Dynamic Behavior Study of Functionally Graded Porous Nanoplates

2021 ◽  
Vol 33 ◽  
pp. 83-92
Author(s):  
Hadj Mostefa Adda ◽  
Bouchafa Ali ◽  
Merdaci Slimane
Keyword(s):  
Natural Frequencies ◽  
Plate Theory ◽  
Functionally Graded ◽  
Small Scale ◽  
Dimensionless Frequency ◽  
Equilibrium Equations ◽  
Local Principle ◽  
Behavior Study ◽  
Small Scale Effect ◽  
The Impact

This paper introduces the analytical solutions of complex behavior analysis utilizing high-order shear deformation plate theory of functionally graded FGM nano-plate content consisting of a mixture of metal and ceramics with porosity. To incorporate the small-scale effect, the non-local principle of elasticity is used. The impact of variance of material properties such as thickness-length ratio, aspect ratio, power-law exponent and porosity factor on natural frequencies of FG nano-plate is examined. Compared to those achieved from other researchers, the latest solutions are. Using the simulated displacements theory, equilibrium equations are obtained. Current solutions of the dimensionless frequency are compared with those of the finite element method. The effect of geometry, material variations of nonlocal FG nano-plates and the porosity factor on their natural frequencies are investigated in this review. The results are in good agreement with those of the literature.

Elastic Foundation Analysis of Uniformly Loaded Functionally Graded Viscoelastic Sandwich Plates

2012 ◽  
Vol 28 (3) ◽  
pp. 439-452 ◽  
Author(s):  
A. M. Zenkour ◽  
M. Sobhy
Keyword(s):  
Power Law ◽  
Sandwich Plate ◽  
Plate Theory ◽  
Functionally Graded ◽  
Sandwich Plates ◽  
Equilibrium Equations ◽  
Graded Material ◽  
Plate Aspect Ratio ◽  
Type V ◽  
Power Law Index

AbstractThis paper deals with the static response of simply supported functionally graded material (FGM) viscoelastic sandwich plates subjected to transverse uniform loads. The FG sandwich plates are considered to be resting on Pasternak's elastic foundations. The sandwich plate is assumed to consist of a fully elastic core sandwiched by elastic-viscoelastic FGM layers. Material properties are graded according to a power-law variation from the interfaces to the faces of the plate. The equilibrium equations of the FG sandwich plate are given based on a trigonometric shear deformation plate theory. Using Illyushin's method, the governing equations of the viscoelastic sandwich plate can be solved. Parametric study on the bending analysis of FG sandwich plates is being investigated. These parameters include (i) power-law index, (ii) plate aspect ratio, (iii) side-to-thickness ratio, (iv) loading type, (v) foundation stiffnesses, and (vi) time parameter.

scholarly journals Non-Local Buckling Analysis of Functionally Graded Nanoporous Metal Foam Nanoplates

Coatings ◽  
2018 ◽  
Vol 8 (11) ◽  
pp. 389 ◽  
Author(s):  
Yanqing Wang ◽  
Zhiyuan Zhang
Keyword(s):  
Metal Foam ◽  
Plate Theory ◽  
Constitutive Relations ◽  
Equations Of Motion ◽  
Local Buckling ◽  
Functionally Graded ◽  
Small Scale ◽  
Refined Plate Theory ◽  
Nanoporous Metal ◽  
Non Local

In this study, the buckling of functionally graded (FG) nanoporous metal foam nanoplates is investigated by combining the refined plate theory with the non-local elasticity theory. The refined plate theory takes into account transverse shear strains which vary quadratically through the thickness without considering the shear correction factor. Based on Eringen’s non-local differential constitutive relations, the equations of motion are derived from Hamilton’s principle. The analytical solutions for the buckling of FG nanoporous metal foam nanoplates are obtained via Navier’s method. Moreover, the effects of porosity distributions, porosity coefficient, small scale parameter, axial compression ratio, mode number, aspect ratio and length-to-thickness ratio on the buckling loads are discussed. In order to verify the validity of present analysis, the analytical results have been compared with other previous studies.

A closed form solution for bending/stretching analysis of functionally graded circular plates under asymmetric loading using the Green function

2010 ◽  
Vol 224 (6) ◽  
pp. 1153-1163 ◽  
Author(s):  
A R Saidi ◽  
A Naderi ◽  
E Jomehzadeh
Keyword(s):  
Green Function ◽  
Closed Form ◽  
Volume Fraction ◽  
Plate Theory ◽  
Closed Form Solution ◽  
Form Solution ◽  
Functionally Graded ◽  
Transverse Displacement ◽  
Circular Plates ◽  
Equilibrium Equations

In this article, a closed-form solution for bending/stretching analysis of functionally graded (FG) circular plates under asymmetric loads is presented. It is assumed that the material properties of the FG plate are described by a power function of the thickness variable. The equilibrium equations are derived according to the classical plate theory using the principle of total potential energy. Two new functions are introduced to decouple the governing equilibrium equations. The three highly coupled partial differential equations are then converted into an independent equation in terms of transverse displacement. A closed-form solution for deflection of FG circular plates under arbitrary lateral eccentric concentrated force is obtained by defining a new coordinate system. This solution can be used as a Green function to obtain the closed-form solution of the FG plate under arbitrary loadings. Also, the solution is employed to solve some different asymmetric problems. Finally, the stress and displacement components are obtained exactly for each problem and the effect of volume fraction is also studied.

Low-Velocity Impact on a Functionally Graded Circular Thin Plate

2006 ◽  
Author(s):  
Pantele Chelu ◽  
Liviu Librescu
Keyword(s):  
Plate Theory ◽  
Equation System ◽  
Functionally Graded ◽  
Low Velocity Impact ◽  
Thin Plates ◽  
Low Velocity ◽  
Alternative Analysis ◽  
Velocity Impact ◽  
Graded Material ◽  
The Impact

In this paper, an alternative analysis strategy based on a Wavelet-Galerkin scheme specially tailored to solve impact problems of functionally graded orthotropic thin plates subjected to low-velocity impact is presented. The plate considered to be circular, is assumed to be clamped on its lateral edge and has internal supports of rigid, elastic and viscoelastic types. The material properties of the plate are represented in the form of exponential functions of the thickness coordinate. A rigid spherical indenter impacts the plate. The study is based on the classical lamination plate theory (CLT). An advanced contact law of the Hertzian type is adopted. A nonlinear Volterra integral equation system is obtained in the following unknown functions: the impact force and the dynamic reaction forces at the rigid, elastic and viscoelastic internal point supports. Numerical simulations displaying the contact force, the transversal displacement and the penetration depth are graphically presented, and pertinent conclusions regarding the implications of incorporation of graded material systems are outlined.

Computing Buckling Characteristics of Double-Layered Graphene Film Embedded in an Elastic Foundation

2019 ◽  
Vol 19 (06) ◽  
pp. 1950065
Author(s):  
Zhengtian Wu ◽  
Yang Zhang ◽  
Weicheng Ma
Keyword(s):  
Elastic Foundation ◽  
Plate Theory ◽  
Graphene Film ◽  
Nonlocal Theory ◽  
Small Scale ◽  
Type Model ◽  
Classical Plate Theory ◽  
Buckling Behavior ◽  
Small Scale Effect ◽  
Simulation Results

Given the unique and extremely valuable properties, research has significantly focussed on graphene sheets (GSs). To premeditate the small-scale effect, the present work applies the nonlocal theory to study the buckling behavior of a double-layered GS (DLGS) embedded in an elastic foundation. To derive the equation, classical plate theory is adopted. For the elastic foundation, Pasternak-type model is used. In terms of buckling response, a meshless method is utilized to compute simulation results. Accordingly, we examine the effects of aspect ratio, geometry, boundary conditions and nonlocal parameters on the buckling responses of DLGSs.

scholarly journals A Novel Higher-Order Shear and Normal Deformable Plate Theory for the Static, Free Vibration and Buckling Analysis of Functionally Graded Plates

2017 ◽  
Vol 2017 ◽  
pp. 1-20 ◽  
Author(s):  
Shi-Chao Yi ◽  
Lin-Quan Yao ◽  
Bai-Jian Tang
Keyword(s):  
Natural Frequencies ◽  
Plate Theory ◽  
Closed Form Solution ◽  
Higher Order ◽  
Form Solution ◽  
Functionally Graded ◽  
The Novel ◽  
Functionally Graded Plates ◽  
Graded Materials ◽  
Different Shapes

Closed-form solution of a special higher-order shear and normal deformable plate theory is presented for the static situations, natural frequencies, and buckling responses of simple supported functionally graded materials plates (FGMs). Distinguished from the usual theories, the uniqueness is the differentia of the new plate theory. Each individual FGM plate has special characteristics, such as material properties and length-thickness ratio. These distinctive attributes determine a set of orthogonal polynomials, and then the polynomials can form an exclusive plate theory. Thus, the novel plate theory has two merits: one is the orthogonality, where the majority of the coefficients of the equations derived from Hamilton’s principle are zero; the other is the flexibility, where the order of the plate theory can be arbitrarily set. Numerical examples with different shapes of plates are presented and the achieved results are compared with the reference solutions available in the literature. Several aspects of the model involving relevant parameters, length-to-thickness, stiffness ratios, and so forth affected by static and dynamic situations are elaborate analyzed in detail. As a consequence, the applicability and the effectiveness of the present method for accurately computing deflection, stresses, natural frequencies, and buckling response of various FGM plates are demonstrated.

Analytical investigation on nonlinear dynamic behavior and free vibration analysis of laminated nanocomposite plates

2019 ◽  
Vol 233 (19-20) ◽  
pp. 6866-6878 ◽  
Author(s):  
Nguyen Dinh Khoa ◽  
Pham Dinh Nguyen
Keyword(s):  
Carbon Nanotubes ◽  
Dynamic Behavior ◽  
Natural Frequencies ◽  
Plate Theory ◽  
Geometrical Nonlinearity ◽  
Free Vibration Analysis ◽  
Composite Plates ◽  
Analytical Investigation ◽  
Functionally Graded ◽  
Geometrical Parameters

This work presents the results of the dynamic behavior and natural frequencies of laminated polymer plates that are reinforced by carbon nanotubes. The laminated nanocomposite plates have two components: carbon nanotubes reinforced in different polymer matrices. The nonlinear equations are obtained by Reddy's third-order laminated plate theory with von Kármán's geometrical nonlinearity and solved by both Runge–Kutta and Galerkin methods. Detailed studies for the influences of carbon nanotubes' different types of reinforcements and weight fractions, geometrical parameters, Winkler and Pasternak foundations on the deflection–time curves, and natural frequencies of laminated functionally graded carbon nanotube-reinforced composite plates are examined.

scholarly journals A nonlocal sinusoidal plate model for micro/nanoscale plates

2014 ◽  
Vol 228 (14) ◽  
pp. 2652-2660 ◽  
Author(s):  
Huu-Tai Thai ◽  
Thuc P Vo ◽  
Trung-Kien Nguyen ◽  
Jaehong Lee
Keyword(s):  
Boundary Conditions ◽  
Shear Deformation ◽  
Transverse Shear ◽  
Plate Theory ◽  
Equations Of Motion ◽  
Nonlocal Elasticity Theory ◽  
Small Scale ◽  
Plate Model ◽  
Proposed Model ◽  
Small Scale Effect

A nonlocal sinusoidal plate model for micro/nanoscale plates is developed based on Eringen’s nonlocal elasticity theory and sinusoidal shear deformation plate theory. The small-scale effect is considered in the former theory while the transverse shear deformation effect is included in the latter theory. The proposed model accounts for sinusoidal variations of transverse shear strains through the thickness of the plate, and satisfies the stress-free boundary conditions on the plate surfaces, thus a shear correction factor is not required. Equations of motion and boundary conditions are derived from Hamilton’s principle. Analytical solutions for bending, buckling, and vibration of simply supported plates are presented, and the obtained results are compared with the existing solutions. The effects of small scale and shear deformation on the responses of the micro/nanoscale plates are investigated.

Maximization of Natural Frequencies for Functionally Graded Rectangular Plates

2021 ◽  
Vol 891 ◽  
pp. 116-121
Author(s):  
Aleksander Muc
Keyword(s):  
Analytical Methods ◽  
Natural Frequencies ◽  
Plate Theory ◽  
Free Vibrations ◽  
Functionally Graded ◽  
Optimization Techniques ◽  
Point Of View ◽  
Rectangular Plates ◽  
Classical Plate Theory ◽  
Arbitrary Boundary

In this paper optimal design of free vibrations for functionally graded plates is studied using the analytical methods. The analytical methods can be employed for the solution of six of 21 arbitrary boundary conditions (the combinations of clamped, simply supported and free). The influence of various models of porosity and forms of different reinforcements with nanoplatelets and carbon nanotubes are investigated, including variations of stiffness/density along the thickness of a plate. The analysis is carried out for the classical plate theory. Parametric studies illustrate the possibility of increasing natural frequencies and the necessity of implementing the optimization techniques to find the best solutions from the engineering point of view.

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