STATIC AND VIBRATION ANALYSIS OF COMPOSITE BEAMS USING FINITE ELEMENT
METHODS
G. Kalyan Chakravarthi
1, G. Venkatasubbaiah
21
Pursuing M.Tech Machine Design (Mechanical),
2Asst. Professor of Mechanical Department
Vignana Bharathi Institute of Technology, Pallavolu (V),Chapadu(M),Proddatur(T), Kadapa (D), (India)
ABSTRACT
Beams are structural members which are widely used and its dynamic characteristics under loading has great importance. Thus, the purpose of this paper is to carry out an efficient and accurate simulation for static and modal analysis of uniform beam using Ansys 14.5. Displacement and frequencies of cantilever beam are studied with distributed as well as surface load. Composite materials have interesting properties such as high strength to weight ratio, ease of fabrication, good electrical and thermal properties compared to metals. A composite material consists of layers of a composite mixture consisting of matrix. In this project a cantilever composite beam with both upper and lower surfaces symmetrically bonded by piezoelectric ceramic and the beam is made up of t300/976 graphite/epoxy composites. Design engineer must consider several alternatives such as best stacking sequence, optimum fiber angles in each layer as well as number of layers itself based on criteria such as achieving highest natural frequency loads of such structure. Analysis of such composite materials starts with estimation of resultant material properties. The created configuration interface rearranges the outline procedure to some degree. The dynamic examination as far as central normal recurrence and basic static burden is delineated by utilizing these general material constants as a later piece of investigation.
I. INTRODUCTION
A combination of two or more materials with different properties, or a system composed of two or more physically distinct phases separated by a distinct interface whose combination produces aggregate properties that are superior in many ways, to its individual constituents. A material with combination of two or more material can provide enhanced properties that produce a synergistic effect.
In composite materials there are two constituents one is grid and other is fortification. The constituents which is continuous and present in greater quantity is called matrix. The main functions of the matrix is to holds or bind the fibre together, distribute the load evenly between fibres, protect the fibre joint from mechanical and environmental damage and also carry shear. While the other is reinforced; its primary objective is to enhance the mechanical properties e.g. solidness, strength and so on. The mechanical property depends upon the shape and dimensions of reinforcement. On the premise of sort framework material, composites can be grouped into three
main categories, polymer, metallic and ceramic
II. OBJECTIVES
The project aims at detail FEM examination of shaft. The accompanying are the primary destinations of the venture.
1. Building a 3-D Solid parametric model of cantilever beam in CATIA V5.
2. Meshing the model by ANSYS MESHER in ANSYS 14.5.
3. Rigid body modes and Normal modes- we have calculated in free vibration analysis for cantilever composite beam.
4. Experimental modal analysis carried out using FFT ANALYSER MACHINE to validate our CAE work.
5. Behaviour of torsional modes, twisting modes and joined methods of vibration we have concentrated on for all frameworks.
6. ansys 14.5 is used to find out the deformation and stress-strain from given boundary condition.
7. Analysis is done for both ordinary cantilever beam and coated cantilever beam Dynamic response and investigation of critical stresses are found out by incorporating the boundary conditions at the journal bearing positions and tangential and radial forces on corresponding nodes.
For this ANSYS MESHER used for meshing and ANSYS used as solver.
Beams have always been used extensively in building materials and structures. Depending on the application and working environment they are frequently under dynamic loading condition. Hence, from the standpoint of proper functioning and safety, study of response of these structural elements under dynamic loading is of utmost importance.
Dynamic analysis of a structure or structural element consists of two different aspects, namely, free and forced vibration studies. The main purpose of a free vibration analysis is to predict the natural frequencies of various vibration modes of the component under no load and loaded conditions. The natural frequencies of the structure under some form of static loading are generally known as loaded natural frequencies. Determination of these frequencies is important to avoid resonance condition, where the external excitation frequency coincides with the system natural frequencies. At resonance condition, the element vibrates with large amplitude resulting in deterioration of structural health. This deterioration usually causes local increase in flexibility, which is a serious threat to life and performance of structural component.
These analyses are made in the static analysis module under ANSYS solution task. The stiffness matrix of the system is obtained with the static analysis by using the finite component strategy. Relocation values for each hub are computed by utilizing the comparison beneath under particular stacking. The overall equilibrium equations for linear structural static analysis are:
KuF Where; K= Total stiffness matrix u= Nodal displacement vector F= Total applied load vector Modal Analysis:
Natural frequencies of the system and mode shapes have to be calculated for the full solution method and mode superposition method which will be used in dynamic analysis step. Reaction of the framework for the outer constraining is dictated by compelling recurrence shapes.
ANSYS software is used for creating the model and performing the analysis of this study. APDL stands for ANSYS Parametric Design Language, a scripting that one can use to automate the common tasks or even building the model in term of parameters. In this paper, a double-acting hydraulic cylinder is used in the analysis. The model shown in Figure 4.1 is created as finite elements. In this fem, with eight nodes and three degrees of freedom in each node and layered 191 is chosen from ANSYS element library. All the dimensions of the cylinder are parametric and the dimensions used in the analysis are shown in Figure shown below
Figure 4.1 The Finite Element Model
In the analysis, two different boundary conditions are considered for bar with coating and with out. It is assumed that, the surface force is directly applied to the surface or to the body in two different coundation types and the static and dynamic analyses is made for these two mounting types. The degree of freedom boundary conditions is shown in Figure 4.2 and 2.3 working surface force of bar is taken as 10000N.
Figure 4.2 Boundary Condition a) with Coating-Type 1
Cantilever , modelled as FEM, is made of t300/976 graphite/epoxy compositesl. The properties of steel is given as
Modulus of Elasticity, E 150 GPa
Poisson Ratio, n 0.3
Density, 1600 Kg / m3
Cantilever beam coating, modeled as FEM, is made of piezoelectric ceramic properties. The properties of steel are given as.
Modulus of
Elasticity, Poisson Shear
E (GPa) Ratio, n ModuluGPa Density
E1=63 0.3 24.2 1.5(10)6
E2=63 0.3 24.2
E3=63 0.3 24.2
III. RESULTS AND DISCUSSIONS
Figure 4.4 Static Displacement Distributions of Cantilever Beam,
Figure 4.5 Static Stress Distributions of Cantilever Beam,
Figure 4.5 Static Stress Distributions of Cantilever Beam,
Figure 4.6 Von Mises Stress
Figure 4.7 Static Strain Energy
Figure 4.8 Modal Deformation
WITH COATINGWITH OUT COATING TOTAL
DEFORMATION,(M)
0.16989 0.66672
EQUIVALENT ELASTIC STRAIN,(M/M)
0.055383 0.14821
EQUIVALENT STRESS,(PA)
8.2026e9 2.2138e10
STRAIN ENERGY,(J) 82.62 J 48.663
Table 4.1Comparision of Deflection of Cylinder for Different Materials and Boundary
Conditions
mode With out coating
deformation With coating
deformation
Mode 1
174.85 Max :
4.5706
Freq : 152.67
Max : 1.4822
Min : 0 Min : 0
Mode 2
687.63 Max : 4.549 Freq : 383.35
Max : 1.4732
Min : 0 Min : 0
Mode 3
1090 Max : 4.5683
Freq:
942.58
Max : 1.476
Min : 0 Min : 0
Mode 4
2290.4 Max : 5.6795
Freq : 1685.1
Max : 1.6938
Min : 0 Min : 0
Table 4.3 Natural Frequencies of Cylinder, Bc-1type of carbon/Epoxy
Figure 4.Modal Deformation IV. CONCLUSIONS
Composite design is designed using CATIA V5 R20 and analysis is done in ANSYS 16 in structural and modal workbench. We first designed a rectangle bar in CATIA with required dimensions and then it is imported in ANSYS 16 work bench for further structural and modal workbench...later on the same process is repeated with coating. After thorough analysis we conclude that by applying piezoelectric ceramic coating there is change in deformation, von misses stress and strain. We even observed very low damping frequency in modal workbench with very low deformation.
We conclude that by applying piezo electric ceramic coating to cantilever composite beam there is a lot of difference in deformation and stress factor , so it is suggestible.
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AUTHOR DETAILS
G KALYAN CHAKRAVARTHI pursuing M-Tech in Vignana Bharathi Institute Of Technology, Pallavolu (village), Chapadu (mandal), Proddatur (taluqa), Kadapa (dist)
G.VENKATASUBBAIAH working as Associate Professor in Mechanical Engineering in Vignana Bharathi Institute of Technology, Proddatur, Kadapa dist, A. P., India , He is having more than Seven years of teaching experience.
