Optimal Location of Piezoelectric Patch on Composite Structure using Viewing Method

A useful material which is manufactured by mixing of two or three different materials in homogeneous level is termed as composite material. In now day’s composite materials are used in wide area such as aerospace, automobiles, satellite, bullet proof jackets, rotor blades etc. In this paper modal analysis of composite material, mixture of polyester as matrix and glass as fiber, is carried out by using ABAQUS software. The modal analysis of composite material for fiber orientation 450 is carried out. In this paper by viewing the different mode shapes of the composite material, the optimal location of piezoelectric patch is carried out.


1.INTRODUCTION
Composite materials are formed by combining two or more different materials in homogeneous level that have quite different properties. The different materials work together to give a useful composite material of unique properties, but within the composite anyone can easily tell the different materials apart because they do not dissolve or blend into each other. Some of the properties that can be enhanced by forming composite material are fatigue life, corrosion resistant, strength, stiffness, wear resistant, weight, thermal insulation, temperature dependent behavior, attractiveness, thermal conductivity, acoustical insulation [1]. But naturally all these properties are not improved at the same time because some properties are conflict to each other such as thermal insulation and thermal conductivity.
Industrial and commercial applications of composite materials are so vast that it's impossible to list all of them. So some of the structural applications which includes aircrafts, aerospace, sporting goods, marine, electronics (printed circuit boards), furniture (chair spring), medical industries (bone plates) and many more [2].
Analytical and finite element method is used to solve the different problems under different loads and boundary conditions. FEM modeling can done using different software such as ANSYS, MATLAB, ABAQUS [11] etc. Modal analysis of any composite materials always results in three parameters that are natural frequencies, mode shapes and damping factor [12].
Composite materials are also used for vibration control [5] because of having distinct properties from normal materials. Analytical and FEM modeling of composite material with piezoelectric patch [12] is used to find out the variation in deflection when it will be stretched and pressed. Modal analysis of composite materials for different fiber orientations is used to analysis the effect of fiber orientation on different properties. Optimal location of piezoelectric patch on composite structures set to be on a position where it will present proper detection and should not coincide with nodes of that mode shape [12]. In this paper by viewing the mode shapes of the composite beams the desired location of piezoelectric patch is carried out.

FINITE ELEMENT MODELLING OF COMPOSITE MATERIAL
In this section the finite element modeling of composite material as well as modal analysis is carried out by using ABAQUS software.

Modeling of composite material in ABAQUS software
Composite material mainly consists of two phases that is matrix phase and fiber phase. The matrix plays an important role to keep the fibers at desired positions. The desired distribution of the fibers is very important from micromechanical point of view. Mainly the function of fibers is to carry load and to provide high strength to the composite material, different fiber orientations results in different strength or enhancing different properties. In this paper, as shown in Fig.1, fiber orientation 45 0 is selected because it helps to resist shear of the composite beam. Properties of Glass-Polyester Composite Beam [3] are E 1 =37.41GPa E 2 =13.67GPa G 12 =5.478GPa G 13 =6.03GPa G 23 =6.666GPa 12 =0.3 =1768.9Kg/m3. The dimensions of beam are L x =0.11179m L y =12.7×10-3m and L z = 3.38×10-3m and mesh size is 10×1.

Modal analysis of composite material
In this section modal analysis of composite material is carried out. Before proposing viewing method, results of modal analysis are validated with [3] using ABAQUS software. Well satisfying results comes out with percentage error of 0.5%. In modal analysis four mode shapes are considered in which there is no node formation for 1 st mode shape but for 2 nd mode shape there is one node, for 3 rd mode shape there is two nodes similarly for 4 th mode shape there are three nodes.

OPTIMAL LOCATION OF PIEZOELECTRIC PATCH USING MODAL ANALYSIS
In Table ii first column represents the different locations of the piezoelectric patch on composite beam as L1, L2, L3, L4 and L5. For each position of piezoelectric patch four mode shapes were analyzed as shown in second column with particular frequencies. At L1 location for 4 th mode shape there are three nodes out which 3 rd node is coincide with the location of piezoelectric patch due to which the deflection won't be detected hence this position can't be set as optimal location. Similarly for location L2, L3 and L4, nodes are coinciding with piezoelectric patch for mode shapes 2 nd , 3 rd , 4 th respectively, so these locations are not considered as an optimal location but at L5 location by viewing all the mode shapes it is clear that there is no nodes which are coincide with this location so L5 is the optimal location for piezoelectric patch. Although by comparing 1 st mode shapes for all the locations it is analyzed that natural frequency goes on increasing with decrease in the distance of patch from fixed boundary condition [12].

CONCLUSION
In this paper, the choice of optimal location of piezoelectric patch on composite beam is proposed using the modal analysis. The natural frequencies and mode shapes of the composite beam are find out using ABAQUS software. By viewing the mode shapes, the optimal location of piezoelectric patch is estimated. The estimated location is near the boundary of the cantilever beam. To validate this in this paper the piezoelectric patch is shifted at different location on the cantilever beam. It is seen that when the piezoelectric patch is located at the tip of the cantilever beam less strain produced in the patch. The effect is there is less change in the overall natural frequency of the system. When the piezoelectric patch is near the boundary of cantilever beam the natural frequency of the overall system is increased. It means the piezoelectric patch adds stiffness to the composite beam.

ACKNOWLEDGMENT
The first author is thankful to Lovely Professional University (Punjab/INDIA) for giving appropriate knowledge and research labs to use it for this research.