Free Vibration Analysis of Cylindrical and Rectangular Sandwich Panels with a Functionally Graded Core

doi:10.1007/s12204-015-1684-x

Abstract

Abstract:

Based on the Reissner assumptions, the free vibration analysis of simply supported cylindrical and rectangular sandwich panels with isotropic face sheets and a functionally graded core is concerned. Firstly, the expressions of the displacements, stresses and internal forces are presented according to the constitutive relations and stress states of the core and face sheets. Then, the dynamic stability and compatibility equations are given for cylindrical sandwich panels with functionally graded core, elastic modulus and density in which vary continuously in the thickness direction. Finally, the proposed solutions are validated by comparing the results of degenerate example with classical solutions, and a numerical analysis is performed on the example of simply supported cylindrical and rectangular sandwich panels. The elastic modulus and density of the functionally graded core are assumed to be graded by a power law distribution of volume fractions of the constituents, and the Poisson ratio is held constant. The effects of the distribution of functionally graded core's properties, the thickness-side ratios and ratio of radius $(R)$ to length $(l)$ $\kappa =R/l$ are also examined.

Key words: functionally graded materials|cylindrical sandwich panel|rectangular sandwich plate|simply supported|free vibration

CLC Number:

O 345
TB 332

Hua-dong LI, Xi ZHU, Zhi-yuan MEI, Ying-jun ZHANG. Free Vibration Analysis of Cylindrical and Rectangular Sandwich Panels with a Functionally Graded Core[J]. Journal of Shanghai Jiao Tong University(Science), 2015, 20(6): 735-742.

References 14

[1]	Nie G J, Zhong Z.Semi-analytical solution for three-dimensional vibration of functionally graded circular plates[J]. Computer Methods in Applied Mechanics and Engineering, 2007, 196: 4901-4910.
[2]	Abdelaziz H H, Atmane H A, Mechab I,et al.Static analysis of functionally graded sandwich plates using an efficient and simple refined theory[J]. Chinese Journal of Aeronautics, 2011, 24: 434-448.
[3]	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[J]. Composite Structures, 2010, 92: 130-143.
[4]	Wu Z, Chen W J.A C0-type higher-order theory for bending analysis of laminated composite and sandwich plates[J]. Composite Structures, 2010, 92: 653-661.
[5]	Pradyumna S, Bandyopadhyay J N.Free vibration analysis of functionally graded curved panels using a higher-order finite element formulation[J]. Journal of Sound and Vibration, 2008, 318: 176-192.
[6]	Zhao X, Lee Y Y, Liew K M. Free vibration analysis of functionally graded plates using the element-free $kp$-Ritz method [J]. Journal of Sound and Vibration, 2009, 319: 918-939.
[7]	Li Q, Lu V P, Kou K P.Three-dimensional vibration analysis of functionally graded material sandwich plates[J]. Journal of Sound and Vibration, 2008, 311: 498-515.
[8]	Rahmani O, Khalili S M R, Malekzadeh K, et al. Free vibration analysis of sandwich structures with a flexible functionally graded syntactic core[J]. Composite Structures, 2009, 91: 229-235.
[9]	Amirani M C, Khalili S M R, Nemati N. Free vibration analysis of sandwich beam with FG core using the element free Galerkin method[J]. Composite Structures, 2009, 90: 373-379.
[10]	Neves A M A, Ferreira A J M, Carrera E, et al. Static, free vibration and buckling analysis of isotropic and sandwich functionally graded plates using a quasi-3D higher-order shear deformation theory and a meshless technique[J]. Composites: Part B, 2013, 44: 657-674.
[11]	Alibeigloo A, Liew K M.Free vibration analysis of sandwich cylindrical panel with functionally graded core using three-dimensional theory of elasticity[J]. Composite Structures, 2014, 113: 23-30.
[12]	Institute of Mechanics, Chinese Academy of Science. The bending stability and vibration of sandwich plates and shells [M]. Beijing: Science Press, 1977.
[13]	Chakraborty A, Gopalakrishnan S, Reddy J N.A new beam finite element for the analysis of functionally graded materials[J]. International Journal of Mechanical Sciences, 2003, 45: 519-539.
[14]	Bayat M, Sahari B B, Saleem M,et al.Bending analysis of a functionally graded rotating disk based on the first order shear deformation theory[J]. Applied Mathematical Modelling, 2009, 33: 4215-4230.

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