Dynamic Modelling of Annular Plates of Functionally Graded Structure Resting on Elastic Heterogeneous Foundation with Two Modules

2015 ◽  
Vol 31 (5) ◽  
pp. 493-504 ◽  
Author(s):  
A. Wirowski ◽  
B. Michalak ◽  
M. Gajdzicki
Keyword(s):  
Mathematical Model ◽  
Dynamic Behaviour ◽  
Effective Properties ◽  
Plate Thickness ◽  
Dynamic Modelling ◽  
Composite Plates ◽  
Free Vibrations ◽  
Functionally Graded ◽  
Annular Plates ◽  
Heterogeneous Foundation

AbstractThe contribution is devoted to formulate an averaged mathematical model describing the dynamic behaviour of the composite annular plates resting on elastic heterogeneous foundation with two foundation modules. The plates are made of two-phased, functionally graded — type composites. In contrast to most of the papers in which material properties vary through the plate thickness, in the presented study we have dealt with the plate and foundation in which effective properties vary in a radial direction of the plate. The formulation of the macroscopic mathematical model for the analysis of the dynamic behaviour of these plates will be based on the tolerance averaging technique (Woźniak, Michalak, Jędrysiak, [ed]). This averaging method is an alternative to known asymptotic homogenization. The general results of the contribution will be illustrated by the analysis of free vibrations of the composite plates on heterogeneous foundation. The results obtained from the tolerance model were compared with the results obtained from FEM. There were compared the first four natural frequencies. A good consistency of the results from both methods was obtained.

Large Amplitude Free Vibration Analysis of Functionally Graded Annular Plates

2014 ◽  
Vol 971-973 ◽  
pp. 548-564 ◽  
Author(s):  
Boutahar Lhoucine ◽  
Khalid El Bikri ◽  
Benamar Rhali
Keyword(s):  
Free Vibration ◽  
Material Properties ◽  
Effective Properties ◽  
Plate Thickness ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Graphical Form ◽  
Wide Range ◽  
Non Linear

The geometrically non-linear axisymmetric free vibration of functionally graded annular plate (FGAP) having both edges clamped is analyzed in this paper. The material properties of the constituents are assumed to be temperature-independent and the effective properties of FGAP are graded in thickness direction according to a simple power law function in terms of the volume fractions. Based on the classical Plate theory and von Karman type non-linear strain-displacement relationships, the nonlinear governing equations of motion are derived using Hamilton’s principle. The problem is solved by a numerical iterative procedure in order to obtain more accurate results for vibration amplitudes up to twice the plate thickness. The numerical results are given for the first two axisymmetric non-linear mode shapes, for a wide range of vibration amplitudes and they are presented either in a tabular or in a graphical form, to show the significant effects that the large vibration amplitudes and the variation in material properties have on the non-linear frequencies and the associated bending stresses of the FGAP.

Thermally induced postbuckling of thin CNT-reinforced composite plates under nonuniform in-plane temperature distributions

2020 ◽  
pp. 089270572096217
Author(s):  
Le Thi Nhu Trang ◽  
Hoang Van Tung
Keyword(s):  
Thermal Load ◽  
Effective Properties ◽  
Plate Theory ◽  
Composite Plates ◽  
Functionally Graded ◽  
Postbuckling Behavior ◽  
Classical Plate Theory ◽  
Temperature Distributions ◽  
Basic Equations ◽  
Plane Temperature

This paper presents an analytical investigation on postbuckling behavior of thin plates reinforced by carbon nanotubes (CNTs) and subjected to nonuniform thermal loads. Unlike many previous works considered ideal case of thermal load is that uniform temperature rise, the present study considers more practical situations of thermal load are that sinusoidal and linear in-plane temperature distributions. CNTs are reinforced into matrix through functionally graded distributions and effective properties of nanocomposite are estimated according to extended rule of mixture. Basic equations are based on classical plate theory taking into account Von Karman nonlinearity, initial geometrical imperfection, interactive pressure from elastic foundations and elasticity of tangential constraints of simply supported boundary edges. Basic equations are solved by using analytical solutions and Galerkin method. From the obtained closed-form relations, thermal buckling and postbuckling behavior of nanocomposite plates are analyzed through numerical examples.

Buckling of Functionally Graded Circular/Annular Plates Based on the First-Order Shear Deformation Plate Theory

2004 ◽  
Vol 261-263 ◽  
pp. 609-614 ◽  
Author(s):  
L.S. Ma ◽  
Tie Jun Wang
Keyword(s):  
Shear Deformation ◽  
Material Properties ◽  
Volume Fraction ◽  
Plate Theory ◽  
Plate Thickness ◽  
Shear Deformation Theory ◽  
Outer Radius ◽  
Functionally Graded ◽  
First Order ◽  
Annular Plates

Based on the first-order shear deformation theory of plate, governing equations for the axisymmetric buckling of functionally graded circular/annular plates are derived. The coupled deflections and rotations in the pre-buckling state of the plates are neglected in analysis. The material properties vary continuously through the thickness of the plate, and obey a power law distribution of the volume fraction of the constituents. The resulting differential equations are numerically solved by using a shooting method. The critical buckling loads of circular and annular plates are obtained, which are compared with those obtained from the classical plate theory. Effects of material properties, ratio of inter to outer radius, ratio of plate thickness to outer radius, and boundary conditions on the buckling behavior of FGM plates are discussed.

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.

Geometrically nonlinear large deformation of CNT-reinforced composite plates with internal column supports

2017 ◽  
Vol 1 (1) ◽  
Author(s):  
L. W. Zhang
Keyword(s):  
Large Deformation ◽  
Volume Fraction ◽  
Ritz Method ◽  
Plate Thickness ◽  
Composite Plates ◽  
Functionally Graded ◽  
Width Ratio ◽  
Various Boundary Conditions ◽  
Modified Newton Method ◽  
Element Free

AbstractThe geometrical nonlinear analysis of internally supported nanocomposite plates subjected to a uniformly distributed load is carried out. This study investigates the effects of internal point/column supports on the large deformation bending of nanocomposite plates reinforced by carbon nanotubes (CNTs) with different types of distributions, namely, uniform and two kinds of functionally graded distributions through the thickness of the plates. Two-dimensional displacement field of the plate is approximated by a set of Improved Moving Least Squares (IMLS) functions. The arc-length iterative algorithm with the modified Newton method is employed to obtain the nonlinear response of nanocomposite plates. Convergence studies indicate the validity and effectiveness of the element-free IMLS-Ritz method. The effects of plate thickness-to-width ratio, volume fraction ratio, and plate aspect ratio on the large deformation behavior of nanocomposite plates under various boundary conditions are examined. To the best of the authors’ knowledge, the problem has not been attempted in the open literature.

Vibration Analysis of Carbon Nanotube Reinforced Composite Plates

2014 ◽  
Vol 553 ◽  
pp. 681-686 ◽  
Author(s):  
Feng Lin ◽  
Yang Xiang
Keyword(s):  
Ritz Method ◽  
Plate Thickness ◽  
Micromechanical Model ◽  
Composite Plates ◽  
Single Walled Carbon Nanotubes ◽  
Functionally Graded ◽  
Reinforced Composite ◽  
Support Conditions ◽  
Plate Vibration Problem ◽  
Walled Carbon Nanotubes

This paper presents an investigation on the free vibration of rectangular nanocomposite plates reinforced by aligned single-walled carbon nanotubes (SWCNTs). The CNT reinforcement may be uniformly distributed (UD) or functionally graded (FG) over the thickness direction of a plate. The material properties of the CNT composite are determined through a micromechanical model. The eigenvalue equation governing the plate vibration problem is derived by the p-Ritz method through minimizing the virtual strain and kinetic energies of a CNT composite plate. The influences of CNT distribution and reinforcing angle, plate thickness ratio, aspect ratio and support conditions on the vibration behaviour of the plates are discussed.

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