scholarly journals Free vibration of functionally graded carbon-nanotube-reinforced composite plates with cutout

2016 ◽  
Vol 7 ◽  
pp. 511-523 ◽  
Author(s):  
Mostafa Mirzaei ◽  
Yaser Kiani
Keyword(s):  
Carbon Nanotubes ◽  
Carbon Nanotube ◽  
Free Vibration ◽  
Solution Method ◽  
Volume Fraction ◽  
Plate Theory ◽  
Ritz Method ◽  
Composite Plates ◽  
Functionally Graded ◽  
Plane Boundary

During the past five years, it has been shown that carbon nanotubes act as an exceptional reinforcement for composites. For this reason, a large number of investigations have been devoted to analysis of fundamental, structural behavior of solid structures made of carbon-nanotube-reinforced composites (CNTRC). The present research, as an extension of the available works on the vibration analysis of CNTRC structures, examines the free vibration characteristics of plates containing a cutout that are reinforced with uniform or nonuniform distribution of carbon nanotubes. The first-order shear deformation plate theory is used to estimate the kinematics of the plate. The solution method is based on the Ritz method with Chebyshev basis polynomials. Such a solution method is suitable for arbitrary in-plane and out-of-plane boundary conditions of the plate. It is shown that through a functionally graded distribution of carbon nanotubes across the thickness of the plate, the fundamental frequency of a rectangular plate with or without a cutout may be enhanced. Furthermore, the frequencies are highly dependent on the volume fraction of carbon nanotubes and may be increased upon using more carbon nanotubes as reinforcement.

Static and Free Vibration Analyses of Functionally Graded Carbon Nanotube Reinforced Composite Plates using CS-DSG3

2019 ◽  
Vol 17 (03) ◽  
pp. 1850133 ◽  
Author(s):  
T. Truong-Thi ◽  
T. Vo-Duy ◽  
V. Ho-Huu ◽  
T. Nguyen-Thoi
Keyword(s):  
Carbon Nanotubes ◽  
Carbon Nanotube ◽  
Free Vibration ◽  
Numerical Solutions ◽  
Composite Plates ◽  
Functionally Graded ◽  
Triangular Element ◽  
Reinforced Composite ◽  
Strain Smoothing ◽  
Discrete Shear Gap

This study presents an extension of the cell-based smoothed discrete shear gap method (CS-DSG3) using three-node triangular elements for the static and free vibration analyses of carbon nanotube reinforced composite (CNTRC) plates. The single-walled carbon nanotubes (SWCNTs) are assumed to be uniformly distributed (UD) and functionally graded (FG) distributed along the thickness direction. The material properties of carbon nanotube-reinforced composite plates are estimated according to the rule of mixture. The governing equations are developed based on the first-order shear deformation plate theory (FSDT). In the CS-DSG3, each triangular element will be divided into three sub-triangles, and in each sub-triangle, the stabilized discrete shear gap method is used to compute the strains and to avoid the transverse shear locking. Then the strain smoothing technique on the whole triangular element is used to smooth the strains on these three sub-triangles. Effects of several parameters, such as the different distribution of carbon nanotubes (CNTs), nanotube volume fraction, boundary condition and width-to-thickness ratio of plates are investigated. In addition, the effect of various orientation angles of CNTs is also examined in detail. The accuracy and reliability of the proposed method are verified by comparing its numerical solutions with those of other available results in the literature.

Bending and free vibration analyses of antisymmetrically laminated carbon nanotube-reinforced functionally graded plates

2016 ◽  
Vol 51 (22) ◽  
pp. 3111-3125 ◽  
Author(s):  
Bin Huang ◽  
Yan Guo ◽  
Ji Wang ◽  
Jianke Du ◽  
Zhenghua Qian ◽  
...  
Keyword(s):  
Carbon Nanotube ◽  
Free Vibration ◽  
Volume Fraction ◽  
Shear Deformation Theory ◽  
Composite Plates ◽  
Functionally Graded ◽  
Width Ratio ◽  
Variable Theory ◽  
First Order ◽  
First Order Theory

In this paper, a simple four-variable first-order shear deformation theory is further applied to solve the bending and free vibration problems of antisymmetrically laminated functionally graded carbon nanotube (FG-CNT)-reinforced composite plates. The adopted four-variable theory contains only four unknowns in its displacement field which is less than the Reddy’s first-order theory. The equations of motion are derived from the Hamilton’s principle with the help of specific boundary conditions. Laminated FG-CNT-reinforced plates with different distribution types of carbon nanotube through the thickness are considered. The material properties of individual layer are estimated by using the extended rule of mixture. Analytical solutions of various simply supported antisymmetric cross-ply and angle-ply laminates are given for case study. The effects of carbon nanotube volume fraction, length to width ratio and thickness to width ratio on the non-dimensional fundamental frequency and the central deflection are investigated for antisymmetrically laminated FG-CNT-reinforced plates.

Refined zigzag theory for vibration analysis of viscoelastic functionally graded carbon nanotube reinforced composite microplates integrated with piezoelectric layers

2016 ◽  
Vol 231 (13) ◽  
pp. 2464-2478 ◽  
Author(s):  
A Ghorbanpour Arani ◽  
M Mosayyebi ◽  
F Kolahdouzan ◽  
R Kolahchi ◽  
M Jamali
Keyword(s):  
Carbon Nanotubes ◽  
Carbon Nanotube ◽  
Free Vibration ◽  
Sandwich Plate ◽  
Volume Fraction ◽  
Damping Ratio ◽  
Plate Boundary ◽  
Functionally Graded ◽  
Reinforced Composite ◽  
Zigzag Theory

Damped free vibration of carbon nanotube reinforced composite microplate bounded with piezoelectric sensor and actuator layers are investigated in this study. For the mathematical modeling of sandwich structure, the refined zigzag theory is applied. In addition, to present a realistic model, the material properties of system are supposed as viscoelastic based on Kelvin–Voigt model. Distributions of single-walled carbon nanotubes along the thickness direction of the viscoelastic carbon nanotube reinforced composite microplate are considered as four types of functionally graded distribution patterns. The viscoelastic functionally graded carbon nanotube reinforced composite microplate subjected to electromagnetic field is embedded in an orthotropic visco-Pasternak foundation. Hamilton’s principle is employed to establish the equations of motion. In order to calculate the frequency and damping ratio of sandwich plate, boundary condition of plate is assumed as simply-supported and an exact solution is used. The effects of some significant parameters such as damping coefficient of viscoelastic plates, volume fraction of carbon nanotubes, different types of functionally graded distributions of carbon nanotubes, magnetic field, and external voltage on the damped free vibration of system are investigated. Results clarify that considering viscoelastic property for system to achieve accurate results is essential. Furthermore, the effects of volume fraction and distribution type of carbon nanotubes are remarkable on the vibration of sandwich plate. In addition, electric and magnetic fields are considerable parameters to control the behavior of viscoelastic carbon nanotube reinforced composite microplate. It is hoped that the results of this study could be applied in design of nano/micromechanical sensor and actuator systems.

Mechanical behavior of laminated functionally graded carbon nanotube reinforced composite plates resting on elastic foundations in thermal environments

2018 ◽  
Vol 53 (9) ◽  
pp. 1159-1179 ◽  
Author(s):  
Tao Fu ◽  
Zhaobo Chen ◽  
Hongying Yu ◽  
Zhonglong Wang ◽  
Xiaoxiang Liu
Keyword(s):  
Carbon Nanotubes ◽  
Carbon Nanotube ◽  
Volume Fraction ◽  
Plate Thickness ◽  
Shear Deformation Theory ◽  
Composite Plates ◽  
Functionally Graded ◽  
Numerical Comparison ◽  
Thermal Environments ◽  
Reinforced Composite

The present study is concerned with static and free vibration analyses of laminated functionally graded carbon nanotube reinforced composite rectangular plates on elastic foundation based on nth-order shear deformation theory. Four types of carbon nanotubes distributions along the plate thickness are considered, which include uniformly distributed and three other functionally graded distributions. Governing differential equations are derived by means of Hamilton’s principle. The differential quadrature method is developed to formulate the problem, and rapid convergence is observed in this study. A numerical comparison with available results in the literature is carried out to show the validity of the proposed theory. Furthermore, effects of the carbon nanotubes volume fraction, thickness side ratio, aspect ratio, foundation parameters, different thermal environments, the number of layers, lamination angle, boundary condition, and carbon nanotubes distribution types on the static response of laminated functionally graded carbon nanotube reinforced composite plates are also investigated.

Vibratory response and acoustic radiation behavior of laminated functionally graded composite plates in thermal environments

2019 ◽  
Vol 22 (5) ◽  
pp. 1681-1706 ◽  
Author(s):  
Tao Fu ◽  
Zhaobo Chen ◽  
Hongying Yu ◽  
Qingjun Hao ◽  
Yanzheng Zhao
Keyword(s):  
Carbon Nanotubes ◽  
Carbon Nanotube ◽  
Volume Fraction ◽  
Plate Thickness ◽  
Shear Deformation Theory ◽  
Composite Plates ◽  
Functionally Graded ◽  
Numerical Comparison ◽  
Thermal Environments ◽  
Reinforced Composite

The present study is concerned with vibro-acoustic behavior analyses of laminated functionally graded carbon nanotube reinforced composite plates based on Reddy’s higher order shear deformation theory. Four types of carbon nanotubes distributions along the plate thickness are considered, which include uniformly distributed and three other functionally graded distributions. Governing differential equations are derived by means of Hamilton’s principle. The sound pressure and radiation efficiency are calculated with Rayleigh integral. A numerical comparison with available results in the literature is carried out to show the validity of the present model. Furthermore, effects of the carbon nanotubes volume fraction, different thermal environments, lamination angle and carbon nanotubes distribution types on the structural and acoustic response of laminated functionally graded carbon nanotube reinforced composite plates are also investigated.

Free Vibration Analysis of Nanocomposite Plates Reinforced by Graded Carbon Nanotubes Based on First-Order Shear Deformation Plate Theory

2013 ◽  
Vol 5 (1) ◽  
pp. 90-112 ◽  
Author(s):  
S. Jafari Mehrabadi ◽  
B. Sobhaniaragh ◽  
V. Pourdonya
Keyword(s):  
Carbon Nanotubes ◽  
Free Vibration ◽  
Shear Deformation ◽  
Material Properties ◽  
Volume Fraction ◽  
Plate Theory ◽  
Functionally Graded ◽  
First Order ◽  
Shear Deformation Plate Theory ◽  
Effective Material Properties

AbstractBased on the Mindlin’s first-order shear deformation plate theory this paper focuses on the free vibration behavior of functionally graded nanocomposite plates reinforced by aligned and straight single-walled carbon nanotubes (SWCNTs). The material properties of simply supported functionally graded carbon nanotube-reinforced (FGCNTR) plates are assumed to be graded in the thickness direction. The effective material properties at a point are estimated by either the Eshelby-Mori-Tanaka approach or the extended rule of mixture. Two types of symmetric carbon nanotubes (CNTs) volume fraction profiles are presented in this paper. The equations of motion and related boundary conditions are derived using the Hamilton’s principle. A semi-analytical solution composed of generalized differential quadrature (GDQ) method, as an efficient and accurate numerical method, and series solution is adopted to solve the equations of motions. The primary contribution of the present work is to provide a comparative study of the natural frequencies obtained by extended rule of mixture and Eshelby-Mori-Tanaka method. The detailed parametric studies are carried out to study the influences various types of the CNTs volume fraction profiles, geometrical parameters and CNTs volume fraction on the free vibration characteristics of FGCNTR plates. The results reveal that the prediction methods of effective material properties have an insignificant influence of the variation of the frequency parameters with the plate aspect ratio and the CNTs volume fraction.

Free vibration of functionally graded carbon nanotube reinforced composite cylindrical panels with general elastic supports

2018 ◽  
Vol 5 (1) ◽  
pp. 95-115
Author(s):  
Fei Xie ◽  
Jinyuan Tang ◽  
Ailun Wang ◽  
Cijun Shuai ◽  
Qingshan Wang
Keyword(s):  
Carbon Nanotube ◽  
Free Vibration ◽  
Volume Fraction ◽  
Ritz Method ◽  
Functionally Graded ◽  
Elastic Supports ◽  
Various Boundary Conditions ◽  
Reinforced Composite ◽  
Cylindrical Panels ◽  
Classical Boundary

Abstract In this paper, a unified solution for vibration analysis of the functionally graded carbon nanotube reinforced composite (FG-CNTRC) cylindrical panels with general elastic supports is carried out via using the Ritz method. The excellent accuracy and reliability of the present method are compared with the results of the classical boundary cases found in the literature. New results are given for vibration characteristics of FG-CNTRC cylindrical panels with various boundary conditions. The effects of the elastic restraint parameters, thickness, subtended angle and volume fraction of carbon nanotubes on the free vibration characteristic of the cylindrical panels are also reported.

NUMERICAL ANALYSIS ON NONLINEAR FREE VIBRATION OF CARBON NANOTUBE REINFORCED COMPOSITE BEAMS

2013 ◽  
Vol 14 (01) ◽  
pp. 1350056 ◽  
Author(s):  
F. LIN ◽  
Y. XIANG
Keyword(s):  
Carbon Nanotube ◽  
Free Vibration ◽  
Volume Fraction ◽  
Ritz Method ◽  
Axial Direction ◽  
Functionally Graded ◽  
Nonlinear Free Vibration ◽  
Third Order ◽  
First Order ◽  
Beam Theories

This paper investigates the free vibration of nanocomposite beams reinforced by single-walled carbon nanotubes (SWCNTs). The distribution of the SWCNTs may vary through the thickness of a beam and are aligned along the beam axial direction. The virtual strain and kinetic energies of the carbon nanotube (CNT) composite beam are obtained using the classical variational method of Hamilton's principle, and the geometric nonlinearity of von Kármán sense is also included. The eigenvalue equation for free vibration of the beam is derived by the p-Ritz method. Vibration frequency parameters for the uniformly distributed (UD) and functionally graded (FG) CNT beams based on the first-order and third-order beam theories are presented and the effects of CNT filler volume fraction, distribution, beam length to depth ratio and end support conditions on the nonlinear free vibration characteristics of the beams are discussed. Comparison studies for UD-CNT and FG-CNT beams based on the first-order and the third-order beam theories are also performed and the differences in vibration frequencies and the nonlinear to linear frequency ratios between these two theories are highlighted.

Frequency optimization of laminated functionally graded carbon nanotube reinforced composite quadrilateral plates using smoothed FEM and evolution algorithm

2017 ◽  
Vol 52 (14) ◽  
pp. 1971-1986 ◽  
Author(s):  
T Vo-Duy ◽  
T Truong-Thi ◽  
V Ho-Huu ◽  
T Nguyen-Thoi
Keyword(s):  
Carbon Nanotube ◽  
Optimization Problem ◽  
Volume Fraction ◽  
Differential Evolution Algorithm ◽  
Composite Plates ◽  
Functionally Graded ◽  
Optimization Approach ◽  
Reinforced Composite ◽  
Design Variables ◽  
Evolution Algorithm

The paper presents an efficient numerical optimization approach to deal with the optimization problem for maximizing the fundamental frequency of laminated functionally graded carbon nanotube-reinforced composite quadrilateral plates. The proposed approach is a combination of the cell-based smoothed discrete shear gap method (CS-DSG3) for analyzing the first natural frequency of the functionally graded carbon nanotube reinforced composite plates and a global optimization algorithm, namely adaptive elitist differential evolution algorithm (aeDE), for solving the optimization problem. The design variables are the carbon nanotube orientation in the layers and constrained in the range of integer numbers belonging to [−900 900]. Several numerical examples are presented to investigate optimum design of quadrilateral laminated functionally graded carbon nanotube reinforced composite plates with various parameters such as carbon nanotube distribution, carbon nanotube volume fraction, boundary condition and number of layers.

Sign in / Sign up

Export Citation Format

Share Document