Mechanical analysis of functionally graded carbon nanotube reinforced composites: A review

Free vibration analysis of rotating functionally graded CNT reinforced composite cylindrical shells with arbitrary boundary conditions

Free vibration analysis of laminated FG-CNT reinforced composite rectangular plates using the kp-Ritz method

Free vibration and static bending of functionally graded (FG) graphene nanoplatelet (GPL) reinforced composite doubly-curved shallow shells with three distinguished distributions are analyzed. Material properties with gradient variation in the thickness aspect are evaluated by the modified Halpin-Tsai model. Mathematical model of the simply supported doubly-curved shallow shells rests upon Hamilton Principle and a higher order shear deformation theory (HSDT). The free vibration frequencies and bending deflections are gained by taking into account Navier technique. The agreement between the obtained results and ANSYS as well as the prior results in the open literature verifies the accuracy of the theory in this article. Further, parametric studies are accomplished to highlight the significant influence of GPL distribution patterns and weight fraction, stratification number, dimensions of GPLs and shells on the mechanical behavior of the system.

Vibration and bending behavior of functionally graded nanocomposite doubly-curved shallow shells reinforced by graphene nanoplatelets

In this study, free vibration analysis of conical and cylindrical shells and annular plates made of composite laminated and functionally graded materials (FGMs) is investigated. Carbon nanotubes reinforced (CNTR) composite case is also taken consideration for FGM. The equations of motion for conical shell are obtained via Hamilton's principle using the transverse shear deformation theory. To obtain the eigenvalue problem of the system, the method of discrete singular convolution is employed. Material properties are graded in the thickness direction according to a volume fraction power law and four-parameter power law indexes for FGM cases. Five types of distributions of CNTR material are also considered. To verify the accuracy of this method, comparisons of the present results are made with results available in the open literature. Free vibrations of cylindrical shells and annular plates with FGM are treated as special cases. Results are also presented for carbon nanotubes reinforced (CNTR) composite cylindrical shells and annular plates. It is found that the convergence and accuracy of the present DSC method is very good for vibration problem of shells with functionally graded materials (FMG) and CNTR functionally graded materials.

Free vibration of carbon nanotubes reinforced (CNTR) and functionally graded shells and plates based on FSDT via discrete singular convolution method

The free vibration behavior of quadrilateral laminated thin-to-moderately thick plates with carbon nanotube reinforced composite (CNTRC) layers is studied. The governing equations are based on the first-order shear deformation theory (FSDT). The solution procedure is based on transforming the governing differential equations from an arbitrary straight-sided physical domain to a regular computational one, and discretization of the spatial derivatives by employing the differential quadrature method (DQM) as an efficient and accurate numerical tool. Four different profiles of single walled carbon nanotubes (SWCNTs) distribution through the thickness of layers are considered, which are uniformly distributed (UD) and three others are functionally graded (FG) distributions. The fast rate of convergence of the presented approach is numerically demonstrated and to show its high accuracy, wherever possible comparison studies with the available results in the open literature are performed. Then, the effects of volume fraction of carbon nanotubes (CNTs), geometrical shape parameters, thickness-to-length and aspect ratios, different kinds of CNTs distribution along the layers thickness and different boundary conditions on the natural frequencies of laminated plates are studied.

A.R. Zarei

Papers

Free vibration of quadrilateral laminated plates with carbon nanotube reinforced composite layers