Nonlinear Analysis of a Thin Circular Functionally Graded Plate and Large Deflection Effects on the Forces and Moments

2008 ◽  
Vol 130 (1) ◽  
Author(s):  
A. Allahverdizadeh ◽  
A. Rastgo ◽  
M. H. Naei
Keyword(s):  
Nonlinear Analysis ◽  
Large Deflection ◽  
Volume Fraction ◽  
Plate Thickness ◽  
Functionally Grade ◽  
Functionally Graded ◽  
Governing Equations ◽  
Temperature Dependent ◽  
Harmonic Vibrations ◽  
Graded Material

Nonlinear analysis of a thin circular functionally grade plate is formulated in terms of von Karman’s dynamic equations. The plate thickness is constant and temperature-dependent functionally graded material (FGM) properties vary through the thickness of the plate. Forces and moments of the plate, due to large vibration amplitudes, are developed in this paper by solving the governing equations for harmonic vibrations. Corresponding results are illustrated in the case of steady-state free vibration. The results show that the variation of volume fraction index is influential in forces, moments, and FGM properties.

Dynamic Response of Cantilever FGM Cylindrical Shell

2011 ◽  
Vol 130-134 ◽  
pp. 3986-3993 ◽  
Author(s):  
Yu Xin Hao ◽  
Wei Zhang ◽  
L. Yang ◽  
J.H. Wang
Keyword(s):  
Cylindrical Shell ◽  
Volume Fraction ◽  
Nonlinear Oscillations ◽  
Equations Of Motion ◽  
Functionally Graded ◽  
Governing Equations ◽  
Temperature Dependent ◽  
Graded Materials ◽  
First Order ◽  
Two Degree Of Freedom

An analysis on the nonlinear dynamics of a cantilever functionally graded materials (FGM) cylindrical shell subjected to the transversal excitation is presented in thermal environment.Material properties are assumed to be temperature-dependent. Based on the Reddy’s first-order shell theory,the nonlinear governing equations of motion for the FGM cylindrical shell are derived using the Hamilton’s principle. The Galerkin’s method is utilized to discretize the governing partial equations to a two-degree-of-freedom nonlinear system including the quadratic and cubic nonlinear terms under combined external excitations. It is our desirable to choose a suitable mode function to satisfy the first two modes of transverse nonlinear oscillations and the boundary conditions for the cantilever FGM cylindrical shell. Numerical method is used to find that in the case of non-internal resonance the transverse amplitude are decreased by increasing the volume fraction index N.

Thermoelastic Transient Behavior for a Clamped FGM Circular Plate

2014 ◽  
Vol 14 (04) ◽  
pp. 1450005 ◽  
Author(s):  
Hong-Liang Dai ◽  
Xiang Yan ◽  
Lei Yang
Keyword(s):  
Circular Plate ◽  
Volume Fraction ◽  
Plate Thickness ◽  
Transient Behavior ◽  
Functionally Graded ◽  
Thin Plates ◽  
Power Law Distribution ◽  
Graded Material ◽  
Index Ratio ◽  
The Galerkin Method

In this paper, the thermoelastic transient behavior of a clamped circular plate composed of functionally graded material (FGM) is investigated. The material properties of the FGM circular plate are assumed to vary through the plate thickness according to a power law distribution of the volume fraction of constituent materials, except Poisson's ratio, which is assumed as constant. Based on the von Karman equation and classical theory of thin plates, the equation of motion for the FGM circular plate is derived by the Hamilton principle. The nonlinear governing equation is solved by the Galerkin method, along with Newmark's integration method, in an iterative manner. Numerical results reveal that the functional gradient index, ratio of thickness to radius, thermal and mechanical loads have significant effect on the thermoelastic transient behavior of the clamped FGM circular plate. The result presented herein may be used as a reference for solving other transient coupled problems of thermoelasticity.

ON VIBRATION OF FUNCTIONALLY GRADED PLATES ACCORDING TO A REFINED TRIGONOMETRIC PLATE THEORY

2005 ◽  
Vol 05 (02) ◽  
pp. 279-297 ◽  
Author(s):  
ASHRAF M. ZENKOUR
Keyword(s):  
Shear Deformation ◽  
Natural Frequencies ◽  
Volume Fraction ◽  
Plate Theory ◽  
Plate Thickness ◽  
Series Representation ◽  
Free Vibration Analysis ◽  
Present Theory ◽  
Functionally Graded ◽  
Graded Material

The displacement components are expressed by trigonometric series representation through the plate thickness to develop a two-dimensional theory. This trigonometric shear deformation plate theory is used to perform free-vibration analysis of a simply supported functionally graded thick plate. Lamé's coefficients and density for the material of the plate are assumed to vary in the thickness direction only. Effects of rotatory inertia are considered in the present theory and the vibration natural frequencies are investigated. The results obtained from this theory are compared with those obtained from a 3D elasticity analysis and various equivalent theories that are available. A detailed analysis is carried out to study the various natural frequencies of functionally graded material plates. The influences of the transverse shear deformation, plate aspect ratio, side-to-thickness ratio and volume fraction distributions are investigated.

Influence of Porosity on the Flexural and Free Vibration Responses of Functionally Graded Plates in Thermal Environment

2018 ◽  
Vol 18 (01) ◽  
pp. 1850013 ◽  
Author(s):  
Ankit Gupta ◽  
Mohammad Talha
Keyword(s):  
Free Vibration ◽  
Deformation Theory ◽  
Volume Fraction ◽  
Thermal Environment ◽  
Plate Thickness ◽  
Functionally Graded ◽  
Future Studies ◽  
Graded Material ◽  
Vibration Responses ◽  
Free Vibration Response

This paper examines the influence of porosities on the flexural and free vibration response of functionally graded material (FGM) plates based on the authors’ recently developed non-polynomial higher-order shear and normal deformation theory. The theory accommodates the nonlinear variation in the in-plane and transverse displacements in the thickness coordinates. It also contains the hyperbolic shear strain shape function in the displacement field with only four unknowns. A new mathematical model has also been proposed to incorporate the effects of porosity in the FGM plate. Various numerical examples have been solved to ascertain the accuracy, efficiency, and applicability of the present formulation. The effects of porosity, volume fraction index, plate thickness, aspect ratio, boundary conditions and temperature have been discussed in details. The obtained results can be treated as a benchmark for future studies.

Buckling and free vibration analysis of skew sandwich plates with viscoelastic core and functionally graded material constraining layer

2017 ◽  
Vol 233 (1) ◽  
pp. 369-381 ◽  
Author(s):  
Shince V Joseph ◽  
SC Mohanty
Keyword(s):  
Free Vibration ◽  
Functionally Graded Material ◽  
Sandwich Plate ◽  
Volume Fraction ◽  
Equations Of Motion ◽  
Functionally Graded ◽  
Skew Angle ◽  
Governing Equations ◽  
Viscoelastic Core ◽  
Graded Material

The present study is concerned with the free vibration and buckling analysis of a skew sandwich plate with a viscoelastic material core fixed between a functionally graded material constraining layer and a base layer of elastic material. The sandwich plate theory is followed to obtain the governing equations of motion in which the displacement fields of the viscoelastic core are assumed to have a linear variation between those of the two face layers. Finite element method based on first-order shear deformation theory is used to develop the governing equations of motion of the plate. The effects of different parameters such as skew angle, aspect ratio, thickness ratio, and volume fraction index on static and dynamic characteristics of the plate are examined. The increase in the skew angle has increasing effect on both natural the frequencies and critical buckling loads, whereas the fundamental loss factor decreases. The volume fraction index and various boundary conditions also have significant effects on the static and dynamic behavior of the plate.

TSDT theory for free vibration of functionally graded plates with various material properties

2021 ◽  
Vol 8 (4) ◽  
pp. 691-704
Author(s):  
M. Janane Allah ◽  
◽  
Y. Belaasilia ◽  
A. Timesli ◽  
A. El Haouzi ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Volume Fraction ◽  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Third Order ◽  
Implicit Algorithm ◽  
Proposed Model ◽  
Graded Material ◽  
Composite Modeling

In this work, an implicit algorithm is used for analyzing the free dynamic behavior of Functionally Graded Material (FGM) plates. The Third order Shear Deformation Theory (TSDT) is used to develop the proposed model. In this contribution, the formulation is written without any homogenization technique as the rule of mixture. The Hamilton principle is used to establish the resulting equations of motion. For spatial discretization based on Finite Element Method (FEM), a quadratic element with four and eight nodes is adopted using seven degrees of freedom per node. An implicit algorithm is used for solving the obtained problem. To study the accuracy and the performance of the proposed approach, we present comparisons with literature and laminate composite modeling results for vibration natural frequencies. Otherwise, we examine the influence of the exponent of the volume fraction which reacts the plates "P-FGM" and "S-FGM". In addition, we study the influence of the thickness on "E-FGM" plates.

Manufacturing and Measuring Mechanical Properties of Continuous Functionally Graded Beam

2021 ◽  
Vol 21 (2) ◽  
pp. 7-11
Author(s):  
Ahmed Mansoor Abbood ◽  
Haider K. Mehbes ◽  
Abdulkareem. F. Hasan
Keyword(s):  
Mechanical Properties ◽  
Young’S Modulus ◽  
Volume Fraction ◽  
Young's Modulus ◽  
Functionally Graded ◽  
High Concentration ◽  
Functionally Graded Beam ◽  
Low Concentration ◽  
Graded Material ◽  
Vertical Gravity

In this study, glass-filled epoxy functionally graded material (FGM) was prepared by adopting the hand lay-up method. The vertical gravity casting was used to produce a continuous variation in elastic properties. A 30 % volume fraction of glass ingredients that have mean diameter 90 μm was spread in epoxy resin (ρ = 1050 kg/m3). The mechanical properties of FGM were evaluated according to ASTM D638. Experimental results showed that a gradually relationship between Young’s modulus and volume fraction of glass particles, where the value of Young’s modulus at high concentration of glass particles was greater than that at low concentration, while the value of Poisson’s ratio at high concentration of glass particles was lower than that at low concentration. The manufacture of this FG beam is particularly important and useful in order to benefit from it in the field of various fracture tests under dynamic or cyclic loads.

Design Model and Prediction Model on Preparation of Functionally Graded Material by Co-Sedimentation

2005 ◽  
Vol 492-493 ◽  
pp. 471-476 ◽  
Author(s):  
Zhi Guang Zhou ◽  
Lian Meng Zhang ◽  
Qiang Shen ◽  
Dao Ren Gong
Keyword(s):  
Prediction Model ◽  
Volume Fraction ◽  
Functionally Graded ◽  
Design Model ◽  
Design Experiment ◽  
Mathematical Relationship ◽  
Graded Material ◽  
Powder Properties ◽  
Set Up ◽  
The Relationship

From the process of sedimentation the mathematical relationship between deposition volume and powder properties as well as sedimentation parameters was deduced in this paper. The relationship was expressed by using indirect method. Based on the formula, design model and prediction model were set up. The models can be used to design powder properties and predict the volume fraction of FGM. Programs to solve the models were developed in numerical methods. As examples, TiC-Ni system FGM were designed and predicted. The prediction results fit well with the design. Experiment of Mo-Ti system FGM was used to validate the prediction model.

Thermal Effects on the Vibration of Functionally Graded Deep Beams with Porosity

2017 ◽  
Vol 09 (05) ◽  
pp. 1750076 ◽  
Author(s):  
Şeref Doğuşcan Akbaş
Keyword(s):  
Mechanical Properties ◽  
Finite Element Method ◽  
Finite Element ◽  
Thermal Effects ◽  
Functionally Graded ◽  
Deep Beam ◽  
Material Distribution ◽  
Governing Equations ◽  
Temperature Dependent ◽  
Deep Beams

The purpose of this study is to investigate the thermal effects on the free vibration of functionally graded (FG) porous deep beams. Mechanical properties of the FG deep beam are temperature-dependent and vary across the height direction with different porosity models. The governing equations problem is obtained by using the Hamilton’s principle. In the solution of the problem, plane piecewise solid continua model and finite element method are used. The effects of porosity parameters, material distribution, porosity models and temperature rising on the vibration characteristics are presented and discussed with porosity effects for FG deep beams.

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