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.

Free Vibration and Buckling Analysis of Sandwich Beams with Functionally Graded Carbon Nanotube-Reinforced Composite Face Sheets

2015 ◽  
Vol 15 (07) ◽  
pp. 1540011 ◽  
Author(s):  
Helong Wu ◽  
Sritawat Kitipornchai ◽  
Jie Yang
Keyword(s):  
Carbon Nanotube ◽  
Free Vibration ◽  
Volume Fraction ◽  
Slenderness Ratio ◽  
Micromechanical Model ◽  
Sandwich Beam ◽  
Sheet Thickness ◽  
Functionally Graded ◽  
Sandwich Beams ◽  
Reinforced Composite

This paper investigates the free vibration and elastic buckling of sandwich beams with a stiff core and functionally graded carbon nanotube reinforced composite (FG-CNTRC) face sheets within the framework of Timoshenko beam theory. The material properties of FG-CNTRCs are assumed to vary in the thickness direction, and are estimated through a micromechanical model. The governing equations and boundary conditions are derived by using Hamilton's principle and discretized by employing the differential quadrature (DQ) method to obtain the natural frequency and critical buckling load of the sandwich beam. A detailed parametric study is conducted to study the effects of carbon nanotube volume fraction, core-to-face sheet thickness ratio, slenderness ratio, and end supports on the free vibration characteristics and buckling behavior of sandwich beams with FG-CNTRC face sheets. The vibration behavior of the sandwich beam under an initial axial force is also discussed. Numerical results for sandwich beams with uniformly distributed carbon nanotube-reinforced composite (UD-CNTRC) face sheets are also provided for comparison.

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.

scholarly journals Free Vibration Of Functionally Graded Carbon Nanotube Reinforced Composite Annular Sector Plate With General Boundary Supports

2018 ◽  
Vol 5 (1) ◽  
pp. 49-67 ◽  
Author(s):  
Fuzhen Pang ◽  
Haichao Li ◽  
Yuan Du ◽  
Yanhe Shan ◽  
Fang Ji
Keyword(s):  
Carbon Nanotube ◽  
Free Vibration ◽  
Ritz Method ◽  
Admissible Function ◽  
Functionally Graded ◽  
General Boundary ◽  
Reinforced Composite ◽  
Annular Sector ◽  
Sector Plate ◽  
Annular Sector Plate

Abstract In this paper, an efficient and unified approach for free vibration analysis of the moderately thick functionally graded carbon nanotube reinforced composite annular sector plate with general boundary supports is presented by using the Ritz method and the first-order shear deformation theory. For the distribution of the carbon nanotubes in thickness direction, it may be uniform or functionally graded. Properties of the composite media are based on a refined rule of the mixture approach which contains the efficiency parameters. A modified Fourier series is chosen as the basic function of the admissible function to eliminate all the relevant discontinuities of the displacements and their derivatives at the edges. To establish the general boundary supports of the annular sector plate, the artificial spring boundary technique is implemented at all edges. The desired solutions are obtained through the Ritz-variational energy method. Some numerical examples are considered to check the accuracy, convergence and reliability of the present method. In addition, the parameter studies of the functionally graded carbon nanotube reinforced composite annular sector plate are carried out as well.

scholarly journals FREE VIBRATION OF TAPERED FUNCTIONALLY GRADED CARBON NANOTUBE-REINFORCED COMPOSITE BEAMS USING A HIERARCHICAL BEAM ELEMENT

2020 ◽  
Vol 57 (6A) ◽  
pp. 107
Author(s):  
Trinh Thi Hien
Keyword(s):  
Carbon Nanotube ◽  
Free Vibration ◽  
Volume Fraction ◽  
Shear Deformation Theory ◽  
Longitudinal Direction ◽  
Beam Element ◽  
Variable Coefficients ◽  
Functionally Graded ◽  
Published Data ◽  
Reinforced Composite

Free vibration of tapered functionally graded carbon nanotube-reinforced composite (FG-CNTRC) beams is investigated. The beams with four types of carbon nanotube distribution in the thickness, namely the uniform (UD-CNT), X-type (FGX-CNT), A-type (FGA-CNT) and O-type (FGO-CNT), are assumed to be linearly tapered in longitudinal direction by three different taper cases. Based on the first-order shear deformation theory, equations of motion with variable coefficients are derived from Hamilton’s principle. Using hierarchical functions to interpolate the displacement field, a two-node beam element with nine degrees of freedom is formulated and employed to compute frequencies of the beams. The accuracy of the derived formulation is confirmed by comparing frequencies obtained in the present work with the published data. The effects of the total CNT volume fraction, CNT distribution type, taper cases, taper ratio, aspect ratio, boundary conditions, etc., on the vibration characteristics of the beams are examined and discussed.

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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