means of a power series solution. Finally, a sensitivity analysis including evaluation of effects of various edge conditions, thickness variations, coefficients of the elastic foundation, and material loss factor and heterogeneity on the natural frequencies and modal loss factors is accomplished.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Gasik, M.M. and Ueda, S., Micromechanical modeling of functionally graded W-Cu materials for divertor plate components in a fusion reactor. Materials Science Forum, 1999, 308–311: 603–607.

    Article  Google Scholar 

  2. Chin, E.S.C., Army focused research team on functionally graded armor composites. Materials Science and Engineering A, 1999, 259: 155–161.

    Article  Google Scholar 

  3. Yamada, K., Sakamura, J. and Nakamura, K., Broadband ultrasound transducers using piezoelectrically graded materials. Materials Science Forum, 1999, 308–311: 527–532.

    Article  Google Scholar 

  4. Watari, F., Yokoyama, A., Matsuno, H., Saso, F., Uo, M. and Kawasaki, T., Biocompatibility of titanium/hydroxyapatite and titanium/cobalt functionally graded implants. Materials Science Forum, 1999, 308–311: 356–361.

    Article  Google Scholar 

  5. Pompe, W., Worch, H., Epple, M., Friess, W., Gelinsky, M., Greil, P., Hempel, U., Scharnweber, D. and Schulte, K., Functionally graded materials for biomedical applications. Materials Science and Engineering A, 2003, 362: 40–60.

    Article  Google Scholar 

  6. Zhao, J., Ai, X. and Huang, X.P., Relationship between the thermal shock behavior and the cutting performance of a functionally graded ceramic tool. Journal of Materials Processing Technology, 2002, 129: 161–166.

    Article  Google Scholar 

  7. Nie, G.J. and Zhong, Z., Semi-analytical solution for three-dimensional vibration of functionally graded circular plates. Computational Methods in Applied Mechanics and Engineering, 2007, 196: 4901–4910.

    Article  Google Scholar 

  8. Gupta, U.S., Lal, R. and Sharma, S., Vibration analysis of non-homogeneous circular plate of nonlinear thickness variation by differential quadrature method. Journal of Sound and Vibration, 2006, 298: 892–906.

    Article  Google Scholar 

  9. Dong, C.Y., Three-dimensional free vibration analysis of functionally graded annular plates using the Chebyshev-Ritz method. Materials & Design, 2008, 29: 1518–1525.

    Article  Google Scholar 

  10. Malekzadeh, P., Three-dimensional free vibration analysis of thick functionally graded plates on elastic foundations. Composite Structures, 2009, 89: 367–373.

    Article  Google Scholar 

  11. Shariyat, M. and Alipour, M.M., Differential transform vibration and modal stress analyses of circular plates made of two-directional functionally graded materials resting on elastic foundations. Archive of Applied Mechanics, 2011, 81: 1289–1306.

    Article  Google Scholar 

  12. Alipour, M.M., Shariyat, M. and Shaban, M., A semi-analytical solution for free vibration of variable thickness two-directional-functionally graded plates on elastic foundations. International Journal of Mechanics and Materials in Design, 2010, 6: 293–304.

    Article  Google Scholar 

  13. Alipour, M.M. and Shariyat, M., Semi-analytical buckling analysis of heterogeneous variable thickness viscoelastic circular plates on elastic foundations. Mechanics Research Communications, 2011, 38: 594–601.

    Article  Google Scholar 

  14. Bailey, P.B. and Chen, P., Natural modes of vibration of linear viscoelastic circular plates with free edges. International Journal of Solids and Structures, 1987, 23: 785–795.

    Article  Google Scholar 

  15. Saravanos, D.A. and Pereira, J.M., Effects of interply damping layers on the dynamic characteristics of composite plates. AIAA Journal, 1992, 30: 2906–2913.

    Article  Google Scholar 

  16. Yu, S.C. and Huang, S.C., Vibration of a three-layered viscoelastic sandwich circular plate. International Journal of Mechanical Sciences, 2001, 43: 2215–2236.

    Article  Google Scholar 

  17. Wang, H.J. and Chen, L.W., Vibration and damping analysis of a three-layered composite annular plate with a viscoelastic mid-layer. Composite Structures, 2002, 58: 563–570.

    Article  Google Scholar 

  18. Roy, P.K. and Ganesan, N., A vibration and damping analysis of circular plates with constrained damping layer treatment. Computers and Structures, 1993, 49: 269–274.

    Article  Google Scholar 

  19. Yu, S.C. and Huang, S.C., Vibration of a three-layered viscoelastic sandwich circular plate. International Journal of Mechanical Sciences, 2001, 43: 2215–2236.

    Article  Google Scholar 

  20. Bolton, R., Stresses in circular plates on elastic foundations. Proceedings of the American Society of Civil Engineers, Journal of the Engineering Mechanics Division, 1972, 98: 629–640.

    Google Scholar 

  21. Dumir, P.C., Non-linear vibration and post buckling of isotropic thin circular plates on elastic foundation. Journal of Sound and Vibration, 1986, 107: 253–263.

    Article  Google Scholar 

  22. Liew, K.M., Han, J.B. and Xiao, Z.M., Vibration analysis of circular Mindlin plates using differential quadrature method. Journal of Sound and Vibration, 1997, 205: 617–630.

    Article  Google Scholar 

  23. Liew, K.M., Hung, K.C. and Lim, M.K., Vibration of Mindlin plates using boundary characteristic orthogonal polynomials. Journal of Sound and Vibration, 1995, 182: 77–90.

    Article  Google Scholar 

  24. Lee, J. and Schultz, W.W., Eigenvalue analysis of Timoshenko beams and axisymmetric Mindlin plates by the pseudospectral method. Journal of Sound and Vibration, 2004, 269: 609–621.

    Article  Google Scholar 

  25. Ferreira, A.J.M., Free vibration analysis of Timoshenko beams and Mindlin plates by radial basis functions. International Journal of Computational Methods, 2005, 2: 15–31.

    Article  Google Scholar 

  26. Wu, T.Y., Wang, Y.Y. and Liu, G.R., Free vibration analysis of circular plates using generalized differential quadrature rule. Computational Methods in Applied Mechanics and Engineering, 2002, 191: 5365–5380.

    Article  Google Scholar 

  27. Chen, C.K. and Ho, S.H., Application of differential transformation to eigenvalue problems. Applied Mathematical Computation, 1996, 79: 173–188.

    Article  MathSciNet  Google Scholar 

  28. Ho, S.H. and Chen, C.K., Analysis of general elastically end restrained non-uniform beams using differential transform. Applied Mathematical Modelling, 1998, 22: 219–234.

    Article  Google Scholar 

  29. Jang, M.J., Chen, C.L. and Liu, Y.C., On solving the initial value problems using the differential transformation method. Applied Mathematical Computation, 2000, 115: 145–160.

    Article  MathSciNet  Google Scholar 

  30. Bhaskar, K. and Dhaoya, J., Straightforward power series solutions for rectangular plates. Composite Structures, 2009, 89: 253–261.

    Article  Google Scholar 

  31. Abdel-Halim Hassan, I.H., Differential transformation technique for solving higher-order initial value problems. Applied Mathematical Computation, 2004, 154: 299–311.

    Article  MathSciNet  Google Scholar 

  32. Lakes,R.S., Viscoelastic Materials. 1st edition. Cambridge University Press, 2009.

  33. Hal, F., Brinson, L. and Brinson, C., Polymer Engineering Science and Viscoelasticity: An Introduction. Springer, LLC, 2008.

    Google Scholar 

  34. Shariyat, M., A double-superposition global-local theory for vibration and dynamic buckling analyses of viscoelastic composite/sandwich plates: a complex modulus approach. Archive of Applied Mechanics, 2011, 81: 1253–1268.

    Article  Google Scholar 

  35. Shariyat, M., Nonlinear thermomechanical dynamic buckling analysis of imperfect viscoelastic composite/sandwich shells by a double-superposition global-local theory and various constitutive models. Composite Structures, 2011, 93: 2833–2843.

    Article  Google Scholar 

  36. Shariyat, M., A nonlinear double-superposition global-local theory for dynamic buckling of imperfect viscoelastic composite/sandwich plates: A hierarchical constitutive model. Composite Structures, 2011, 93: 1890–1899.

    Article  Google Scholar 

  37. Alipour, M.M. and Shariyat, M., An elasticity-equilibrium-based zigzag theory for axisymmetric bending and stress analysis of the functionally graded circular sandwich plates, using a Maclaurin-type series solution. European Journal of Mechanics — A/Solids, 2012, 34: 78–101.

    Article  MathSciNet  Google Scholar 

  38. Shariyat, M., Non-linear dynamic thermo-mechanical buckling analysis of the imperfect sandwich plates based on a generalized three-dimensional high-order global-local plate theory. Composite Structures, 2010, 92: 72–85.

    Article  Google Scholar 

  39. Shariyat, M., A generalized high-order global-local plate theory for nonlinear bending and buckling analyses of imperfect sandwich plates subjected to thermo-mechanical loads. Composite Structures, 2010, 92: 130–143.

    Article  Google Scholar 

  40. Shariyat, M., A generalized global-local high-order theory for bending and vibration analyses of sandwich plates subjected to thermo-mechanical loads. International Journal of Mechanical Sciences, 2010, 52: 495–514.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Mechanical Engineering, K.N. Toosi University of Technology, Tehran, 19991-43344, Iran

    M. Shariyat, A. A. Jafari & M. M. Alipour

Authors
  1. M. Shariyat
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. A. Jafari
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. M. Alipour
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Shariyat.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shariyat, M., Jafari, A.A. & Alipour, M.M. Investigation of the Thickness Variability and Material Heterogeneity Effects on Free Vibration of the Viscoelastic Circular Plates. Acta Mech. Solida Sin. 26, 83–98 (2013). https://doi.org/10.1016/S0894-9166(13)60009-9

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1016/S0894-9166(13)60009-9

Key words

Search

Navigation