• Steel and Composite Structures
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• v.50 no.2
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• pp.135-148
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• 2024

This paper analytically investigates the free vibration analysis of functionally graded-carbon nanotube reinforced composite (FG-CNTRC) plates by dynamic stiffness method (DSM). The properties of CNTRC are determined with the extended rule of mixture. The governing differential equations of motion based on the first-order shear deformation theory of CNTRC plate are derived using Hamilton's principle. The FG-CNTRC plates are studied for a uniform and two different distributions of carbon nanotubes (CNTs). The accuracy and performance of the DSM are compared with the results obtained from closed closed-form and semi-analytical solution methods in previous studies. In this study, the effects of boundary condition, distribution type of CNTs, plate aspect ratio, plate length to thickness ratio, and different values of CNTs volume fraction on the natural frequencies of the FG-CNTRC plates are investigated. Finally, various natural frequencies of the plates in different conditions are provided as a benchmark for comparing the accuracy and precision of the other analytical and numerical methods.

• Advances in nano research
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• v.16 no.4
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• pp.413-426
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• 2024

This paper investigates the dynamic behavior of a simply supported viscoelastic plate made of functionally graded carbon nanotube reinforced composite under dynamic loading. Carbon nanotubes are distributed in 5 different shapes: U, V, A, O and X, depending on the shape they form through the thickness of the plate. The displacement fields are derived in the Laplace domain using a higher-order shear deformation theory. Equations of motion are obtained through the application of the energy method and Hamilton's principle. The resulting equations of motion are solved using Navier's method. Transforming the Laplace domain displacements into the time domain involves Durbin's modified inverse Laplace transform. To validate the accuracy of the developed algorithm, a free vibration analysis is conducted for simply supported plate made of functionally graded carbon nanotube reinforced composite and compared against existing literature. Subsequently, a parametric forced vibration analysis considers the influence of various parameters: volume fractions of carbon nanotubes, their distributions, and ratios of instantaneous value to retardation time in the relaxation function, using a linear standard viscoelastic model. In the forced vibration analysis, the dynamic distributed load applied to functionally graded carbon nanotube reinforced composite viscoelastic plate is obtained in terms of double trigonometric series. The study culminates in an examination of maximum displacement, exploring the effects of different carbon nanotube distributions, volume fractions, and ratios of instantaneous value to retardation times in the relaxation function on the amplitudes of maximum displacements.

• Steel and Composite Structures
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• v.12 no.6
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• pp.491-504
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• 2012

In this paper, the nonlinear cylindrical bending of simply supported, functionally graded nanocomposite plates reinforced by single-walled carbon nanotubes (SWCNTs), is studied. The plates are subjected to uniform pressure loading in thermal environments and their geometric nonlinearity is introduced in the strain-displacement equations based on Von-Karman assumptions. The material properties of SWCNTs are assumed to be temperature-dependent and are obtained from molecular dynamics simulations. The material properties of functionally graded carbon nanotube-reinforced composites (FG-CNTCRs) are assumed to be graded in the thickness direction, and are estimated through a micromechanical model. The governing equations are reduced to linear differential equation with nonlinear boundary conditions yielding a simple solution procedure. Numerical results are presented to show the effect of the material distribution on the deflections and stresses.

• Computers and Concrete
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• v.19 no.6
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• pp.677-687
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• 2017

The nonlinear buckling response of nano composite anti-symmetric functionally graded polymeric microplate reinforced by single-walled carbon nanotubes (SWCNTs) rested on orthotropic elastomeric foundation with temperature dependent properties is investigated. For the carbon-nanotube reinforced composite (CNTRC) microplate, a uniform distribution (UD) and four types of functionally graded (FG) distribution are considered. Based on orthotropic Mindlin plate theory, von Karman geometric nonlinearity and Hamilton's principle, the governing equations are derived. Generalized differential quadrature method (GDQM) is employed to calculate the non-linear buckling response of the plate. Effects of FG distribution type, elastomeric foundation, aspect ratio (thickness to width ratio), boundary condition, orientation of foundation orthotropy and temperature are considered. The results are validated. It is found that the critical buckling load without elastic medium is significantly lower than considering Winkler and Pasternak medium.

• Steel and Composite Structures
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• v.28 no.4
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• pp.495-508
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• 2018

In this paper, the effect of matrix cracks on the buckling of a hybrid laminated plate is investigated. The plate is composed of carbon nanotube reinforced functionally graded (CNTR-FG) layers and conventional fiber reinforced composite (FRC) layers. Different distributions of single walled carbon nanotubes (SWCNTs) through the thickness of layers are considered. The cracks are modeled as aligned slit cracks across the ply thickness and transverse to the laminate plane, and the distribution of cracks is assumed statistically homogeneous corresponding to an average crack density. The first-order shear deformation theory (FSDT) is employed to incorporate the effects of rotary inertia and transverse shear deformation, and the meshless kp-Ritz method is used to obtain the buckling solutions. Detailed parametric studies are conducted to investigate the effects of matrix crack density, CNTs distributions, CNT volume fraction, plate aspect ratio and plate length-to-thickness ratio, boundary conditions and number of layers on buckling behaviors of hybrid laminated plates containing CNTR-FG layers.

• Steel and Composite Structures
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• v.14 no.4
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• pp.335-347
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• 2013

In this paper, the nonlinear cylindrical bending behavior of functionally graded nanocomposite plates reinforced by single-walled carbon nanotubes (SWCNTs) is studied using an efficient and simple refined theory. This theory is based on assumption that the in-plane and transverse displacements consist of bending and shear components in which the bending components do not contribute toward shear forces and, likewise, the shear components do not contribute toward bending moments. The material properties of SWCNTs are assumed to be temperature-dependent and are obtained from molecular dynamics simulations. The material properties of functionally graded carbon nanotube-reinforced composites (FG-CNTCRs) are assumed to be graded in the thickness direction, and are estimated through a micromechanical model. The fundamental equations for functionally graded nanocomposite plates are obtained using the Von-Karman theory for large deflections and the solution is obtained by minimization of the total potential energy. The numerical illustrations concern the nonlinear bending response of FG-CNTRC plates under different sets of thermal environmental conditions, from which results for uniformly distributed CNTRC plates are obtained as comparators.

• Steel and Composite Structures
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• v.23 no.5
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• pp.529-541
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• 2017

In the present study, vibration analysis of functionally graded carbon nanotube reinforced composite (FGCNTRC) plate moving in two directions is investigated. Various types of shear deformation theories are utilized to obtain more accurate and simplest theory. Single-walled carbon nanotubes (SWCNTs) are selected as a reinforcement of composite face sheets inside Poly methyl methacrylate (PMMA) matrix. Moreover, different kinds of distributions of CNTs are considered. Based on extended rule of mixture, the structural properties of composite face sheets are considered. Motion equations are obtained by Hamilton's principle and solved analytically. Influences of various parameters such as moving speed in x and y directions, volume fraction and distribution of CNTs, orthotropic viscoelastic surrounding medium, thickness and aspect ratio of composite plate on the vibration characteristics of moving system are discussed in details. The results indicated that thenatural frequency or stability of FGCNTRC plate is strongly dependent on axially moving speed. Moreover, a better configuration of the nanotube embedded in plate can be used to increase the critical speed, as a result, the stability is improved. The results of this investigation can be used in design and manufacturing of marine vessels and aircrafts.

• Steel and Composite Structures
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• v.29 no.5
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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.

• Steel and Composite Structures
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• v.22 no.2
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• pp.277-299
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• 2016

In this paper, free vibration, forced vibration, resonance and stress wave propagation behavior in nanocomposite plates reinforced by wavy carbon nanotube (CNT) are studied by a mesh-free method based on first order shear deformation theory (FSDT). The plates are resting on Winkler-Pasternak elastic foundation and subjected to periodic or impact loading. The distributions of CNTs are considered functionally graded (FG) or uniform along the thickness and their mechanical properties are estimated by an extended rule of mixture. In the mesh-free analysis, moving least squares (MLS) shape functions are used for approximation of displacement field in the weak form of motion equation and the transformation method is used for imposition of essential boundary conditions. Effects of CNT distribution, volume fraction, aspect ratio and waviness, and also effects of elastic foundation coefficients, plate thickness and time depended loading are examined on the vibrational and stresses wave propagation responses of the nanocomposite plates reinforced by wavy CNT.

• Computers and Concrete
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• v.26 no.2
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• pp.137-150
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• 2020

In this paper, the bending behavior of single-walled carbon nanotube-reinforced composite (CNTRC) laminated plates is studied using various shear deformation plate theories. Several types of reinforcement material distributions, a uniform distribution (UD) and three functionally graded distributions (FG), are inspected. A generalized higher-order deformation plate theory is utilized to derive the field equations of the CNTRC laminated plates where an analytical technique based on Navier's series is utilized to solve the static problem for simply-supported boundary conditions. A detailed numerical analysis is carried out to examine the influence of carbon nanotube volume fraction, laminated composite structure, side-to-thickness, and aspect ratios on stresses and deflection of the CNTRC laminated plates.