A Dynamic Analysis of Randomly Oriented Functionally Graded Carbon Nanotubes/Fiber-Reinforced Composite Laminated Shells with Different Geometries (original) (raw)
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Journal of Composites Science, 2019
In this paper, a new four-variable refined shell theory is developed for free vibration analysis of multi-layered functionally graded carbon nanotube-reinforced composite (FG-CNTRC) doubly curved shallow shell panels. The theory has only four unknowns and satisfies zero stress conditions at the free surfaces without correction factor. Five different types of carbon nanotube (CNTs) distribution through the thickness of each FG-CNT layer are considered. Governing equations of simply supported doubly curved FG-CNTRC panels are derived from Hamilton’s principle. The resultant eigenvalue system is solved to obtain the frequencies and mode shapes of the anti-symmetric cross-ply laminated panels by using the Navier solution. The numerical results in the comparison examples have proved the accuracy and efficiency of the developed model. Detailed parametric studies have been carried out to reveal the influences of CNTs volume fraction, CNTs distribution, CNTs orientation, dimension ratios an...
Free Vibration of Grid-Stiffened Composite Cylindrical Shell Reinforced with Carbon Nanotubes
Mechanics of Composite Materials, 2020
A linear free vibration analysis is presented for computing the natural frequencies of a grid-stiffened carbonnanotube-reinforced composite cylindrical shell. The carbon nanotubes (CNTs) are supposed to be oriented unidirectionally across the shell thickness, and the elastic moduli of the CNT-reinforced polymer composite are calculated using a modified rule of mixtures. In order to obtain the equivalent stiffness parameters of the grid-stiffened cylindrical shell, the smeared stiffness method is employed. The stiffeners are assumed to support the transverse shear loads, bending moments, and axial loads. An analytical method based on the first-order shear deformation theory is used. To validate the results obtained, a 3-D finite-element model is employed using the ABAQUS CAE software. Recently, many computational methods have been developed for investigating the vibration behavior of composite cylindrical shells. Soldatos [7] presented a review of three dimensional dynamic analyses of circular cylinders and cylindrical shells.
Nanomaterials
In this work, we discuss the free vibration behavior of thin-walled composite shell structures reinforced with carbon nanotubes (CNTs) in a nonlinear setting and resting on a Winkler–Pasternak Foundation (WPF). The theoretical model and the differential equations associated with the problem account for different distributions of CNTs (with uniform or nonuniform linear patterns), together with the presence of an elastic foundation, and von-Karman type nonlinearities. The basic equations of the problem are solved by using the Galerkin and Grigolyuk methods, in order to determine the frequencies associated with linear and nonlinear free vibrations. The reliability of the proposed methodology is verified against further predictions from the literature. Then, we examine the model for the sensitivity of the vibration response to different input parameters, such as the mechanical properties of the soil, or the nonlinearities and distributions of the reinforcing CNT phase, as useful for des...
Aerospace Science and Technology, 2017
This paper presents a new approach-using analytical solution to investigate nonlinear dynamic response and vibration of imperfect functionally graded carbon nanotube reinforced composite (FG-CNTRC) double curved shallow shells. The double curved shallow shells are reinforced by single-walled carbon nanotubes (SWCNTs) which vary according to the linear functions of the shell thickness. The shells are resting on elastic foundations and subjected to blast load and temperature. The shell's effective material properties are assumed to depend on temperature and estimated through the rule of mixture. By applying higher order shear theory, Galerkin method and fourth-order Runge-Kutta method and the Airy stress function, nonlinear dynamic response and natural frequency for thick imperfect FG-CNTRC double curved shallow shells are determined. In numerical results, the influences of geometrical parameters, elastic foundations, initial imperfection, temperature increment and nanotube volume fraction on the nonlinear vibration of the FG-CNTRC double curved shallow shells are investigated. The proposed results are validated by comparing with those of other authors.
Journal of Building Materials and Structures
The main interest of this paperwork is to examinate the dynamic behavior (free vibrational response) of carbon nanotubes (CNT) composite beams standing on an elastic foundation of Winkler-Pasternak’s. The affected beam consists of a polymer matrix reinforced with single-wall carbon nanotubes (SWCNT’s), in which, a large number of CNT’s reinforcement of infinite length are distributed in a linear elastic polymer matrix. In this study the CNT’s are considered either aligned or randomly oriented on the matrix. A refined high-order beam theory (RBT) is adopted in the present analysis using a new shape function. The refined beam theory which is summarized by differentiating the displacement along the beam transverse section into shear and bending components, initially the material properties of the composite beam (CNTRC) are estimated using the Mori-Tanaka’s method. The beam is considered simply supported on the edge-lines. NAVIER’s solutions are proposed to solve the boundary conditions...
In this paper, a refined plate theory is applied to investigate the free vibration analysis of functionally graded nanocomposite sandwich plates reinforced by randomly oriented straight carbon nanotube (CNT). The refined shear deformation plate theory (RSDT) uses only four independent unknowns and accounts for a quadratic variation of the transverse shear strains across the thickness, and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. The motion equations are derived using Hamilton's energy principle and Navier's method and is applied to solve this equation. The sandwich plates are considered simply supported and resting on a Winkler/Pasternak elastic foundation. The material properties of the functionally graded carbon nanotube reinforced composites (FG-CNTRCs) are graded along the thickness and estimated though the Mori-Tanaka method. Effects of CNT volume fraction, geometric dimensions of sandwich plate, and elastic foundation parameters are investigated on the natural frequency of the FG-CNTRC sandwich plates.
Mechanics of Composite Materials, 2021
Equilibrium equations of a rib grid-stiffened composite cylindrical shell reinforced with carbon nanotubes (CNTs) are derived based on the first-order shear deformation theory considering the effect of shear deformation and moment of inertia. The distribution of CNTs across the shell thickness is assumed uniform, and the elastic modulus of the CNT-reinforced polymer is calculated using the rule of mixtures. In order to determine the equivalent stiffness of the grid-stiffened composite cylindrical shell, the smeared stiffness method is used. Equilibrium equations for free and forced vibration of the rib grid-stiffened composite cylindrical shell are solved using the Galerkin method, and the effects of grid ribs on the dynamic response of the shell are investigated. The results found indicate that the use of circumferential ribs in the structure can increase the frequency, change the fundamental mode shape, and reduce the radial displacement by ~12% (especially in higher modes). In addition, the results demonstrate that a 5-degree increase in the angle of helical ribs can decrease the radial displacement linearly by 5%. Eventually, the corresponding outcomes reveal that the rib thickness and presence of CNTs may significantly increase the natural frequencies and decrease the radial displacement of such shells.
DOAJ (DOAJ: Directory of Open Access Journals), 2013
In this study, based on the three-dimensional theory of elasticity, free vibration characteristics of nanocomposite cylindrical panels reinforced by single-walled carbon nanotubes are considered. The carbon nanotube reinforced (CNTRC) cylindrical panels have smooth variation of carbon nanotube (CNT) fraction in the radial direction and the material properties are estimated by the extended rule of mixture. Suitable displacement functions that identically satisfy the boundary conditions at the simply supported edges are used to reduce the equilibrium equations to a set of coupled ordinary differential equations with variable coefficients, which can be solved by a generalized differential quadrature (GDQ) method. The results show that the kind of distribution and volume fraction of CNT have a significant effect on the normalized natural frequency.
Composites Part B: Engineering, 2019
This work studies the agglomeration effect of continuously graded single-walled carbon nanotubes (SWCNTs) on the vibration of SWCNTs/fiber/polymer/metal laminates cylindrical shell. The strain-displacement relations are applied according to the Kirchhoff Love's first approximation shell theory, whereas the dimensionless frequencies of the structure are obtained by means of the beam modal function model. Fiber, carbon nanotubes (CNTs), polymer matrix and metal are four phases constituting the agglomerated CNTs/fiber/polymer/metal laminate (CNTFPML) cylindrical shell. In the first step, we introduce the CNTs randomly within the matrix, such that the volume fraction can be assumed to be continuously graded in the thickness direction. We determine the effect of the CNTs agglomeration on the elastic properties of CNTreinforced composites, by means of the Eshelby-Mori-Tanaka approach here applied on an equivalent fiber. In the second step, the fiber is introduced as reinforcement phase in the CNTreinforced composite. Finally, the adhesive fiber prepreg is combined with the thin metal layers. Thus, we study the sensitivity of the vibration behavior of the cylindrical shell to the following input parameters, namely: the CNTs agglomeration and distribution, the mass and volume fractions of the fiber, the boundary condition and lay-ups.
This paper deals with the free vibration and buckling analysis of Nanotube) reinforced FG (Functionally Graded)Timoshenko properties of the nano-composite distributions which includ (FG-Χ, FG-V and FG-Λ) of the volume fraction of CNTs through beam. Mori–Tanaka method resulting composite beam. Timoshenko beam theory is behaviour of the beam. The finite element method is employed to discretize the model and obtain a numerical approximation of the motion equation. Free vibration analysis is carried out to obtain the natural frequencies of the beam for different conditions. Critical buckling load are obtained for different boundary conditions. Effects of CNTs volume fraction, orientation, distribution, slenderness ratios and critical buckling load are also investigated. The results addition of CNT and its distribution has a substantial as well as on the dynamic composite beam have better dynamic responses conventional composite beams. deals with the free vibration and buckling analysis of Nanotube) reinforced FG (Functionally Graded)Timoshenko beams. Material composite are obtained by considering various includes uniform distribution (UD) and some FG) of the volume fraction of CNTs through the thickness of the method is employed for finding the material properties of the resulting composite beam. Timoshenko beam theory is employed to study behaviour of the beam. The finite element method is employed to discretize the model and obtain a numerical approximation of the motion equation. Free vibration analysis is carried out to obtain the natural frequencies of the beam for different conditions. Critical buckling load are obtained for nano-composite different boundary conditions. Effects of CNTs volume fraction, orientation, , slenderness ratios and boundary conditions on both natural frequency ical buckling load are also investigated. The results clearly indicate that the distribution has a substantial effect on the elastic properties as well as on the dynamic characteristics of beam. It is also perceived that the beam have better dynamic responses as compared to the existing conventional composite beams. deals with the free vibration and buckling analysis of CNT (Carbon beams. Material various type of CNTs FG distributions the thickness of the material properties of the to study the dynamic behaviour of the beam. The finite element method is employed to discretize the model and obtain a numerical approximation of the motion equation. Free vibration analysis is carried out to obtain the natural frequencies of the beam for different boundary composite beams with different boundary conditions. Effects of CNTs volume fraction, orientation, and boundary conditions on both natural frequency indicate that the effect on the elastic properties of beam. It is also perceived that the nano-compared to the existing