scholarly journals Nonlinear Vibration Analysis of Functionally Graded Carbon Nanotube Reinforced Fluid-Conveying Tube in Thermal Environment

2021 ◽  
Author(s):  
Xu Chen ◽  
Jing-Lei Zhao ◽  
Gui-Lin She ◽  
Yan Jing ◽  
Huayan Pu ◽  
...  
Keyword(s):  
Carbon Nanotube ◽  
Volume Fraction ◽  
Thermal Environment ◽  
Nonlinear Partial Differential Equations ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Nonlinear Frequency ◽  
Environment Temperature ◽  
Vibration Responses ◽  
Walled Carbon Nanotubes

Abstract In this paper, the nonlinear free vibration responses of functionally graded nanocomposite fluid-conveying tube reinforced by single-walled carbon nanotubes (SWNTs) in thermal environment is investigated. The SWCNTs gradient distributed in the thickness direction of the tube forms different reinforcement patterns. The materials properties of the functionally graded carbon nanotube-reinforced composites (FG-CNTRC) are estimated by rule of mixture. A higher-order shear deformation theory and Hamilton’s variational principle are employed to derive the motion equations incorporating the thermal and fluid effects. A two-step perturbation method is implemented to obtain the closed-form asymptotic solution for these nonlinear partial differential equations. The nonlinear frequency under several patterns of reinforcement are presented and discussed. We conducted a series of studies aimed at revealing the effects of the flow velocity, environment temperature, geometrical ratios and carbon nanotube volume fraction on the nature frequency.

scholarly journals Buckling and postbuckling of axially-loaded CNT-reinforced composite cylindrical shell surrounded by an elastic medium in thermal environment

2018 ◽  
Author(s):  
Hoang Van Tung
Keyword(s):  
Carbon Nanotubes ◽  
Elastic Medium ◽  
Volume Fraction ◽  
Effective Properties ◽  
Thermal Environment ◽  
Cylindrical Shells ◽  
Functionally Graded ◽  
Environment Temperature ◽  
Classical Shell Theory ◽  
Walled Carbon Nanotubes

Buckling and postbuckling behaviors of nanocomposite cylindrical shells reinforced by single walled carbon nanotubes (SWCNTs), surrounded by an elastic medium, exposed to a thermal environment and subjected to uniform axial compression are investigated in this paper. Material properties of carbon nanotubes (CNTs) and isotropic matrix are assumed to be temperature dependent, and effective properties of nanocomposite are estimated by extended rule of mixture. The CNTs are embedded into matrix via uniform distribution (UD) or functionally graded (FG) distribution along the thickness direction. Governing equations are based on Donnell’s classical shell theory taking into account von Karman-Donnell nonlinear terms and interaction between the shell and surrounding elastic medium. Three-term form of deflection and stress function are assumed to satisfy simply supported boundary conditions and Galerkin method is applied to obtain load-deflection relation from which buckling and postbuckling behaviors are analyzed. Numerical examples are carried out to analyze the effects of CNT volume fraction and distribution types, geometrical ratios, environment temperature and surrounding elastic foundation on the buckling loads and postbuckling strength of CNTRC cylindrical shells.

Effect of carbon nanotube-reinforced magneto-electro-elastic facings on the pyrocoupled nonlinear deflection of viscoelastic sandwich skew plates in thermal environment

2021 ◽  
pp. 146442072110440
Author(s):  
Vinyas Mahesh
Keyword(s):  
Carbon Nanotube ◽  
Complex Modulus ◽  
Thermal Environment ◽  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Energy Principle ◽  
Design Engineers ◽  
Total Potential ◽  
Viscoelastic Core

This work presents a finite-element-based numerical formulation to evaluate the nonlinear deflections of magneto-electro-elastic sandwich skew plates with a viscoelastic core and functionally graded carbon nanotube-reinforced magneto-electro-elastic face sheets. Meanwhile, the proposed formulation accommodates the geometrical skewness as well. The magneto-electro-elastic sandwich skew plate is operated in the thermal environment and subjected to various multiphysics loads, including electric and magnetic loads. The viscoelastic core is modelled via the complex modulus approach. Two different forms of viscoelastic cores, such as Dyad 606 and EC 2216, are considered in this study. Also, different thickness configurations of core and facing arrangements are taken into account. The plate kinematics is presumed through higher-order shear deformation theory, and von Karman's nonlinear strain displacement relations are incorporated. The global equations of motion are arrived at through the total potential energy principle and solved via the direct iterative method. Special attention is paid to assessing the influence of pyroeffects, coupling fields and electromagnetic boundary conditions on the nonlinear deflections of magneto-electro-elastic sandwich plates working in the thermal environment and subjected to electromagnetic loads, which is the first of its kind. Also, parametric studies dealing with the skew angles, carbon nanotube distributions and volume fractions, thickness ratio, and aspect ratio have been discussed. The results of this work are believed to be unique and serve as a guide for the design engineers towards developing sophisticated smart structures for various engineering applications.

Vibration control of sandwich plate–reinforced nanocomposite face sheet and porous core integrated with sensor and actuator layers using perturbation method

2020 ◽  
pp. 107754632094833 ◽  
Author(s):  
Rasoul Rostami ◽  
Mehdi Mohammadimehr
Keyword(s):  
Carbon Nanotube ◽  
Perturbation Method ◽  
Vibration Control ◽  
Sandwich Plate ◽  
Volume Fraction ◽  
Shear Deformation Theory ◽  
Face Sheet ◽  
Scale Transformation ◽  
Nonlinear Frequency ◽  
Porous Core

In this article, the vibration control of the sandwich plate reinforced by carbon nanotube in the face sheet and porous core integrated with sensor and actuator layers is investigated. The piezoelectric layers at the bottom and top surfaces of the sandwich plate play the role of the sensor and actuator. By applying the Hamilton’s principle, the governing equations of the structure are derived based on the first-order shear deformation theory. The perturbation method is used to find the relationships between nonlinear frequency and amplitude response of the sandwich plate. The effect of porosity coefficient, temperature, volume fraction of carbon nanotube, and geometric parameters on nonlinear frequency and vibration control of the sandwich plate is studied. Moreover, the influence of material type of sensor and actuator and scale transformation parameter on the nonlinear frequency and vibration control of the system is investigated. According to the obtained results, in the case of ε < 0, the system stiffness presents softening behavior, whereas in the case of ε > 0, the system stiffness becomes hardening. By considering the effect of the voltage coefficient on the vibration control and the needed time for stabilization, the results of this article can be used to design, manufacture, and control modern structures.

Free Vibration Responses of Functionally Graded Spherical Shell Panels Using Finite Element Method

2013 ◽  
Author(s):  
Vishesh Ranjan Kar ◽  
Subrata Kumar Panda
Keyword(s):  
Mathematical Model ◽  
Free Vibration ◽  
Spherical Shell ◽  
Volume Fraction ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Bottom Surface ◽  
Power Law Distribution ◽  
Vibration Responses ◽  
Support Conditions

Free vibration responses of functionally graded spherical shell panels are investigated in the present article. A general mathematical model is developed based on higher order shear deformation theory mid-plane kinematics. The effective material properties are graded in the thickness direction according to a power-law distribution and it varies continuously from metal (bottom surface) to ceramic (top surface). The model is discretized using a nine noded quadrilateral Lagrangian element. A convergence test has been done with different mesh refinement and compared with the available published results. In addition to that the present study includes an ANSYS model check with the developed mathematical model to show the efficacy. New results are computed for different parameters such as volume fraction, thickness ratio, curvature ratio and support conditions which indicates the effect of parametric study on non-dimensional frequency parameters.

Characteristics of Power Law and Sigmoid FGMs Models in Thermal Effect

2016 ◽  
Vol 829 ◽  
pp. 90-94
Author(s):  
Seok Hyeon Kang ◽  
Ji Hwan Kim
Keyword(s):  
Power Law ◽  
Volume Fraction ◽  
Thermal Environment ◽  
Virtual Work ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Temperature Dependent ◽  
Graded Materials ◽  
Virtual Work Principle ◽  
Temperature Dependent Properties

In thermal environment, vibration behavior of Functionally Graded Materials (FGMs) plates is investigated, and the materials are developed with mixing ceramic and metal. Present study is based on the first-order shear deformation theory of plate. Then, mixture methods such as Power law (P-) and Sigmoid (S-) models are chosen. According to a volume fraction, the material properties are assumed to vary continuously through the thickness direction and to be temperature dependent properties. Further, thermal effects are considered as uniform temperature rise and one dimensional heat transfer. For the structure analysis, FEM is used to obtain the natural frequencies based on the virtual work principle.

scholarly journals Effect of Thickness Variable on the Bending Analysis of Rotating Functionally polymer Graded Carbon Nanotube Reinforced Cylindrical Panels

2019 ◽  
Vol 25 (4) ◽  
pp. 155-172
Author(s):  
Hamad Mohammed Hasan ◽  
Methaq Jasam Swadi
Keyword(s):  
Carbon Nanotubes ◽  
Variable Thickness ◽  
Volume Fraction ◽  
Shear Deformation Theory ◽  
Longitudinal Direction ◽  
Functionally Graded ◽  
Elastic Response ◽  
Good Correspondence ◽  
Cylindrical Panels ◽  
Walled Carbon Nanotubes

This study offers the elastic response of the variable thickness functionally graded (FG) by single walled carbon nanotubes reinforced composite (CNTRC) moderately thick cylindrical panels under rotating and transverse mechanical loadings. It’s considered that, three kinds of distributions of carbon nanotubes which are uniaxial aligned in the longitudinal direction and two functionally graded in the transverse direction of the cylindrical panels. Depending on first order shear deformation theory (FSDT), the governing equations can be derived. The partial differential equations are solved by utilizing the technique of finite element method (FEM) with a program has been built by using FORTRAN 95. The results are calculated to investigate the influence of the variable thickness, geometric parameters, rotating velocity, carbon nanotubes (CNTs) volume fraction for different boundary conditions on the non-dimensional deflection of the cylindrical panels. A comparison study has been carried out between the results of present study and that available in the open literature and found very good correspondence between the two results.  

Free vibration response of carbon nanotube reinforced pretwisted conical shell under thermal environment

2019 ◽  
Vol 234 (3) ◽  
pp. 770-783 ◽  
Author(s):  
Pabitra Maji ◽  
Mrutyunjay Rout ◽  
Amit Karmakar
Keyword(s):  
Carbon Nanotubes ◽  
Finite Element ◽  
Carbon Nanotube ◽  
Free Vibration ◽  
Conical Shell ◽  
Dynamic Equilibrium ◽  
Thermal Environment ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Mode Shapes

Finite element procedure is employed to analyze the free vibration characteristics of rotating functionally graded carbon nanotubes reinforced composite conical shell with pretwist under the thermal environment. In this paper, four types of carbon nanotube grading are considered, wherein the distribution of carbon nanotubes are made through the thickness direction of the conical shell. An eight-noded isoparametric shell element is used in the present formulation to model the panel based on the first-order shear deformation theory. For moderate rotational speeds, the generalized dynamic equilibrium equation is derived from Lagrange’s equation of motion, neglecting the Coriolis effect. The finite element code is developed to investigate the effect of twist angle, temperature, aspect ratio, and rotational speed on natural frequencies. The mode shapes of a carbon nanotube reinforced functionally graded conical shell at different twist angles and rotational speeds are also presented.

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.

FREE VIBRATION OF FUNCTIONALLY GRADED ARBITRARY STRAIGHT-SIDED QUADRILATERAL PLATES RESTING ON ELASTIC FOUNDATIONS

2011 ◽  
Vol 03 (04) ◽  
pp. 825-843 ◽  
Author(s):  
A. ALIBEYGI BENI
Keyword(s):  
Free Vibration ◽  
Elastic Foundation ◽  
Volume Fraction ◽  
Thermal Environment ◽  
Differential Quadrature Method ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Geometrical Shape ◽  
Computational Domain ◽  
Fg Plates

The free vibration of functionally graded (FG) arbitrary straight-sided quadrilateral plates rested on two-parameter elastic foundation and in thermal environment is presented. The formulation is based on the first-order shear deformation theory (FSDT). The material properties are assumed to be temperature-dependent and graded in the thickness direction. The solution procedure is composed of transforming the governing equations from physical domain to computational domain and then the discretization of the spatial derivatives by employing the differential quadrature method (DQM) as an efficient and accurate numerical tool. After studying the convergence of the method, its accuracy is demonstrated by comparing the obtained solutions with the existing results in literature for isotropic rectangular and FG rectangular and skew plates. Then, the effects of thickness-to-length ratio, elastic foundation parameters, volume fraction index, geometrical shape and the boundary conditions on the frequency parameters of the FG plates are studied.

Thermomechanical nonlinear stability of pressure-loaded functionally graded carbon nanotube-reinforced composite doubly curved panels with tangentially restrained edges

2019 ◽  
Vol 233 (16) ◽  
pp. 5848-5859 ◽  
Author(s):  
Le Thi Nhu Trang ◽  
Hoang Van Tung
Keyword(s):  
Carbon Nanotubes ◽  
Carbon Nanotube ◽  
Nonlinear Stability ◽  
Volume Fraction ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Nonlinear Load ◽  
Reinforced Composite ◽  
Doubly Curved ◽  
Curved Panels

Geometrically nonlinear response of doubly curved panels reinforced by carbon nanotubes exposed to thermal environments and subjected to uniform external pressure are presented in this paper. Carbon nanotubes are reinforced into isotropic matrix through uniform and functionally graded distributions. Material properties of constituents are assumed to be temperature dependent, and effective elastic moduli of carbon nanotube-reinforced composite are determined according to an extended rule of mixture. Basic equations for carbon nanotube-reinforced composite doubly curved panels are established within the framework of first-order shear deformation theory. Analytical solutions are assumed, and Galerkin method is used to derive closed-form expressions of nonlinear load–deflection relation. Separate and combined effects of carbon nanotube distribution and volume fraction, elasticity of in-plane constraint, elevated temperature, initial imperfection, geometrical ratios and stiffness of elastic foundations on the nonlinear stability of nanocomposite doubly curved panels are analyzed through numerical examples.

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