Free Vibration Analysis of Sandwich Plates with Temperature-Dependent Properties of the Core Materials and Functionally Graded Face Sheets

Chapter
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 31)

Abstract

In the present chapter, the free vibration of sandwich plates with power-law functionally graded face sheets in different thermal environments is performed. The material properties of the core, such as Young’s modulus, density, thermal expansion coefficient and Poisson’s ratio, are assumed to be temperature dependent by a nonlinear function of temperature and the material properties of the face sheets are assumed to vary continuously through the thickness according to a power-law distribution in terms of the volume fractions of the constituents. Both un-symmetric and symmetric sandwich plates are considered in this analysis. A new approach is used to reduce the equations of motion from twenty three equations to eleven equations and then solve them. The new solution approach consists of isolating six of the unknowns in the displacements of the face sheets using the compatibility equations, followed by isolating the additional six Lagrange multipliers using the equations of the face sheets. Finally, the isolated unknowns are substituted into the eleven equations of the core. Good agreement is found between theoretical predictions of the fundamental frequency parameters and the results obtained from other references for simply supported sandwich plates with FG face sheets. The results also reveal that as the side-to-thickness ratio, the core-to-face sheet thickness ratio and temperature changes, affect the fundamental frequency parameters significantly.

Keywords

Free Vibration Sandwich Plate Face Sheet Sandwich Beam Core Thickness 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Allen, H.G.: Analysis and design of structural sandwich panels. Pergamon Press, London (1969)Google Scholar
  2. 2.
    Plantema, F.J.: Sandwich Construction. Wiley, New York (1966)Google Scholar
  3. 3.
    Librescu, L., Hause, T.: Recent developments in the modeling and behavior of advanced sandwich constructions: a survey. Compos. Struct. 48(1), 1–17 (2000)CrossRefGoogle Scholar
  4. 4.
    Mindlin, R.D.: Influence of transverse shear deformation on the bending of classical plates. Trans. ASME J. Appl. Mech. 8, 18–31 (1951)Google Scholar
  5. 5.
    Reddy, J.N.: Energy Principles and Variational Methods in Applied Mechanics. Wiley, New York (1984)Google Scholar
  6. 6.
    Petras, A., Sutcliffe, M.P.F.: Indentation resistance of sandwich beams. J. Compos. Struct. 46, 413–424 (1999)CrossRefGoogle Scholar
  7. 7.
    Frostig, Y., Baruch, M., Vilnay, O., Sheinman, I.: A high order theory for the bending of sandwich beams with a flexible core. J. ASCE EM Div. 118(5), 1026–1043 (1992)CrossRefGoogle Scholar
  8. 8.
    Frostig, Y., Baruch, M.: Localized load effects in high-order bending of sandwich panels with flexible core. J. Engrg. Mech. 122(11), 1069–1076 (1996)CrossRefGoogle Scholar
  9. 9.
    Frostig, Y., Thomsen, O.T.: High-order free vibration of sandwich panels with a flexible core. Int. J. Solids Struct. 41(5–6), 1697–1724 (2004)CrossRefGoogle Scholar
  10. 10.
    Malekzadeh, K., Khalili, M.R., Mittal, R.K.: Local and global damped vibrations of sandwich plates with a viscoelastic soft flexible core: an improved high-order approach. J. Sandwich Struct. Mater. 7(5), 431–456 (2005)CrossRefGoogle Scholar
  11. 11.
    Frostig, Y., Thomsen, O.T.: On the free vibration of sandwich panels with a transversely flexible and temperature-dependent core material—Part I: Mathematical formulation. J. Compos. Sci. Technol. 69, 856–862 (2009)CrossRefGoogle Scholar
  12. 12.
    Shen, H., Li, S.: Postbuckling of sandwich plates with FGM face sheets and temperature-dependent properties. Compos. Part B 39, 332–344 (2008)CrossRefGoogle Scholar
  13. 13.
    Zhao, J., Li, Y., Ai, X.: Analysis of transient thermal stress in sandwich plate with functionally graded coatings. Thin Solid Films 516, 7581–7587 (2008)CrossRefGoogle Scholar
  14. 14.
    Reddy J.N: Thermo mechanical behavior of functionally graded materials. Texas, (1998)Google Scholar
  15. 15.
    Li, Q., Iu, V.P., Kou, K.P.: Three-dimensional vibration analysis of functionally graded material sandwich plates. J. Solid Vib. 311, 498–515 (2008)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Qazvin Branch, Faculty of Industrial and Mechanical EngineeringIslamic Azad UniversityQazvinIran
  2. 2.Center of Excellence for Research in Advanced Materials and Structures, Faculty of Mechanical EngineeringK. N. Toosi University of TechnologyTehranIran
  3. 3.Faculty of EngineeringKingston UniversityLondonUK

Personalised recommendations