ISSN
2230- 9373
Volume-IX , Issue-1
January-March, 2019
Free Vibration Analysis of a FG Plate under First Order Shear
Deformation using Ansys
Atul Kumar, Prof R.R.Dash
Department of Mechanical Engineering, CET, Bhubaneswar E-mail: [email protected]
ABSTRACT
Functionally graded material (FGM) – functionally graded material belong to advanced material may be characterized by the variation in composition and structure gradually over volume by changes in the properties of material. Actually FGM is composed of a ceramic concentration and metal concentration layer by layer. The composition layers gradually from the metal to the ceramic, through the material. The material can be designed for specific function and applications. Various approaches based on the particulate processing, perform processing, layer processing and melt processing are used to fabricate the functionally graded materials. In this work free vibration on a fixed FG (functionally graded) plate is analysed by ANSYS software under first order shear deformation using SHELL element.
INTRODUCTION
In many engineering application we use alloy not pure metal. Pure metal are of less demand or use in engineering application. Suppose we want create a machine component which has malleable or ductile as well as hard, that is not possible because there is no such material existing in nature. So we will create this component by alloy i.e. combination (in liquid state) of one metal with another metal or non-metal. Alloying gives a property that gives a property that is different from the parent materials. Ex brass (alloy of copper and zinc), bronze (copper and tin), Babbitt material etc. since we have been experimenting with one form of alloy are called composite material.
A composite material is a material made from two or more constituent materials which have different physical or chemical properties that when combined, produce a material with characteristics different from the individual components. Ex. Plywood, fibre- reinforced, fibre glass etc.
An alloy is a mixture of at least two elements with one of those elements being a metal. Alloys can come in both solid and solution forms. Those alloys that only contain two elements are called binary alloys, while those that contain three elements are called ternary alloys. The amount of a particular element in side of an alloy is usually measured in mass with a percentage attached to it. Alloying gives a property that gives a property that is different from the parent materials. Ex brass (alloy of copper and zinc), bronze (copper and tin), Babbitt material etc.
Compositeis, much like an alloy, a combination of at least two or more components. However, while
an alloy always contains a metal in it, a composite does not have any metal included in its mixture. There are two different types of constituent materials that make up a composite. They are known as matrix and reinforcement materials. One example of natural composite is wood .it contains a combination of cellulose fibres and lignin.
Main difference between alloys and composites is alloys can be either homogeneous or heterogeneous mixtures but composites are always heterogeneous.
Functionally graded material
Functionally graded material (FGM) – functionally graded material belong to advanced material may be characterized by the variation in composition and structure gradually over volume by changes in the properties of material.
Actually FGM is composed of a ceramic and metal by layer by layer. The composition layers gradually from the metal to the ceramic, through the material. The material can be designed for specific function and applications. Various approaches based on the particulate processing, perform processing, layer processing and melt processing are used to fabricate the functionally graded material.
This material is not homogeneous, consisting of two or more than two different materials. The overall properties of FMG are unique and different from any of the individual materials that form it.
FGM have a variation through the material volume, moving from one state/composition to another in a defined transition pattern from one side of the material volume to the other.
The term “composite material “is not equivalent to the term “functionally graded material” .composite material includes, at least, two different components. But the FGM may be monocomponental material with gradient caused, for example, by non –uniform (gradient) distribution of residual stresses.
In a simple way we can say material with changing composition, microstructure, or porosity across the volume of the material are called functionally graded material (FGM). Properties of FGM are not uniform across the entire material and properties of FGM depend on the spatial position of the material in the bulk structure of the material.
Most of the FGMs are made by ceramic and metal and ceramic provides good thermal resistance and metal provides mechanical properties as a toughness and hardness.
TYPES OF FUNCTIONALLY GRADED MATERIALS
There are mainly three types of functionally graded materials, which area) Chemical composition gradient functionally gradient materials
b) Microstructure gradient functionally gradient materials
c) Porosity gradient functionally gradient materials
material. Single phase FGM is produced by a single phase i.e. single phage functionally graded material is produced when the composite is produced by a single phase, as a result of the solubility of the chemical elements of one phase to another phase. This is occurring during the sintering process. In sintering process, some of metallic powders will react and form different chemical compounds and phases. Most of FGMs are multiphase. The phases and chemical composition are made to vary across the bulk volume of the material.
Microstructure gradient functionally gradient material.
In this type of FGM; microstructure is tailored so that different different microstrucre are produced in the material, this is made to change gradually so we get required properties from the material. In Microstructure gradient FGM, gradation of microstructure (Microstructural gradation) can be achieved during cooling or solidification process, in this process outer surface of material is fast cooling and core of the same material cool very slowly i.e. outer surface quenched. Due to quench we find harder surface. So microstructure gradation can be achieved through heat treatment.
Porosity gradient functionally gradient material
Porosity gradient functionally graded material is also a type of FGM. In this FGM porosity in the material is made to change with the change in the spatial position in the bulk material. According to the required properties of FGM, The shape and size of the pore are designed and varied. This material is mainly used in biomedical. By varying the powder particle sizes which are used at different location in the bulk material during the gradation process; the pore size gradation can be achieved.
1.
Area of application of functionally graded materials.
Today FGMs are applied in a number of industries and we hope with huge potential to be used in other application in the future. Now days it is used in aerospace, automobile, thermo electronics, Opto electronics, energy, defence, medicine, cutting tool, etc.
2.
Relation of young’s modulus and density with thickness.
In this thesis work on Modal analysis of a thin plate which is made by functionally graded material that has 4 different material, metal as well as ceramic.
material Young’s modulus in
Gpa
Poisson ratio Density (kg/m3)
SUS 304 (metal) 201.04 0.33 8166
Aluminum (metal) 68.9 0.33 2700
Zirconia (ceramic) 211 0.33 4500
Si3N4 (ceramic) 348.43 0.24 2370
Power law distribution of the volume fraction is used to express the variation of material properties in FGMs. in this model thickness of the plate in z direction, material property young’s modulus and density along thickness expressed as
E=E (z) = (Ec-Em) (z/t+1/2)q+Em (1.1)
ꝭ= ꝭ (z) = (ꝭc- ꝭm) (z/t+1/2) q + ꝭm(1.2)
E and ꝭdenote the young’s modulus and density of FGM respectively and subscript m and c indicate for
WORKING
In this work we do modal analysis for find the natural frequency of a rectangular plate which is made by functionally graded material. Suppose this plate is made by twenty layers and each layer has same thickness.
Length, width and height of this plate is a, b & t respectively along x, y and z direction.
First we find the natural frequency of a rectangular BEAM dimension 1000x1000x100mm with material (Aluminium)
Young’s modulus (E) =69GPa, Poisson ratio (µ) =.32, density (ꝭ) =2710kg/m3
Boundary condition and solution
Now we will do the same problem with plate (by number of layers.)
Plates
are defined as plane structural elements with a small thickness compared to the planar dimensions. The typical thickness to width ratio of a plate structure is less than 0.1.SHELL181 Element Description
SHELL181 is suitable for analyzing thin to moderately-thick shell structures. It is a four-node element and six degrees of freedom at each node: translations in the x, y, and z directions, and rotations about the x, y, and z-axes.
SHELL181 is used for linear, large rotation, and/or large strain nonlinear applications. Change in shell thickness is accounted for in nonlinear analyses.
SHELL181 can be used for layered applications for modeling composite shells or sandwich construction.
The shell section commands allow for layered shell definition. Options are available for specifying the thickness, material, orientation, and number of integration points through the thickness of the layers.
MODE
We consider on fixed Plate. On this plate we have done modal analysis in ANSYS software
with APDL interface for 20 modes. This plate has 20 layers and each layer has same
thickness and each layer made by aluminium.
Now we consider another material aluminum oxide (AL2O3) this is a ceramic has following properties.
Young’s modulus (E) =393 Gpa, Poisson ratio (µ) =.27, density (ꝭ) =3.7*103kg/m3
We have compared same plate with metal aluminum and ceramic aluminum oxide and we find frequency with ceramic gives more frequency.
In same experiment we change some material properties we have create first 19 layers from Ceramic aluminum oxide and last are made by metal (aluminum) and find frequency.
Frequency decreases compare to full ceramic Concentration.
Now fifteen layers made by metal rest are made by ceramic (75% metal 25%ceramic)
CONCLUSION
In this work we find ceramic concentration gives less vibration as compared to metal. If we create the total body by metal concentration we find very strong and hard body but has very high thermal expansion I.e. heat will be lose. Good conductor of heat and electricity so heat and current will flow, react with chemical .If we create total body by ceramic concentration then we find no stronger body. As we know ceramic has less thermal expansion, not react with water, not oxidized very high corrosion resistance, high melting point (so they are high resistant) ,low electric and thermal conductivity (they are good insulator),they are not reactive with chemicals. But suppose we want both properties i.e. properties of metal as well as ceramic. Then we create layer by layer some layers are made by metal and some ceramic.
REFERENCE
1. A.Shahrjerdi and Mustapha, Second Order Shear Deformation for free Vibration Analysis a Functionally Graded Quadrangle plate.
2. J.N Reddy, Theory and Analysis of elastic Plates and shells.
