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Formulas For Natural Frequency And Mode Shape

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

Nonlinear bending of functionally graded porous micro/nano-beams reinforced with graphene platelets based upon nonlocal strain gradient theory

By means of Non-Uniform Rational B-Splines (NURBS) curves, it is possible to describe arbitrary shapes with holes and discontinuities. These peculiar shapes can be taken into account to describe the reference domain of several nanoplates, where a nanoplate refers to a flat structure reinforced with Carbon Nanotubes (CNTs). In the present paper, a micromechanical model based on the agglomeration of these nanoparticles is considered. Indeed, when this kind of reinforcing phase is inserted into a polymeric matrix, CNTs tend to increase their density in some regions. Nevertheless, some nanoparticles can be still scattered within the matrix. The proposed model allows to control the agglomeration by means of two parameters. In this way, several parametric studies are presented to show the influence of this agglomeration on the free vibrations. The considered structures are characterized also by a gradual variation of CNTs along the plate thickness. Thus, the term Functionally Graded Carbon Nanotubes (FG-CNTs) is introduced to specify these plates. Some additional parametric studies are also performed to analyze the effect of a mesh distortion, by considering several geometric and mechanical configurations. The validity of the current methodology is proven through a comparative assessment of our results with those available from the literature or obtained with different numerical approaches, such as the Finite Element Method (FEM). The strong form of the equations governing a plate is solved by means of the Generalized Differential Quadrature (GDQ) method.

Free vibration analysis of arbitrarily shaped Functionally Graded Carbon Nanotube-reinforced plates

Closed form solution for a nonlocal strain gradient rod in tension

As the parallel to the advancement of technology in nano-sizes, the importance of nanotubes is rising every day. The mostly worked and used nanotubes are Carbon Nanotubes (CNT) due to their superior mechanical and electrical properties. On the other hand, the technology always needs better materials with superior mechanical, electrical conductivity and thermal properties. After a couple years of working with Carbon nanotubes, scientists have discovered different types of nanotube such boron nitride and Silicon carbide nanotubes (SiCNTs). In this work, the stability of the Silicon carbide nanotube is investigated in the static buckling case with surface effect. Nonlocal continuum theory is also used in order to see the difference between two higher-order elasticity theories. The stability of nanotubes has an important role since it is used in high-tech equipment. Buckling behavior of SiCNTs is discussed by using the continuum model based on the Euler-Bernoulli beam theory for different boundary conditions in conjunctions with the surface effect and nonlocal elasticity theory. The harmonic differential quadrature method (HDQ) is used for numerical simulations. Some parametric values for critical buckling loads have been obtained with different geometrical quantities of SiCNTs. The size effects on results have been also investigated by the surface elasticity and Eringen's nonlocal elasticity parameters.

Buckling analysis of Silicon carbide nanotubes (SiCNTs) with surface effect and nonlocal elasticity using the method of HDQ

DSC method for buckling analysis of boron nitride nanotube (BNNT) surrounded by an elastic matrix

The present study deals with buckling analysis of simply supported conical panels based on the Donnell's shell theory. Different material properties have been considered such as isotropic, composite laminated and functionally graded (FG). The governing differential equation for buckling of laminated conical panel is derived. These equations are discrete using method of discrete singular convolution (DSC). Shannon's delta kernel is used for trial functions. To check the presented DSC method and computer program, the critical buckling loads for isotropic and composite conical panels are calculated which compare very well with earlier available results. The effect of some geometric parameters and material parameters on critical buckling of panels is also investigated. It is noticed that the present DSC methodology can predict accurately the buckling loads of conical panels.

Determination of critical buckling loads of isotropic, FGM and laminated truncated conical panel

Abstract In the present manuscript, free vibration response of circular cylindrical shells with functionally graded material (FGM) is investigated. The method of discrete singular convolution (DSC) is used for numerical solution of the related governing equation of motion of FGM cylindrical shell. The constitutive relations are based on the Love’s first approximation shell theory. The material properties are graded in the thickness direction according to a volume fraction power law indexes. Frequency values are calculated for different types of boundary conditions, material and geometric parameters. In general, close agreement between the obtained results and those of other researchers has been found.

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Kadir Mercan

Papers

Buckling analysis of Silicon carbide nanotubes (SiCNTs) with surface effect and nonlocal elasticity using the method of HDQ

DSC method for buckling analysis of boron nitride nanotube (BNNT) surrounded by an elastic matrix

Determination of critical buckling loads of isotropic, FGM and laminated truncated conical panel

Vibration analysis of FG cylindrical shells with power-law index using discrete singular convolution technique

Frequencies of FGM shells and annular plates by the methods of discrete singular convolution and differential quadrature methods