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.

Development of the Cell-based Smoothed Discrete Shear Gap Plate Element (CS-FEM-DSG3) using Three-Node Triangles

2015 ◽  
Vol 12 (04) ◽  
pp. 1540015 ◽  
Author(s):  
T. Nguyen-Thoi ◽  
M. H. Nguyen-Thoi ◽  
T. Vo-Duy ◽  
N. Nguyen-Minh
Keyword(s):  
Static Analysis ◽  
Free Vibration Analysis ◽  
Composite Plates ◽  
Functionally Graded ◽  
Triangular Element ◽  
Plate Element ◽  
Strain Smoothing ◽  
Discrete Shear Gap ◽  
Transverse Shear Locking ◽  
Coarse Meshes

The paper presents the formulation and recent development of the cell-based smoothed discrete shear gap plate element (CS-FEM-DSG3) using three-node triangles. In the CS-FEM-DSG3, each triangular element will be divided into three sub-triangles, and in each sub-triangle, the original plate element DSG3 is used to compute the strains and to avoid the transverse shear locking. Then the cell-based strain smoothing technique (CS-FEM) is used to smooth the strains on these three sub-triangles. The numerical examples illustrate four superior properties of the CS-FEM-DSG3 including: (1) being a strong competitor to many existing three-node triangular plate elements in the static analysis; (2) giving high accurate solutions for problems with skew geometries in the static analysis; (3) giving high accurate solutions in free vibration analysis; (4) providing accurate values of high frequencies of plates by using only coarse meshes. Due to its superior and simple properties, the CS-FEM-DSG3 has been now developed for various analyses such as: flat shells, stiffened plates, functionally graded plates, composite plates, piezoelectricity composite plates, cracked plate and plates resting on the viscoelastic foundation subjected to moving loads, etc.

An Edge-Based Smoothed Discrete Shear Gap Method for Static and Free Vibration Analyses of FG-CNTRC Plates

2019 ◽  
Vol 16 (04) ◽  
pp. 1850102 ◽  
Author(s):  
T. Nguyen-Quoc ◽  
S. Nguyen-Hoai ◽  
D. Mai-Duc
Keyword(s):  
Free Vibration ◽  
Material Properties ◽  
Volume Fraction ◽  
Plate Theory ◽  
Functionally Graded ◽  
Correction Factors ◽  
Reinforced Composite ◽  
Strain Smoothing ◽  
Edge Based ◽  
Discrete Shear Gap

In this paper, an edge-based smoothed stabilized discrete shear gap method (ES-DSG) is integrated with the C0-type high-order shear deformation plate theory (C0-HSDT) for free vibration and static analyses of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plates. The material properties of FG-CNTRC are assumed to be graded through the thickness direction according to several distributions of the volume fraction of carbon nanotubes (CNTs). The stiffness formulation of the ES-DSG based on C0-HSDT is performed by using the strain smoothing technique over the smoothing domains associated with edges of elements. This hence does not require shear correction factors. The accuracy and reliability of the proposed method are confirmed in several numerical examples.

Nonlinear free vibration analysis of functionally graded rotating composite Timoshenko beams reinforced by carbon nanotubes

2019 ◽  
Vol 25 (14) ◽  
pp. 2063-2078 ◽  
Author(s):  
Mahsa Heidari ◽  
Hadi Arvin
Keyword(s):  
Carbon Nanotubes ◽  
Carbon Nanotube ◽  
Free Vibration ◽  
Direct Method ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Timoshenko Beams ◽  
Nonlinear Free Vibration ◽  
Reinforced Composite ◽  
Linear And Nonlinear

In this paper, the linear and nonlinear free vibrations of functionally graded rotating composite Timoshenko beams reinforced by carbon nanotubes are presented. The formulation is based on the assumptions of Timoshenko beam theory in addition to consideration of the nonlinear von Karman strain–displacement relationship. The effective material properties of carbon nanotube reinforced composites are determined employing the Mori–Tanaka micromechanics model and the extended mixture rule. For the carbon nanotube reinforced composite beams, uniform distribution and four types of functionally graded distribution patterns of single-walled carbon nanotube reinforcements are considered. A differential transform method is applied on the nondimensionalized equations of motion to release the flapping modeshapes and the associated natural frequencies. The direct method of multiple scales is implemented to derive the effective nonlinearity and the corresponding nonlinear natural frequency. The accuracy of the present outcomes is validated by the comparison with the results given in the literature. The numerical results are presented in both tabular and graphical forms to investigate the effects of nanotube volume fractions, distribution types of the carbon nanotubes, and rotation speed on linear and nonlinear free vibration characteristics of carbon nanotube reinforced composite beam. The results demonstrate the important role of carbon nanotube distribution profile on linear and nonlinear free vibration features.

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.

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.

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