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.
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References
Allen, H.G.: Analysis and design of structural sandwich panels. Pergamon Press, London (1969)
Plantema, F.J.: Sandwich Construction. Wiley, New York (1966)
Librescu, L., Hause, T.: Recent developments in the modeling and behavior of advanced sandwich constructions: a survey. Compos. Struct. 48(1), 1–17 (2000)
Mindlin, R.D.: Influence of transverse shear deformation on the bending of classical plates. Trans. ASME J. Appl. Mech. 8, 18–31 (1951)
Reddy, J.N.: Energy Principles and Variational Methods in Applied Mechanics. Wiley, New York (1984)
Petras, A., Sutcliffe, M.P.F.: Indentation resistance of sandwich beams. J. Compos. Struct. 46, 413–424 (1999)
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)
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)
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)
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)
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)
Shen, H., Li, S.: Postbuckling of sandwich plates with FGM face sheets and temperature-dependent properties. Compos. Part B 39, 332–344 (2008)
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)
Reddy J.N: Thermo mechanical behavior of functionally graded materials. Texas, (1998)
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)
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Mohammadi, Y., Khalili, S.M.R. (2012). Free Vibration Analysis of Sandwich Plates with Temperature-Dependent Properties of the Core Materials and Functionally Graded Face Sheets. In: Öchsner, A., da Silva, L., Altenbach, H. (eds) Mechanics and Properties of Composed Materials and Structures. Advanced Structured Materials, vol 31. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31497-1_13
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DOI: https://doi.org/10.1007/978-3-642-31497-1_13
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