• Steel and Composite Structures
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• 제25권3호
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• pp.347-360
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• 2017

The goal of this study is to fill this apparent gap in the area about vibration analysis of multiwalled carbon nanotubes (MWCNTs) curved panels by providing 3-D vibration analysis results for functionally graded multiwalled carbon nanotubes (FG-MWCNTs) sandwich structure with power-law distribution of nanotube. The effective material properties of the FG-MWCNT structures are estimated using a modified Halpin-Tsai equation. Modified Halpin-Tsai equation was used to evaluate the Young's modulus of MWCNT/epoxy composite samples by the incorporation of an orientation as well as an exponential shape factor in the equation. The exponential shape factor modifies the Halpin-Tsai equation from expressing a straight line to a nonlinear one in the MWCNTs wt% range considered. Also, the mass density and Poisson's ratio of the MWCNT/phenolic composite are considered based on the rule of mixtures. Parametric studies are carried out to highlight the influence of MWCNT volume fraction in the thickness, different types of CNT distribution, boundary conditions and geometrical parameters on vibrational behavior of FG-MWCNT thick curved panels. Because of using two-dimensional generalized differential quadrature method, the present approach makes possible vibration analysis of cylindrical panels with two opposite axial edges simply supported and arbitrary boundary conditions including Free, Simply supported and Clamped at the curved edges. For an overall comprehension on 3-D vibration analysis of sandwich panel, some mode shape contour plots are reported in this research work.

• Steel and Composite Structures
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• 제26권5호
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• pp.649-662
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• 2018

In this study, based on the three-dimensional theory of elasticity, free vibration characteristics of sandwich sectorial plates with multiwalled carbon nanotube-(MWCNT)-reinforced composite core are considered. Modified Halpin-Tsai equation is used to evaluate the Young's modulus of the MWCNT/epoxy composite samples by the incorporation of an orientation as well as an exponential shape factor in the equation. The exponential shape factor modifies the Halpin-Tsai equation from expressing a straight line to a nonlinear one in the MWCNTs wt% range considered. In this paper, free vibration of thick functionally graded sandwich annular sectorial plates with simply supported radial edges and different circular edge conditions including simply supported-clamped, clamped-clamped, and free-clamped is investigated. A semi-analytical approach composed of two-dimensional differential quadrature method and series solution are adopted to solve the equations of motion. The material properties change continuously through the core thickness of the plate, which can vary according to a power-law, exponentially, or any other formulations in this direction. This study serves as a benchmark for assessing the validity of numerical methods or two-dimensional theories used to analysis of laminated sectorial plates.

• Steel and Composite Structures
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• 제29권5호
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• pp.569-578
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• 2018

This paper aims to investigate the transient vibration behavior of functionally graded carbon nanotube (FG-CNT) reinforced nanocomposite plate resting on Pasternak foundation under pulse excitation. The plate is considered to be composed of matrix material and multi-walled carbon nanotubes (MWCNTs) with distribution as per the functional grading concept. The functionally graded distribution patterns in nanocomposite plate are explained more appropriately with the layer-wise variation of carbon nanotubes weight fraction in the thickness coordinate. The layers are stacked up in such a way that it yields uniform and three other types of distribution patterns. The effective material properties of each layer in nanocomposite plate are obtained by modified Halpin-Tsai model and rule of mixtures. The governing equations of an illustrative case of simply-supported nanocomposite plate resting on the Pasternak foundation are derived from third order shear deformation theory and Navier's solution technique. A converge transient response of nanocompiste plate under uniformly distributed load with triangular pulse is obtained by varying number of layer in thickness direction. The validity and accuracy of the present model is also checked by comparing the results with those available in literature for isotropic case. Then, numerical examples are presented to highlight the effects of distribution patterns, foundation stiffness, carbon nanotube parameters and plate aspect ratio on the central deflection response. The results are extended with the consideration of proportional damping in the system and found that nanocomposite plate with distribution III have minimum settling time as compared to the other distributions.