Vibration Behavior Of Carbon Nanotubes Research Articles

Free vibration response of functionally graded carbon nanotubes double curved shell and panel with piezoelectric layers in a thermal environment

This paper presents free vibration of the double-curved shells and panels with piezoelectric layers in a thermal environment. Vibration characteristics of elliptical, spherical, cycloidal, and toro circular shells of revolution are studied in detail. Vibration behavior of carbon nanotubes (CNTs) reinforced composite shells embedded with piezoelectric layers at the upper and lower surfaces is scrutinized. It is supposed that temperature changes linearly through-thickness direction. Reissner- Mindlin and the first order shear deformation (FSDT) theories are implemented to derive the governing equations of the considered structures. The distribution of nanotubes is assumed to be linear along the thickness direction. For solving the equation, the General Differential Quadrature (GDQ) method is used to obtain a numerical analysis for the dynamics of the objective structures. Finally, the effects of boundary conditions, the thickness of piezoelectric layers, functional distribution of CNTs, thermal environment and kinds of the circuit (opened-circuit and closed-circuit) are analyzed. Eigenvalue system is solved to obtain natural frequencies. It is delineated that the obtained fundamental frequency by the closed -circuit is smaller than those obtained by the opened-circuit. Another interesting result is that the natural frequency is decreased by increasing temperature.

The effect of non-local higher order stress to predict the nonlinear vibration behavior of carbon nanotube conveying viscous nanoflow

In this research, the effect of non-local higher order stress on the nonlinear vibration behavior of carbon nanotube conveying viscous nanoflow resting on elastic foundation is investigated. Physical intuition reveals that increasing nanoscale stress leads to decrease the stiffness of nanostructure which firstly established by Eringen's non-local elasticity theory (previous nonlocal method) while many of papers have concluded otherwise at microscale based on modified couple stress, modified strain gradient theories and surface stress effect. The non-local higher order stress model (new nonlocal method) is used in this article that has been studied by few researchers in other fields and the results from the present study show that the trend of the new nonlocal method and size dependent effect including modified couple stress theory is the same. In this regard, the nonlinear motion equations are derived using a variational principal approach considering essential higher-order non-local terms. The surrounded elastic medium is modeled by Pasternak foundation to increase the stability of system where the fluid flow may cause system instability. Effects of various parameters such as non-local parameter, elastic foundation coefficient, and fluid flow velocity on the stability and dimensionless natural frequency of nanotube are investigated. The results of this research show that the small scale parameter based on higher order stress help to increase the natural frequency which has been approved by other small scale theories such as strain gradient theory, modified couple stress theory and experiments, and vice versa for previous nonlocal method. This study may be useful to measure accurately the vibration characteristics of nanotubes conveying viscous nanoflow and to design nanofluidic devices for detecting blood Glucose.

On the study of the effect of in-plane forces on the frequency parameters of CNT-reinforced composite skew plates

This paper investigates the effect of in-plane forces on the vibration behavior of carbon nanotube (CNT) reinforced composite skew plates. The analysis is performed by implementing the first-order shear deformation theory (FSDT) with the element-free/mesh-free Improved Moving Least Square-Ritz (IMLS-Ritz) method for solution to the problem. Two varieties of carbon nanotube-reinforced composite skew plates, namely uniformly distributed and functionally graded reinforcement are considered. A micromechanical model is employed to estimate the material properties of CNT-reinforced composite plates. Comparison studies are implemented to validate the accuracy of the proposed method. The frequency parameters and mode shapes for the skew plates are presented. A detailed parametric study is carried out to reveal many complicated effect on the frequency parameters of the plate. These effects include in-plane stress ratio, boundary conditions, CNT-volume fraction and geometric size. The obtained results will be references of future research and corresponding engineering project.

Influence of imperfect end boundary condition on the nonlocal dynamics of CNTs

Imperfections that unavoidably occur during the fabrication process of carbon nanotubes (CNTs) have a significant influence on the vibration behavior of CNTs. Among these imperfections, the boundary condition defect is studied in this investigation based on the nonlocal elasticity theory. To this end, a mathematical model of the non-ideal end condition in a cantilever CNT is developed by a strongly non-linear spring to study its effect on the vibration behavior. The weak form equation of motion is derived via Hamilton’s principle and solved based on Rayleigh–Ritz approach. Once the frequency response function (FRF) of the CNT is simulated, it is found that the defect parameter injects noise to the FRF in the range of lower frequencies and as a result the small scale effect on the FRF remains undisturbed in high frequency ranges. Besides, in this work a process is introduced to estimate the nonlocal and defect parameters for establishing the mathematical model of the CNT based on FRF, which can be competitive because of its lower instrumentation and data analysis costs. The estimation process relies on the resonance frequencies and the magnitude of noise in the frequency response function of the CNT. The results show that the constructed dynamic response of the system based on estimated parameters is in good agreement with the original response of the CNT.

Vibration analysis of CNT-reinforced thick laminated composite plates based on Reddy’s higher-order shear deformation theory

In this paper, free vibration behavior of carbon nanotube (CNT) reinforced functionally graded thick laminated composite plates utilizing Reddy’s higher-order shear deformation theory (HSDT) is studied. To the best of authors’ knowledge, this paper is the first to incorporate HSDT with one of the element-free approaches to investigate this issue. The element-free IMLS-Ritz method is employed and four types of CNT distributions are considered. The resulting effective material properties of the CNT-reinforced composite are estimated by a detailed and straightforward Mori–Tanaka approach. The numerical results have been compared with the literature showing excellent agreement. Considering various CNT orientation angles, a parametric study showing the effects of CNT volume fraction, plate aspect ratio, plate width-to-thickness ratio and number of plate’s layers on the non-dimensional natural frequencies is investigated. Finally, the influence of boundary conditions on the sequence of the first six mode shapes for various lamination arrangements is presented.

Free vibration of functionally graded carbon nanotube reinforced composite plates integrated with piezoelectric layers

In the present research, free vibration behavior of carbon nanotube reinforced composite (CNTRC) plates integrated with piezoelectric layers at the bottom and top surfaces is analyzed. Plate is modeled according to the first order shear deformation plate theory. Distribution of CNTs across the plate thickness may be functionally graded (FG) or uniformly distributed (UD). Properties of the composite media are obtained according to a modified rule of mixtures approach which contains efficiency parameters. Distribution of electric potential across the piezoelectric thickness is assumed to be linear. The complete set of motion and Maxwell equations of the system are obtained according to the Ritz formulation suitable for arbitrary in-plane and out-of-plane boundary conditions. Besides, two types of electrical boundary conditions, namely, closed circuit and open circuit are considered for the free surfaces of the piezoelectric layers. Chebyshev polynomials are used as the basis functions in Ritz approximation. The resultant eigenvalue system is solved to obtain the frequencies of the system as well as the mode shapes. It is shown that, fundamental frequency of a closed circuit plate is always higher than a plate with open circuit boundary conditions.

The effect of calibrated nonlocal constant on the modal parameters and stability of axially compressed CNTs

Nowadays investigating the vibration behavior of carbon nanotubes (CNTs) has drawn considerable attention due to the superior mechanical properties of the CNTs. One of the powerful theoretical methods to study the vibration behavior of CNTs is implementing the nonlocal theory. Most of studies on the vibration behavior of CNTs have assumed a fixed value for small scale parameter for all vibration modes, however, this value is mode-dependent. Therefore, in this paper, the small scale parameter is calibrated for a single-walled carbon nanotube (SWCNT) with respect to each vibration mode. For this propose, the governing equation of motion based on the nonlocal beam theory is extracted by applying the Hamilton's principle. Then, by using the power series method, an eigenvalue problem is defined to derive the calibrated value of small scale constant and nonlocal mode shapes of the CNT. By using the expansion theory, the equation of motion is discretized, and the effect of nonlocality on the modal parameters and stability of the CNT under compressive force is investigated. Finally, the possibility of estimating nonlocal parameter based on simulated frequency domain response of the system by using modal analysis methods is studied. The results show that the calibration of small scale constant is important and the critical axial force is highly sensitive to this value.

Vibration analysis of CNT reinforced functionally graded composite plates in a thermal environment based on Reddy’s higher-order shear deformation theory

This paper presents the free vibration behavior of carbon nanotube (CNT) reinforced functionally graded composite plates in a thermal environment based on Reddy’s higher-order shear deformation theory (HSDT). The element-free kp-Ritz method is used in this study. Four different types of CNT distributions are considered. The literature reveals that there is a research gap in investigating the mechanical behaviors of CNT reinforced functionally graded composite plates using Reddy’s HSDT in association with any of the mesh-free methods. To the authors’ knowledge, this paper is the first to use this approach to investigate the vibration behavior of CNT reinforced functionally graded composite plates in a thermal environment. The rule of mixture is used to estimate the resulting effective material properties. To verify the reliability of the present model, the obtained numerical results based on a conversion study have been compared with those found in the literature with evident agreement. Moreover, parametric studies have been conducted on the effects of CNT distribution, boundary conditions, plate aspect ratio, plate thickness-to-width ratio and CNT volume fraction on the non-dimensional natural frequencies. Furthermore, the effects of plate aspect ratio and plate thickness-to-width ratio on the sequence of the first six mode shapes have been investigated.

Torsional Vibration Analysis of Carbon Nanotubes Based on the Strain Gradient Theory and Molecular Dynamic Simulations

In the current study, the torsional vibration of carbon nanotubes is examined using the strain gradient theory and molecular dynamic simulations. The model developed based on this gradient theory enables us to interpret size effect through introducing material length scale parameters. The model accommodates the modified couple stress and classical models when two or all material length scale parameters are set to zero, respectively. Using Hamilton's principle, the governing equation and higher-order boundary conditions of carbon nanotubes are obtained. The generalized differential quadrature method is utilized to discretize the governing differential equation of the present model along with two boundary conditions. Then, molecular dynamic simulations are performed for a series of carbon nanotubes with different aspect ratios and boundary conditions, the results of which are matched with those of the present strain gradient model to extract the appropriate value of the length scale parameter. It is found that the present model with properly calibrated value of length scale parameter has a good capability to predict the torsional vibration behavior of carbon nanotubes.