• Steel and Composite Structures
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• 제29권3호
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• pp.319-332
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• 2018

This paper investigates the free vibration of geometrically imperfect functionally graded car-bon nanotube-reinforced composite (FG-CNTRC) beams that are integrated with two sur-face-bonded piezoelectric layers and subjected to a combined action of a uniform temperature rise, a constant actuator voltage and an in-plane force. The material properties of FG-CNTRCs are assumed to be temperature-dependent and vary continuously across the thick-ness. A generic imperfection function is employed to simulate various possible imperfections with different shapes and locations in the beam. The governing equations that account for the influence of initial geometric imperfection are derived based on the first-order shear deformation theory. The postbuckling configurations of FG-CNTRC hybrid beams are determined by the differential quadrature method combined with the modified Newton-Raphson technique, after which the fundamental frequencies of hybrid beams in the postbuckled state are obtained by a standard eigenvalue algorithm. The effects of CNT distribution pattern and volume fraction, geometric imperfection, thermo-electro-mechanical load, as well as boundary condition are examined in detail through parametric studies. The results show that the fundamental frequency of an imperfect beam is higher than that of its perfect counterpart. The influence of geometric imperfection tends to be much more pronounced around the critical buckling temperature.

• Structural Engineering and Mechanics
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• 제64권3호
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• pp.381-390
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• 2017

Present paper deals with the large amplitude flexural vibration of carbon nanotube reinforced composite (CNTRC) plates. Distribution of CNTs as reinforcements may be uniform or functionally graded (FG). The equivalent material properties of the composite media are obtained according to a refined rule of mixtures which contains efficiency parameters. To account for the large deformations, von $K{\acute{a}}rm{\acute{a}}n$ type of geometrical nonlinearity is included into the formulation. The matrix representation of the governing equations is obtained according to the Ritz method where the basic shape functions are written in terms of the Chebyshev polynomials. Time dependency of the problem is eliminated by means of the Galerkin method and the resulting nonlinear eigenvalue problem is solved employing a direct displacement control approach. Results are obtained for completely clamped and completely simply supported plates. Results are first validated for the especial cases of FG-CNTRC and cross-ply laminated plates. Afterwards, parametric studies are given for FG-CNTRC plates with different boundary conditions. It is shown that, nonlinear frequencies are highly dependent to the volume fraction and dispersion profiles of CNTs. Furthermore, mode redistribution is observed in both simply supported and clamped FG-CNTRC plates.

• Steel and Composite Structures
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• 제19권3호
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• pp.713-733
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• 2015

In this paper, viscous fluid induced nonlinear free vibration and instability analysis of a functionally graded carbon nanotube-reinforced composite (CNTRC) cylindrical shell integrated with two uniformly distributed piezoelectric layers on the top and bottom surfaces of the cylindrical shell are presented. Single-walled carbon nanotubes (SWCNTs) are selected as reinforcement and effective material properties of FG-CNTRC cylindrical shell are assumed to be graded through the thickness direction and are estimated through the rule of mixture. The elastic foundation is modeled by temperature-dependent orthotropic Pasternak medium. Considering coupling of mechanical and electrical fields, Mindlin shell theory and Hamilton's principle, the motion equations are derived. Nonlinear frequency and critical fluid velocity of sandwich structure are calculated based on differential quadrature method (DQM). The effects of different parameters such as distribution type of SWCNTs, volume fractions of SWCNTs, elastic medium and temperature gradient are discussed on the vibration and instability behavior of the sandwich structure. Results indicate that considering elastic foundation increases frequency and critical fluid velocity of system.

• Steel and Composite Structures
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• 제30권6호
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• pp.493-516
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• 2019

This paper is dedicated to nonlinear static and free vibration analysis of Uniform Distributed Carbon Nanotube Reinforced Composite (UD-CNTRC) structures under in-plane loading. The authors have suggested an efficient six-node triangular element. Mixed Interpolation of Tensorial Components (MITC) approach is employed to alleviate the membrane locking phenomena. Moreover, the behavior of the well-known LST element is considerably improved by applying an additional linear interpolation on the strain fields. Based on the rule of mixture, the properties of CNTRC are obtained. In this study, only the uniform distributed CNTs are employed through the thickness direction of element. To achieve the natural frequencies and shape modes, the eigenvalue problem is also solved. Using Total Lagrangian Principles, large amplitude free vibration is considered based on the first normalized mode shape of structure. Different well-known plane problem benchmarks and some proposed ones are studied to validate the accuracy and capability of authors' formulations. In addition, the effects of length to the height ratio of beam, CNT's characteristics, support conditions and normalized amplitude parameter on the linear and nonlinear vibration parameters are investigated.

• Steel and Composite Structures
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• 제29권5호
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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.

• Computers and Concrete
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• 제23권5호
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• pp.361-376
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• 2019

In this research, bending analysis of a micro sandwich skew plate with isotropic core and piezoelectric composite face sheets reinforced by carbon nanotube on the elastic foundations are studied. The classical plate theory (CPT) are used to model micro sandwich skew plate and to apply size dependent effects based on modified strain gradient theory. Eshelby-Mori-Tanaka approach is considered for the effective mechanical properties of the nanocomposite face sheets. The governing equations of equilibrium are derived using minimum principle of total potential energy and then solved by extended Kantorovich method (EKM). The effects of width to thickness ratio and length to width of the sandwich plate, core-to-face sheet thickness ratio, the material length scale parameters, volume fraction of CNT, the angle of skew plate, different boundary conditions and types of cores on the deflection of micro sandwich skew plate are investigated. One of the most important results is the reduction of the deflection by increasing the angle of the micro sandwich skew plate and decreasing the deflection by decreasing the thickness of the structural core. The results of this research can be used in modern construction in the form of reinforced slabs or stiffened plates and also used in construction of bridges, the wing of airplane.

• Advances in nano research
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• 제16권3호
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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.

• 한국고분자학회:학술대회논문집
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• 한국고분자학회 2006년도 IUPAC International Symposium on Advanced Polymers for Emerging Technologies
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• pp.288-288
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• 2006

Natural rubbers (NR) reinforced by multi-wall carbon nanotubes (MWCNT) was found to show extraordinary improvement of mechanical property. We speculated that this was owing to the interfacial phase that surrounded CNT and investigated about the phase by atomic force microscopy (AFM). Using force modulation mode and force-distance curve analyses, we succeeded in obtaining the information of its nanometer-scale rheological property. We found that was actually surrounded by the interfacial phase, that had softer modulus than NR matrix.

• Carbon letters
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• 제10권4호
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• pp.320-324
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• 2009

We investigated the effect of diameter and content of carbon nanotubes (CNTs) on the physical properties of styrenebutadiene rubber (SBR)/CNTs nanocomposites. CNTs-reinforced SBR nanocomposites were prepared by the melt mixing process. CNTs with different diameters were synthesized by the chemical vapor deposition method (CVD). In this work, the mechanical property and other physical properties of SBR/CNTS nanocomposites were discussed as a function of the content and diameter of CNTs.

• Steel and Composite Structures
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• 제35권1호
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• pp.1-12
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• 2020

This article deals with the buckling analysis in the plates containing carbon nanotubes (CNTs) subject to axial load. In order to control the plate smartly, a piezoelectric layer covered the plate. The plate is located in elastic medium which is modeled by spring elements. The Mori-Tanaka low is utilized for calculating the equivalent mechanical characteristics of the plate. The structure is modeled by a thick plate and the governing equations are deduced using Hamilton's principle under the assumption of higher-order shear deformation theory (HSDT). The Navier method is applied to obtain the bulking load. The effects of the applied voltage to the smart layer, agglomeration and volume percent of CNT nanoparticles, geometrical parameters and elastic medium of the structure are assessed on the buckling response. It has been demonstrated that by applying a negative voltage, the buckling load is increased significantly.