• Coupled systems mechanics
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• v.6 no.2
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• pp.207-227
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• 2017

In this paper Timoshenko beam theory is employed to investigate the vibration characteristics of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) Beams with a stiff core in thermal environment. The material characteristic of carbon nanotubes (CNT) are supposed to change in the thickness direction in a functionally graded form. They can also be calculated through a micromechanical model where the CNT efficiency parameter is determined by matching the elastic modulus of CNTRCs calculated from the rule of mixture with those gained from the molecular dynamics simulations. The differential transform method (DTM) which is established upon the Taylor series expansion is one of the effective mathematical techniques employed to the differential governing equations of sandwich beams. Effects of carbon nanotube volume fraction, slenderness ratio, core-to-face sheet thickness ratio, different thermal environment and various boundary conditions on the free vibration characteristics of FG-CNTRC sandwich beams are studied. It is observed that vibration response of FG-CNTRC sandwich beams is prominently influenced by these parameters.

• Steel and Composite Structures
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• v.19 no.5
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• pp.1259-1277
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• 2015

In this work, a trigonometric refined beam theory for the bending, buckling and free vibration analysis of carbon nanotube-reinforced composite (CNTRC) beams resting on elastic foundation is developed. The significant feature of this model is that, in addition to including the shear deformation effect, it deals with only 3 unknowns as the Timoshenko beam (TBM) without including a shear correction factor. The single-walled carbon nanotubes (SWCNTs) are aligned and distributed in polymeric matrix with different patterns of reinforcement. The material properties of the CNTRC beams are assessed by employing the rule of mixture. To examine accuracy of the present theory, several comparison studies are investigated. Furthermore, the effects of different parameters of the beam on the bending, buckling and free vibration responses of CNTRC beam are discussed.

• Advances in aircraft and spacecraft science
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• v.5 no.1
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• pp.107-128
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• 2018

Thermo-mechanical vibration of sandwich beams with a stiff core and face sheets made of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) is investigated within the framework of Timoshenko beam theory. The material properties of FG-CNTRC are supposed to vary continuously in the thickness direction and are estimated through the rule of mixture and are considered to be temperature dependent. The governing equations and boundary conditions are derived by using Hamilton's principle and are solved using an efficient semi-analytical technique of the differential transform method (DTM). Comparison between the results of the present work and those available in literature shows the accuracy of this method. A parametric study is conducted to study the effects of carbon nanotube volume fraction, slenderness ratio, core-to-face sheet thickness ratio, and various boundary conditions on free vibration behavior of sandwich beams with FG-CNTRC face sheets. It is explicitly shown that the vibration characteristics of the curved nanosize beams are significantly influenced by the surface density effects.

• Advances in nano research
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• v.16 no.3
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• pp.251-263
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• 2024

This article investigates the free vibration behavior of carbon nanotube reinforced composite (CNTRC) beams embedded using variational analytical methods and artificial neural networks (ANN). The material properties of layered functionally graded CNTRC (FG-CNTRC) beams are estimated using nonlocal parameters modified power-law with different types of CNT distributions through the thickness direction of the beam. Adopting Eringen's nonlocal elasticity theory to capture the small size effects, the nonlocal governing equations are derived and solved using the analytical method. And also, the problem was analyzed using the ANN method. The architecture of the proposed ANN model is 3-9-1. In the experiments, we used 112 different data to predict the natural frequency using ANN. Based on the nonlocal differential constitutive relations of Eringen, the equations of motion as well as the boundary conditions of the beam are derived using Hamilton's principle. The classical beam theory is used to formulate a governing equation for predicting the free vibration of laminated CNTRC beams. According to the experimental results, the prediction ability of the ANN model is very good and the natural frequency can be predicted in ANN without attempting any experiments.

• Steel and Composite Structures
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• v.46 no.3
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• pp.335-344
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• 2023

This investigation presents nonlinear free vibration of a carbon nanotube reinforced composite beam based on the Von Kármán nonlinearity and the Euler-Bernoulli beam theory The material properties of the structure is considered as made of a polymeric matrix by reinforced carbon nanotubes according to different material distributions. The governing equations of the nonlinear vibration problem is delivered by using Hamilton's principle and the Galerkin's decomposition technique is utilized to discretize the governing nonlinear partial differential equation to nonlinear ordinary differential equation and then is solved by using of multiple time scale method. The nonlinear natural frequency and the nonlinear free response of the system is obtained with the effect of different patterns of reinforcement.

• Steel and Composite Structures
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• v.29 no.3
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• pp.405-422
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• 2018

In this research, experimental tensile test and manufacturing of carbon nanotube reinforced composite beam (CNTRC) is presented. Also, bending, buckling, and vibration analysis of CNTRC based on various beam theories such as Euler-Bernoulli, Timoshenko and Reddy beams are considered. At first, the experimental tensile tests are carried out for CNTRC and composite beams in order to obtain mechanical properties and then using Hamilton's principle the governing equations of motion are derived for Euler Bernoulli, Timoshenko and Reddy theories. The results have a good agreement with the obtained results by similar researches and it is shown that adding just two percent of carbon nanotubes increases dimensionless fundamental frequency and critical buckling load as well as decreases transverse deflection of composite beams. Also, the influences of different manufacturing processes such as hand layup and industrial methods using vacuum pump on composite properties are investigated. In these composite beams, glass fibers used in an epoxy matrix and for producing CNTRC, CNTs are applied as reinforcement particles. Applying two percent of CNTs leads to increase the mechanical properties and increases natural frequencies and critical buckling load and decreases deflection. The obtained natural frequencies and critical buckling load by theoretical method are higher than other methods, because there are some inevitable errors in industrial and hand layup method. Also, the minimum deflection occurs for theoretical methods, in bending analysis. In this study, Young's and shear modulli as well as density are obtained by experimental test and have not been used from the results of other researches. Then the theoretical analysis such as bending, buckling and vibration are considered by using the obtained mechanical properties of this research.

• Advances in aircraft and spacecraft science
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• v.4 no.5
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• pp.585-611
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• 2017

This article covenants with the post buckling witticism of carbon nanotube reinforced composite (CNTRC) beam supported with an elastic foundation in thermal atmospheres with arbitrary assumed random system properties. The arbitrary assumed random system properties are be modeled as uncorrelated Gaussian random input variables. Unvaryingly distributed (UD) and functionally graded (FG) distributions of the carbon nanotube are deliberated. The material belongings of CNTRC beam are presumed to be graded in the beam depth way and appraised through a micromechanical exemplary. The basic equations of a CNTRC beam are imitative constructed on a higher order shear deformation beam (HSDT) theory with von-Karman type nonlinearity. The beam is supported by two parameters Pasternak elastic foundation with Winkler cubic nonlinearity. The thermal dominance is involved in the material properties of CNTRC beam is foreseen to be temperature dependent (TD). The first and second order perturbation method (SOPT) and Monte Carlo sampling (MCS) by way of CO nonlinear finite element method (FEM) through direct iterative way are offered to observe the mean, coefficient of variation (COV) and probability distribution function (PDF) of critical post buckling load. Archetypal outcomes are presented for the volume fraction of CNTRC, slenderness ratios, boundary conditions, underpinning parameters, amplitude ratios, temperature reliant and sovereign random material properties with arbitrary system properties. The present defined tactic is corroborated with the results available in the literature and by employing MCS.

• Computers and Concrete
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• v.34 no.2
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• pp.179-193
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• 2024

The bending and buckling effect for carbon nanotube-reinforced composite (CNTRC) beams can be evaluated by developing the theory of third shear deformation (TSDT). This study examines beams supported by viscoelastic foundations, where single-walled carbon nanotubes (SWCNTs) are dispersed and oriented within a polymer matrix. Four patterns of reinforcement are used for the CNTRC beams. The rule of mixtures is assessed for the material properties of CNTRC beams. The effective functionally graded materials (FGM) properties are studied by considering three different uneven distribution types of porosity. The damping coefficient is considered to investigate the viscosity effect on the foundation in addition to Winkler's and Pasternak's parameters. The accuracy of the current theory is inspected with multiple comparison works. Moreover, the effects of different beam parameters on the CNTRC beam bending and buckling over a viscoelastic foundation are discussed. The results demonstrated that the O-beam is the weakest type of CNTRC beam to resist buckling and flexure loads, whereas the X-beam is the strongest. Moreover, it is indicated that the presence of porosity in the beams decreases the stiffness and increases deflection. In comparison, the deflection was reduced in the presence of a viscoelastic foundation.

• Structural Engineering and Mechanics
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• v.66 no.4
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• pp.495-504
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• 2018

The current study is dedicated to study the thermal effects of wave propagation in beams, reinforced by carbon nanotubes (CNT). Beams, made up of carbon nanotube reinforced composite (CNTRC) are the future materials in various high tech industries. Herein a Winkler elastic foundation is assumed in order to make the model more realistic. Mostly, CNTs are pervaded in cross section of beam, in various models. So, it is tried to use four of the most profitable reconstructions. The homogenization of elastic and thermal properties such as density, Yong's module, Poisson's ratio and shear module of CNTRC beam, had been done by the demotic rule of mixture to homogenize, which gives appropriate traits in such settlements. To make this investigation, a perfect one, various shear deformation theories had been utilized to show the applicability of this theories, in contrast to their theoretical face. The reigning equation had been derived by extended Hamilton principle and the culminant equation solved analytically by scattering relations for propagation of wave in solid bodies. Results had been verified by preceding studies. It is anticipated that current results can be applicable in future studies.

• Smart Structures and Systems
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• v.30 no.2
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• pp.135-143
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• 2022

The object of this paper is to investigate the free vibration behavior under the effect of carbon nanotube distribution in functionally graded carbon nanotube-reinforced composite (FG-CNTRC) by using higher-order shear deformation theories. In this work, we present a novel distribution method for carbon nanotubes in the polymer matrix by using a new exponential power law distribution of carbon nanotube volume fraction. It is assumed that the SWCNTs are aligned along the beam axial direction and the distribution of the SWCNTs may vary through the thickness of the beam with different patterns of reinforcement. The rule of mixtures is used in order to obtain material properties of the CNTRC beams. Hamilton's principle is used in deriving the equations of motion. The validity of the free Vibration results is examined by comparing them with those of the known data in the literature. The results that obtained indicate that the carbon nanotube volume fraction distribution play a very important role on the free vibrations characteristics of the CNTRC beam.