جستجوی مقالات مرتبط با کلیدواژه « Graphene platelets » در نشریات گروه « مکانیک »

In this work, free vibrations of a composite beam is investigated. Considered composite beam is assumed with the presence of pre-twist. One of the beam is without twist while the other end of the beam has the maximum twist angle. Twist rate in the beam is assumed to be non-constant where a higher order polynomial variation of twist angle is assumed. Composite beam of this study is composed of a number of layers where each layer of the beam is reinforced with graphene platelets. Layers may have different amount of graphene which leads to the functionally graded composite laminated beam with pre-twist. Elasticity modulus of the beam is estimated by means of the Halpin-tsai rule while the mass density and Poisson's ratio are assumed using the simple rule of mixtures approach. Timoshenko beam theory is adopted to estimate the displacement field in the beam. Due to the present of twist, five degrees of freedom containing three displacements and two cross-section rotations are considered. Using the Hamilton principle and with the aid of the Ritz method, the equations of motion are discretized. Shape functions of the Ritz method are constructed by means of the Chebyshev polynomials. This set of functions are orthogonal and has high rate of convergency. Matrix representation of the governing equations is obtained using the Chebyshev-Ritz method. The governing equations of the free vibration motion are established and solved as an eigenvalue problem. Results of this study cover the case of free vibration of a graphene platelet reinforced composite laminated pre-twisted beam. At first results of this study are validated with the available data in the open literature and also the required number of shape functions in the Ritz method are estimated through the convergence studies. After that using parametric studies, the influences of different parameters such as number of layers of composite, boundary conditions, twist angle, twist rate, graphene weight fraction and their pattern are explored. Numerical results of this study show that by increasing the weight fraction of graphene platelets, natural frequencies of the beam are enhanced. Also through adoption of a proper pattern, the natural frequencies in the beam may be controlled. The effect of twist angle on the frequencies of the beam is shown. It is depicted that increasing the twist angle may increase/decrease the frequencies depending on the mode number.

This paper analyses the free vibration behavior of truncated conical panels made of a polymeric matrix reinforced with graphene platelets (GPLs). Distribution of GPLs across the thickness of the panel is considered uniform or functionally graded. The mechanical properties of the composite have been calculated using the modified Halpin-Tsai model and the rule of mixtures. Considering strain- displacement relationships as well as first order shear deformation theory (FSDT) of shells, the governing equations have been derived using Hamilton principle. In the next step, to obtain the natural frequencies of the structure, the governing equations have been discretized and solved using Chebyshev polynomial of the first kind and Ritz method which is suitable for structures with different boundary conditions. Comparison of the numerical results of this study with other articles show that the numerical results are highly accurate. Also, parametric studies have been performed to investigate the effect of GPLs distribution patterns, GPLs weight fraction, different boundary conditions, different geometric parameters on the vibrational behavior of the conical panel. The results show that the use of GPLs as a reinforcement for the nanocomposite panel is effective to improve the vibrational behavior and greatly increases the stiffness and resistance of the panel.

The nonlinear bending analysis of a composite beam reinforced by graphene platelets (GPL) nanofillers having nonuniform distribution through the thickness, is presented. Governing nonlinear differential equations are derived based on the first order shear deformation theory with the aid of minimum potential energy principle. The nonlinear differential equations are solved using harmonic differential quadrature method (HDQM). The modified Halpin-Tsai model is implemented to determine the effective Young’s modulus of graphene platelet reinforced composite (GPLRC) beams. Moreover, the rule of mixture is used for definition of the effective Poisson’s ratio. At first, conventional nanocomposite beams are studied for evaluation of the applicability of the proposed method for nonlinear bending analyses. Then for the beams reinforced by graphene platelets, the effects of some parameters including boundary conditions, number of layers, weight fraction and distribution pattern of graphene platelet on the nonlinear bending characteristics of the GPLRC beams, are investigated. This study shows the capability of the proposed method to solve the nonlinear problems and to get the beams behavior under bending loading. In addition, by increasing the weight fraction of graphene platelets in the beam, the bending strength of the beam improves and the beam deflection decreases. Moreover, increasing the number of layers for GPLRC tends to smoother variation of stress through the beam thickness.

In this study, nonlinear vibrations of simply-supported pipes conveying fluid made of multilayer graphene reinforced composite materials have been investigated analytically and based on the Euler-Bernoulli beam theory. The constituent layers of the pipe wall thickness are considered to be made of polymer and graphene platelets and the reinforcing graphene platelets are varied by layers in the pipe wall thickness direction. Four different patterns for distribution of reinforcing graphene platelets, large deformations, and Von-Karman nonlinear strain field are considered. The nonlinear governing equations are derived by the Hamilton principle, they are converted to the ordinary differential equations by the Galerkin method and then are solved analytically using the homotopy analysis method. The variations of the first nonlinear natural frequency of the system with respect to the variation of initial amplitude, fluid velocity, fluid density, pipe length, and also time response of the nonlinear vibrations of the system are presented for different distribution patterns V, X, O and U of the graphene platelets. The results show that the first nonlinear natural frequency of the system for all distribution patterns of graphene platelets is decreased by an increase of pipe length, fluid velocity, and density but increasing the initial amplitude increases the first nonlinear natural frequency and also the distribution pattern V has the highest nonlinear frequency comparing with the other distribution patterns.