Vibration Analysis Of Carbon Nanotubes Research Articles

Exact modal analysis of multilayered FG-CNT plate assemblies using the dynamic stiffness method

The present work deals with the implementation of the dynamic stiffness method (DSM) for exact in-plane and out-of-plane vibration analysis of carbon nanotube (CNT)-reinforced multilayered functionally graded (FG) plates with three different CNT distributions. The frequency-dependent dynamic stiffness matrix is solved using Wittrick-William technique to obtain the natural frequencies and mode shapes of FG-CNT plates having different geometrical configurations. The effect of varying plate parameters is extensively studied. Influence of layer configurations on the dynamic behavior of the plates is highlighted. Most of these reported results are new and will be useful in the design of non-uniform FG-CNT plate structures.

Experimental and finite element vibration analysis of CNT reinforced MR elastomer sandwich beam

In this study, the free vibration analysis of carbon nanotubes reinforced magnetorheological elastomer (CNT-MRE) sandwich beam has been presented. The sandwich specimens are made of thin elastic strips integrated with CNT-MRE core. The viscoelastic properties of MRE and CNT-MRE are identified using ASTM E756-05 standard test. The natural frequencies and damping factors of with and without CNT reinforced MRE sandwich beams have been measured experimentally at various magnetic fields under cantilever condition. The measured natural frequencies are validated through the 3D finite element model. Further, the variations of natural frequencies with the influence of different levels of magnetic fields, boundary conditions, and core-skin thickness ratios of the CNT-MRE sandwich beam are studied. The analysis results demonstrate that the presence of carbon nanotubes improves the vibration behavior of MR elastomer.

Modified nonlocal theory for investigation the specific aspects of nonlinear behavior of carbon nanotube as a nano-resonator

Purpose In this paper, the important aspects of vibration analysis of carbon nanotubes (CNTs) as nano-resonators are studied. This study has covered the important nonlinear phenomena such as jump super-harmonic and chaotic behavior. CNT is modeled by using the modified nonlocal theory (MNT). Design/methodology/approach In previous research studies, the effects of CNT’s rotary inertia, stiffness and shear modulus of the medium were neglected. So by considering these terms in MNT, a comprehensive model of vibrational behavior of carbon nanotube as a nanosensor is presented. The nanotube is modeled as a nonlocal nonlinear beam. The first eigenmode of an undamped simply supported beam is used to extract the nonlinear equation of CNT. Harmonic balance method is used to solve the equation, while to study its super-harmonic behavior, higher-order harmonic terms were used. Findings In light of frequency response equation, jump phenomenon and chaotic behavior of the nanotube with respect to the amplitude of excitation are investigated. Also in each section of the study, the effects of elastic medium and nonlocal parameters on the vibration behavior of nanotube are investigated. Furthermore, parts of the results in linear and nonlinear cases were compared with results of other references. Originality/value The present modification of the nonlocal theory is so important and useful for accurate investigation of the vibrational behavior of nano structures such as a nano-resonator.

Vibration analysis of carbon nanotubes reinforced isotropic doubly-curved nanoshells using nonlocal elasticity theory based on a new higher order shear deformation theory

In this paper, three-dimensional vibrations of carbon nanotubes (CNTs) reinforced isotropic doubly-curved nanoshells using nonlocal elasticity theory based on a new higher-order shear deformation theory (HSDT) is investigated. The considering higher-order shear deformation theory is a combination of sinus and exponential power with cosine function which is one of the most accurate shear deformation theory. One can conclude that combination of important theories such as Reddy's doubly-curved shells theory, nonlocal elasticity theory and higher-order shear deformation theory to a more complicated structure such as doubly-curved shells leads to important and novel work in context of mechanical engineering. The equations of motion and boundary conditions are derived using Hamilton's principle. The equations of motion are solved via Navier-type, closed-form solutions. From the best knowledge of authors, it is the first time that present formulation is used to investigate the vibration of carbon nanotubes reinforced doubly-curved nanoshells based on a new higher-order shear deformation theory. Also, it is the first time that small scale effects are considered in carbon nanotubes reinforced doubly-curved nanoshells made of isotropic materials. The effects of mechanical properties, geometrical properties and the different types of CNTs on the vibration frequencies of doubly-curved nanoshell are investigated. The comparison study is carried out to verify the accuracy of the proposed method. Numerical results indicate that the volume fraction and types of distribution of CNTs have considerable effects on the vibration characteristics of CNTs doubly-curved nanoshells. Presented results for vibrations can minister as benchmarks for future analysis of CNTs doubly-curved nanoshells.

Size-dependent vibration analysis of carbon nanotubes

Abstract

Nonlinear vibration analysis of carbon nanotube reinforced composite plane structures

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.

Vibration analysis of carbon nanotubes with multiple cracks in thermal environment

In this study, the thermal loading effect on free vibration characteristics of carbon nanotubes (CNTs) with multiple cracks is studied. Various boundary conditions for nanotube are taken in to account. In order to take the small scale effect, the nonlocal elasticity of Eringen is employed in the framework of Euler-Bernoulli beam theory. This theory states that the stress at a reference point is a function of strains at all points in the continuum. A cracked nanotube is assumed to be consisted of two segments that are connected by a rotational spring which is located in the position of the cracked section. Hamilton's principle is used to achieve the governing equations. Influences of the nonlocal parameter, crack severity, temperature change and the number of cracks on the system frequencies are investigated. Also, it is found that at room or lower temperature the natural frequency for CNT decreases as the value of temperature change increases, while at temperature higher than room temperature the natural frequency of CNT increases as the value of temperature change increases. Various boundary conditions have been applied to the nanotube.

Vibration analysis of carbon nanotubes based on cylindrical shell by inducting Winkler and Pasternak foundations

ABSTRACTIn this article, vibration analysis of single-walled carbon nanotubes (SWCNTs) based on Love's thin shell theory has been investigated along with five sort of boundary conditions (S-S), (C-C), (C-F), (C-Sl), and (F-S). Three different shapes such as Armchair, Zigzag, and Chiral are taken into account under the influence of Winkler and Pasternak foundations. The wave propagation approach is employed to formulate the eigenvalue problem. MATLAB software package in used to obtain the vibrational natural frequencies of SWCNTs. The axial modal dependence is measured by the complex exponential functions implicating the axial modal numbers.

Free vibration analysis of carbon nanotube reinforced composite Timoshenko beam

The paper deals with the free vibration analysis of nano-composite beams. The nano-composite beams are a combination of single walled carbon nano-tubes (SWCNT) as reinforcement fibre and are dispersed in the epoxy matrix. Material properties of the resulting nano-composite material are extracted using the Timoshenko beam theory. Finite element method (FEM) is employed to solve the governing equations of motion. The effect of various parameters such as boundary conditions, carbon nanotube (CNT) volume fraction, slenderness ratio and the distribution of nano-material on the natural frequency of the composite structure are studied and presented. The obtained results reveal that CNT volume fraction and distribution have substantial effect on the properties of the nano-composite beam.

Free vibration analysis of carbon nanotube reinforced composite Timoshenko beam

The paper deals with the free vibration analysis of nano-composite beams. The nano-composite beams are a combination of single walled carbon nano-tubes (SWCNT) as reinforcement fibre and are dispersed in the epoxy matrix. Material properties of the resulting nano-composite material are extracted using the Timoshenko beam theory. Finite element method (FEM) is employed to solve the governing equations of motion. The effect of various parameters such as boundary conditions, carbon nanotube (CNT) volume fraction, slenderness ratio and the distribution of nano-material on the natural frequency of the composite structure are studied and presented. The obtained results reveal that CNT volume fraction and distribution have substantial effect on the properties of the nano-composite beam.

Application of the Green function method to flow-thermoelastic forced vibration analysis of viscoelastic carbon nanotubes

In this paper, the Green function method (GFM) is implemented for forced vibration analysis of carbon nanotubes (CNTs) conveying fluid in thermal environment. The Eringen’s nonlocal elasticity theory is used to take into account the size effect of CNT with modeling the CNT wall–fluid flow interaction by means of slip boundary condition and Knudsen number (Kn). The derived governing differential equations are solved by GFM which demonstrated to have high precision and computational efficiency in the vibration analysis of CNTs. The validity of the present analytical solution is confirmed by comparing the results with those reported in other literature, and good agreement is observed. The analytical examinations are accomplished, while the emphasis is placed on considering the influences of nonlocal parameter, boundary conditions, temperature change, structural damping of the CNT, Knudsen number, fluid velocity and visco-Pasternak foundation on the dynamic deflection response of the fluid-conveying CNTs in detail.

Radial Nonlocal Effect on the Vibration Characteristics of Carbon Nano-tube Supported in Winkler Type Elastic Foundation

Background: In the upcoming era carbon nanotubes have proved to be the most promising material in the field of science and technology. In the analysis of carbon nanotube, nonlocal elasticity is found to be highly effective as it regards the small scale effects in the analysis. The small scale effect is found to be considered via nonlocal elasticity in both axial and radial direction. Objective: In the present article, radial nonlocal effect on the vibration of carbon nanotubes supported in Winkler type elastic foundation is studied. Method: In the analysis, Timoshenko beam theory is employed to derive the governing differential equations. Finite element model is developed. Results: It is observed radial nonlocal effect has a dominating effect over Winkler modulus parameter and at higher diameter, the effect of Winkler modulus disappears. Conclusion: The observation indicates that radial scale effect has significant influence in the vibration analysis of carbon nanotubes supported on Winkler foundation. Keywords: Carbon nanotubes, finite element method, radial nonlocal effect, timoshenko beam theory, vibration analysis, winkler type elastic foundation.

Size-dependent nonlinear vibration analysis of carbon nanotubes conveying multiphase flow

An understanding of the dynamic behavior of the carbon nanotubes (CNTs) conveying fluid is very important for exploring the applications in nanoscale systems. Due to the molecular network disruption, the passing flow has multiphase nature. In this regard, the nonlinear vibration behavior of the CNT conveying multiphase flow is investigated by considering the small scale effects based on the nonlocal theory. The effect of the multiphase flow on the CNT's vibration behavior is modeled by the resultant random uncertainty in the external excitation along with considering the slip flow velocity profile. After extraction of the governing equation by implementing Hamilton's principle and discretizing it by the Galerkin method, the resulting equations are solved numerically. Due to the stochastic nature of the differential equations, the statistical parameters of the response have been obtained by Monte–Carlo simulation. By studying the deflection of the midpoint of the CNT and also considering corresponding upper and lower limit band (confidence interval), extended results of uncertainty effects have been obtained. Moreover the effect of nonlocal parameter, flow velocity and Knudsen number on the statistical dynamic behavior of the system have been investigated. The results show that as the molecular behavior of the flow increases the uncertainty in the system and the confidence interval increase.

Application of Halpin-Tsai Method in Modelling and Size-dependent Vibration Analysis of CNTs/fiber/polymer Composite Microplates.

In the present study, modelling and vibration analysis of Carbon nanotubes/ fiber/ polymer composite microplates are investigated. The governing equations of the Carbon nanotubes/ fiber/ polymer composite microplates are derived based on first order shear deformation plate theory, rather than other plate theories, due to accuracy and simplicity of polynomial functions. The modified couple stress theory is employed because of its capability to interpret the size effect. Halpin-Tsai model is utilized to evaluate the material properties of two-phase composite consisted of uniformly distributed and randomly oriented Carbon nanotubes through the epoxy resin matrix. Afterwards, the structural properties of carbon nanotubes reinforced polymer matrix, which is assumed as a new matrix, and then, reinforced with E-Glass fiber, they are calculated by fiber micromechanics approach. Employing Hamilton’s principle, the equations of motion are obtained and solved by Hybrid analytical numerical method. The influences of various parameters such as the weight percentage of single-walled carbon nanotube, aspect ratio, and size effect on the vibration characteristics of microplate are discussed in details. Results indicate that the stability of Carbon nanotubes/fiber/polymer composite microplates can be improved by adding appropriate values of Carbon nanotubes. In addition, increase in the frequencies is more pronounced in the case of microplates reinforced with SWCNT compared with MWCNT. These findings can be used in design and manufacturing of marine vessels and aircrafts.

Free vibration analysis of triangular CNT-reinforced composite plates subjected to in-plane stresses using FSDT element-free method

This study conducts the first-known vibration analysis of carbon nanotube (CNT) reinforced functionally graded composite triangular plates subjected to in-plane stresses. The first-order shear deformation theory is applied to study the effect of the transverse shear deformation of the plates and the element-free IMLS-Ritz method is used for numerical computation. Numerical experiments are carried out to examine the convergence and accuracy of the element-free IMLS-Ritz method in its application to the vibration of CNT-reinforced functionally graded composite plates subjected to in-plane stresses. In this study, sets of vibration frequency parameters and mode shapes for various CNT-reinforced functionally graded composite triangular plates are illustrated. The influences of CNT volume fraction, plate thickness-to-width ratio, CNT distribution type, isosceles triangular angle, in-plane stress ratio and boundary conditions on the plate’s vibration behaviors are investigated in detail. These results may serve as a benchmark for future studies.

Three-Dimensional Static and Free Vibration Analysis of Carbon Nano Tube Reinforced Composite Cylindrical Shell Using Differential Quadrature Method

In this paper, bending and free vibration analysis of carbon nanotubes reinforced composite (CNTRC) cylindrical shell is carried out using the three-dimensional theory of elasticity. The single-walled carbon nanotubes (SWCNT) reinforcement is either uniformly distributed (UD) or functionally graded (FG) in the thickness direction which, are specified as the cases [Formula: see text], [Formula: see text], [Formula: see text] and FG-X. Effective material properties of CNTRC cylindrical shell are estimated according to the rule of mixture as well as considering the CNT efficiency parameters. An analytical solution is performed by using Fourier series along the axial coordinate together with state space technique along the radial coordinate for the simply supported CNTRC cylindrical shell. Moreover, for CNTRC cylindrical shell with other edges boundary conditions, a semi-analytical solution is accomplished by using differential quadrature method (DQM) along the axial coordinate and state space technique along the radial coordinate. Present approach is validated by comparing the numerical results with the available published results. Furthermore, effect of types of CNT distributions in the polymer matrix, volume fraction of CNT, edges boundary conditions and radial-to-thickness ratio on the bending and free vibration behavior of FG-CNTRC cylindrical are examined.

Free Vibration Analysis of Carbon Nanotubes by Using Finite Element Method

In the present study, an efficient and accurate finite element model for vibration analysis of carbon nanotubes (CNTs) with both Euler–Bernoulli and Timoshenko beam theory has been presented. For this purpose, an analytical solution for the exact dynamic shape functions of CNTs based on both Euler–Bernoulli and Timoshenko beam theories has been derived. The solution is general and is not restricted to a particular range of magnitudes of the nonlocal parameters. The exact dynamic shape functions have been utilized to derive analytic expressions for the coefficients of the exact dynamic (frequency-dependent) element stiffness matrix. Numerical results are presented to figure out the effects of nonlocal parameter, mode number and slenderness ratio on the vibration characteristics of CNTs. It is shown that these results are in good agreement with those reported in the literature. Present element formulation will be useful for structural analyses of nanostructures with complex geometries, loadings, material properties and boundary conditions.

An analytical solution for vibration analysis of carbon nanotube conveying viscose fluid embedded in visco-elastic medium

In this paper, considering a more realistic model for the carbon nanotube (CNT) conveying viscous fluid which is embedded in a visco-elastic medium, the effect of viscosity of the medium surrounding the CNT has been investigated. By taking into account the influence of the fluid viscosity and using the Navier-Stokes equations, the governing equation of motion has been derived and a new analytical technique based on the power series is presented for its vibration analysis. The frequency equation of the system is obtained by applying the boundary conditions. The influence of the medium parameters and the fluid viscosity on the natural frequencies of the CNT has been studied. The results show that the medium damping has a marked effect on the natural frequencies and the critical fluid velocity. Furthermore, by increasing the fluid viscosity, the natural frequencies and the critical fluid velocity increase. There is a good agreement between the results obtained through the proposed method and the data reported in the literature. The two main advantages of the proposed method are the applicability of the method to all kinds of the boundary conditions and its rapid convergence.

Free Vibration Analysis of Carbon Nanotubes by Timoshenko Beam Model and Thin-Plate Spline Radial Basis Function

Timoshenko beam model and the meshless method based on thin-plate spline radial basis function are used to analyze the free vibration of carbon nanotubes. The natural frequencies of the carbon nanotubes with different length-to-diameter ratios and boudary conditions are compared with the results of published literatures which demonstrate the high accuracy of present method.

Thermal vibration analysis of carbon nanotubes embedded in two-parameter elastic foundation based on nonlocal Timoshenko's beam theory

This paper presents a new model to consider the thermal effects, Pasternak’s shear foundation, transverse shear deformation and rotary inertia on vibration analysis of a single-walled carbon nanotube. Nonlocal elasticity theory is implemented to investigate the small-size effect on thermal vibration response of an embedded carbon nanotube. Based on Hamilton’s principle, the governing equations are derived and then solved analytically, in order to determine the nonlocal natural frequencies. Results show that unlike the Pasternak foundation, the influence of Winkler’s constant on nonlocal frequency is negligible for low temperature changes. Moreover, the nonlocal frequencies are always smaller as compared to their local counterparts. In addition, in high shear modulus along with an increase in aspect ratio, the nonlocal frequency decreases.