A new higher-order shear and normal deformation theory for the static and free vibration analysis of sandwich plates with functionally graded isotropic face sheets

In the present study, the static and free vibration analysis of functionally graded carbon nano-tubes reinforced (FG-CNTR) sandwich plates are studied in the framework of inverse hyperbolic shear deformation theory. The governing differential equations are derived using Hamilton’s principle and solved with the Navier’s solution technique. The analytical approach is used to obtain the deflections, stresses, natural frequencies, and corresponding mode shapes of FG-CNTR sandwich plates with different material properties, stacking sequences, span thickness ratios, core to face sheet thickness ratios, and loading conditions. Different types of reinforcement distribution such as uniformly distribution (UD) and functionally graded (FG) distribution of FG-O, FG-X, FG-/\, and FG-V are considered for the analysis. Also, the efforts are made to achieve the best possible arrangement for the stacking sequences and the appropriate reinforcement distribution that will produce improved static and free vibration responses for the FG-CNTR sandwich plates.

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FREE VIBRATION OF FUNCTIONALLY GRADED PLATES WITH A HIGHER-ORDER SHEAR AND NORMAL DEFORMATION THEORY

International Journal of Structural Stability and Dynamics ◽

10.1142/s0219455413500041 ◽

2013 ◽

Vol 13 (01) ◽

pp. 1350004 ◽

Cited By ~ 12

Author(s):

D. K. JHA ◽

TARUN KANT ◽

R. K. SINGH

Keyword(s):

Free Vibration ◽

Material Properties ◽

Deformation Theory ◽

Numerical Solutions ◽

Volume Fraction ◽

Free Vibration Analysis ◽

Higher Order ◽

Functionally Graded ◽

Normal Deformation ◽

Fg Plates

Free vibration analysis of functionally graded elastic, rectangular, and simply supported (diaphragm) plates is presented based on a higher-order shear and normal deformation theory (HOSNT). Although functionally graded materials (FGMs) are highly heterogeneous in nature, they are generally idealized as continua with mechanical properties changing smoothly with respect to the spatial coordinates. The material properties of functionally graded (FG) plates are assumed here to be varying through the thickness of the plate in a continuous manner. The Poisson ratios of the FG plates are assumed to be constant, but their Young's modulii and densities vary continuously in the thickness direction according to the volume fraction of constituents which is mathematically modeled as a power law function. The equations of motion are derived using Hamilton's principle for the FG plates on the basis of a HOSNT assuming varying material properties. Numerical solutions are obtained by the use of Navier solution method. The accuracy of the numerical solutions is first established through comparison with the exact three-dimensional (3D) elasticity solutions and the present solutions are then compared with available solutions of other models.

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