Vibration Analysis of Laminated Composites Using Experimental and Genetic Algorithms Optimization Technique

In this paper, damage detection for different types of defects (delamination, crack and hole) in the composite laminate plate and cylindrical shell be used to characterize the vibration behavior experimentally which used two types of load (plus and sine load) to find the frequency response. To this end, some plates and cylindrical shells are made using hand-lay-up process. Glass fiber is used as a reinforcement in the form of bidirectional fabric and general purpose polyester resin as matrix for the composite material of plates and cylindrical shells. From the results, the damage detection by using the Genetic algorithms is investigated. Also, these experiments are used to validate the results of free vibration obtained from the finite elements program


INTRODUCTION
n the recent decades the use of composite laminate materials on structural applications has been growing, requiring great effort on development of analysis and design techniques. The large number of design variables and complexity of the mechanical behavior are outstanding characteristics of composite material structures design. Such characteristics turn the project much more difficult and laborious than those involving conventional material. Optimization methods have been used in the sense of turn the composite material structural design a more systematic and well defined task. As alternative to gradient based methods, many other techniques were tested, having the genetic algorithm (GA) stand out the others because it perfectly adjusts to the problem characteristics. GAs are probabilistic optimization methods that seek to minic the biological reproduction and natural selection process through random, but structured, operations. The design variable are coded as genes and grouped together on chromosomes strings that represent an organism. Züleyha Aslan and Mustafa Şahin, 2008. studied the effect of the size of beneath delaminations has no significant on the critical buckling load and compressive failure load of E-glass/epoxy composite laminates with multiple large delaminations, a numerical and experimental study is carried out to determine the buckling load of rectangular composite plates, for the experiments (0º/90º/0º/90º)s oriented cross-ply laminated plates with multiple large delaminations and without delamination are produced by using hand lay up technique and the results are compare with results obtained by ANSYS 11.0 package and good agreement obtained. Jocab L. Pelletier and Senthil S. Vel.,2006, presented a methodology for the multi-objective optimization of laminated composite materials that is based on an integer-coded genetic algorithm. The fiber orientation and fiber volume fractions of the laminae are chosen as the primary optimization variables. Simplified micromechanics equations are used to estimate the stiffness and strength of each lamina using the fiber volume fraction and material properties of the matrix and fibers. The lamina stresses for thin composite coupons subjected to force and/or moment resultants are determined using the classical lamination theory and the first ply failure strength is computed using the Tasi-Wu failure criterion. Kosuke Takahashi, et. al.,2007, proposed new measuring method of multiple electrical resistance changes to perform statistical diagnosis. The proposed method measures electrical resistance changes of multiple segments in a beam although electrical interference must be considered when multiple voltages are charged at once. Next statistical diagnosis is performed on loading to the beam a delamination crack is detected by the change of relative relationship between multiple electrical resistance changes due to damage occurring. M. R. Ghasemi and A. Ehsani,2007, studied the optimum weight and cost of a laminated composite plate, the Tsai-Hill theory is used as the failure criterion and the theory of analysis was based on the Classical lamination theory. A newly type of genetic algorithm as an optimization technique with a direct use of real variables was employed. Yet, since the optimization via genetic algorithm is a long process and the major time is consumed through the analysis, Radial basis function Neural network was employed in predicting the output from the analysis. Felipe Schaedler de Almedia and Armando Miguel Awruch, 2007, presented an optimization technique, using a genetic algorithm, applied to plates and shell of laminate composite materials, two cases are analyzed. In the first case weight and central deflection of a plate under a transverse pressure load are minimized using as optimization variables thickness and the fiber angle of each layer. In the second case, the stiffness maximization of cylindrical shell, under a transverse pressure load, and with geometrically nonlinear behavior, is obtained using as optimization variable the fiber angle of each layer. Shun Fa Hwang, et. al., 2009, presented the method to identify the effective elastic constants of inhomogeneous composite plates is demonstrated. The proposed method is applied successfully to determine the effective elastic constants of a woven composite plate and two PCB's a systematical two step procedure is proposed to

PRODUCTION OF THE LAMINATES SPECIMENS
Glass fiber is used as a reinforcement in the form of bidirectional fabric and general purpose polyester resin as matrix for the composite material of the laminates specimens. The steps of manufacturing the composite shell or plate using hand lay up process are described below.

Preparation of the Mould
The hand lay-up process as shown in Figure (1), is open molding technique. The surface of the mould is thoroughly cleaned to be ready for the use, by removing any dust and dirt from it as shown in the Figure (2a, 2b) for plate and cylindrical shell mould.

Application of the release agent
After the mould surface has been cleaned, the release agent is applied. Where, the mould surface is coated with a free wax using a smooth cloth. Then a film of Polyvinyl alcohol (PVA) is applied over the wax surface using sponge. PVA is a water soluble material and 15% solution in water is used. When water evaporates, a thin film of PVA is formed on the mould surface. PVA film is dried completely before the application of resin coat. This is very important as the surface of final article will be marred with partly dried PVA film otherwise release will not be smooth.

Preparation of the matrix martial
The matrix material is prepared using general purpose (GP) Polyester resin. Cobalt Octate (0.35% by volume of resin) is added to act as accelerator. Methyl ethyl kentone peroxide (MEKP) (1% by volume) is added to act as catalyst. Resin, accelerator and catalyst are thoroughly mixed. The use of accelerator is necessary because without accelerator resin does not cure properly. After adding the accelerator and catalyst to the polyester resin, it has left for some time so that bubbles formed during stirring may die out. The amount of added accelerator and catalyst is not high because a high percentage reduces gel time of polyester resin and may adversely affect impregnation. Preparation of the reinforcement E-glass woven roving of is used as a reinforcement. The fabrics are made of fibers oriented along two perpendicular directions: one is called the warp and the other is called the fill (or weft) direction. The fibers are woven together, which means the fill yarns pass over and under the warp yarns, following a fixed pattern. Figure (3) shows a plain weave where each fill goes over a warp yarn then under a warp yarn and so on. Glass fiber mats (woven-mat), used for making the laminated plate or shell are cut in (5) layers of required size.

Preparation of the laminated plate and cylindrical panel
To preparation of laminate plate, the first layer of mat is laid and resin is spread uniformly over the mat by means of a brush. The second layer of mat is laid and resin is spread uniformly over the mat by means of a brush. After second layer, to enhance wetting and impregnation, a teethed steel roller is used to roll over the fabric before applying resin. This process is repeated till all the five fabric layers are placed. No external pressure is applied while casting or curing because uncured matrix material can squeeze out under high pressure. This results in surface waviness (non-uniform thickness) in the model material. The casting is cured at room temperature for (4-5)

Vibration Analysis of Laminated Composites
Using Experimental and Genetic Algorithms Optimization Technique 3196 hours and finally removed from the mould to get a fine finished composite plate. To preparation the shallow cylindrical laminate, it follow the same way above but the layer are continuous and it be controller by the turning (every 10º) of the cylinder and stopping by gear breaker

MATERIALS AND EXPERIMENTAL TEST SPECIMENS Calculate the volume fraction of composite
The volume fraction of the fiber and voids are calculated from the measured weights and densities of fiber, matrix and composite. The fiber weight fraction of the specimens is measured by burning out the resin of the composite material. In the burning test, four samples have nominal (3.1mm for five layers) thicknesses are cut in rectangular shape of (89.25X85.5)mm and the average of total weight of the samples are (38 gm). An electronic balance is used to measure the weight of the four samples of the tested woven fabric composite and the result specimens from burning process as shown in Figure (5). The average weight of the four samples is measure as (38 gm). The average density of the samples is found to be (1606.3773 Kg/m 3 ). After the burning process, the resin is removed from the composite and the average weighted of the remaining woven roving fiber becomes (22.75 gm). Then the fiber weight fraction of the composite material is calculated to be (59.86%) and the resin weight fraction is (40.14%). The avoid volume fraction v ν is calculated from the measured weights and densities of fiber, matrix and composite, by equation (1). It is found to be 9.28%.
Where W f , W m and W c are the weights of the fiber, matrix, and composite respectively. By using the densities of the fiber f ρ , matrix m ρ , and composite c ρ , respectively, the fiber volume fraction v ν can be obtained by equation (2) (Mohammed F. Aly, et.al., 2010).
and v ν are the volume fractions of the fiber, matrix and voids respectively. Using the relation of equation (2) the fiber volume fraction ( f ν ) is found (36.988%) according to the densities of fiber and matrix presented in Table (1).

Preparation of the test specimens
After the cure process, test specimens are cut from the sheet of five (5) ply laminate of the sizes (350mm X 350mm X 3.1mm) for plate and (320mm X 320mm X 3.1mm) for shallow cylinder by using a diamond impregnated wheel, cooled by running water as shown in Figure (6). All the test specimens are finished by abrading

Vibration Analysis of Laminated Composites
Using Experimental and Genetic Algorithms Optimization Technique 3197 the edges on a fin carborundum paper. The laminated plate is cut at axis angle (0º-90º).

Materials characterization
The mechanical properties of constituents of the test specimens, E-glass woven roving fibers and polyester matrix are listed in Table (1 Table (2).
Where indices m and f denote matrix and fiber, respectively. After calculating elastic constant of the unidirectional composite, elastic constants of the woven fabric composite material are estimated by using the tensile test device and the relation of equation (4) Table (3).

Vibration Analysis of Laminated Composites
Using Experimental and Genetic Algorithms Optimization Technique Where indices UD and WF denote the unidirectional fiber and woven fiber respectively

TYPES OF DAMAGE STRUCTURE
The damage structures investigated in this work are in the form of simple plates and shallow cylindrical. The delamination damage representing by using but the aluminium foil between layers where the delamination size (8X8 cm)for plate and (6.5X6.5 cm) for cylinder, the crack representing by cut depth (0.51 mm) and length (6.5 cm) by using a diamond impregnated wheel and the last type of damage making a hole by using a drill the diameter of hole are (2.4 cm). The place of all damages on the center of the specimens.

EXPERIMENTAL MODAL ANALYSIS
Structural natural frequencies may be measured by applying steady state, random or shock loads to the structure. If shock loads are used (experimental setup I) then in this case it becomes necessary to determine the Fast Fourier Transforms (FFT) of the response of the structure and input force. While the steady state method (experimental setup II), the structures excited by a sine wave of constant amplitude and frequency. The two type which considering in this work.

Pulse load (Experimental setup I)
Through an impact experimental test, it is determined the frequency response functions which relate the response given by the specimen when loaded with a signal, allowing for the determination of the natural frequencies, the impact hammer is used to give the input load (pulse) to the specimen, and the signal is analyzing by using wave record command and the Fast Fourier Transform (FFT) in Matlab program, see the flowchart in bellow, can be obtain the natural frequencies. The block diagram of the different instruments that used for the measurements of natural frequencies is shown in Figure (9), and the model setup of this experimental.

Sine load (Experimental setup II)
The block diagram shows all the instruments that used in the experimental as shown in Figure (11). A shaker was seated at appropriate position to excite the model. This shaker was driven through a power amplifier by a sinusoidal signal generator. The response was measured using a mini accelerometer and displayed on an oscilloscope through a charge amplifier. Figure (12) shows the instrumentation set up.

DAMAGE DETECTION METHOD
Damage detection by means of non-destructive testing plays an important role in ensuring the integrity of structures. These techniques are based on the monitoring of changes in dynamic structural characteristics such as natural frequencies and mode shape. The identification damage is formulated as an optimization problem where the basic procedure is to find a set of damage parameters that yields the optimum correlation between the numerical model and the measured model. The GAs theory is used to find the optimal solution by minimizing or maximize the objective functions, the GA begins by defining a chromosome, (i.e. an The flowchart of the programs for the experimental setup (I).

Vibration Analysis of Laminated Composites Using Experimental and Genetic Algorithms
Optimization Technique 3200 array of variables whose values are to be optimized). In the present work the chromosome has two variables, the damage location and the stiffness reduction. The objective function generates an output from the set of input variables of a chromosome. The goal is to modify the output in some desirable fashion by finding the appropriate values of input variables. Figure (13) shows the block diagram of the method of damage detection using genetic algorithms. The natural frequency used as a diagnostic parameter in structural assessment procedures using vibration monitoring. One great advantage of using only eigenvalue in the damage assessment of structures is that they are cheaply acquired and the approach can give an inexpensive structural assessment technique, Parameter of GA The free vibration of (SSSS) and (CCCC), plate and (CFCF) cylindrical with and without damage is performed. Model responses of the plate and cylindrical are generated using finite element model. The material properties of the laminated composite are listed in Table (4), and Figures (14,15) demonstrate the dimensions of plate and cylindrical respectively. For GA, the values of some parameters need to be selected. These parameters are listed in Table (4).

RESULTS AND DISCUSSION
The deviations of the numerical results and experimental and between two experimental methods, some possible measurement errors can be pointed out such as: measurement noise, positioning of the accelerometers and their mass, non-uniformity in the specimens properties (voids, variations in thickness, non uniform surface finishing). Such factors are not taken into account during the numerical analysis, since the model considers the specimen entirely perfect and with homogeneous properties, what rarely occurs in practice. Another aspect to be considered is that the input properties in the model came from the application of the rule of mixture and they do not take into account effects of fiber matrix interface as well as the irregular distribution of resin on the fibers. Also, these models did not include damping effects, which can have a large influence on the structure behavior. Also the computational numerical program does not allow for the consideration of fibers interweaving present in the fabric used.

Calculate The Natural Frequency Plate and cylindrical shell
Tables (5,6,7,8,9,10,11,12) give the comparison of the first five mode of natural frequency between experimental work and numerical work by used the program and results in reference Nabil Hassan Hadi and Kayser Aziz Ameen, 2011 for five woven laminated plate with different type of defect and different boundary conditions of [0/90] 5 laminated. Also the results can be show in the Figure (16 to 23). The average errors between the experimental setup I, experimental setup II and numerical solution respectively with (CCCC) and (SSSS) boundary condition respectively was (15.5222%, 6.68534%), and (15.506%, 7.1126%) for intact case, (10.3569%, 13.4196%) and (6.176%, 11.56%) for delamination case, (4.7519%%, 14.80645%) and (8.541%, 21.638%) for crack case and (11.66078%, 6.685348%) and (11.661%, 11.042%) for hole case. Also from these Tables good agreements between the experimental setup I, and experimental setup II for different boundary condition  Figure (24, 25, 26 and 27) show the result obtained by using the experimental setup (I).
The deviations of the numerical results and experimental and between the two experimental methods are due to some possible measurement errors that can be pointed out such as: measurement noise, different positioning of the accelerometers and their mass, non-uniformity in the specimens properties (voids, variations in thickness, non uniform surface finishing). Such factors are not taken into account during the numerical analysis, since the model considers the specimen entirely perfect and with homogeneous properties, which rarely occurs in practice. Another aspect to be considered is that the input properties in the model came from the application of the rule of mixture and they do not take into account effects of fiber matrix interface as well as the irregular distribution of resin on the fibers. Also, the computational numerical program does not allow for the consideration of fibers interweaving present in the fabric used.

Damage Detection
The natural frequency used as a diagnostic parameter in structural assessment procedures using vibration monitoring. One great advantage of using only eigenvalue in the damage assessment of structures is that they are cheaply acquired and the approach can give an inexpensive structural assessment technique. The objective function to be maximized is defined as follows. The m i ω are the natural frequencies which are applied to our damage detection system as inputs. An objective value of zero indicates an exact match between the values of frequencies. The first natural frequencies are calculated numerically using finite element model for the test damage element of the simply supported and clamp for all side respectively for plate and clamp-free-clamp-free for shallow cylindrical to three damage cases (delamination, crack and hole).These frequencies were used as test input for GA. After introducing the test natural frequencies, a population of individuals is generated randomly and the natural frequencies are calculated for each chromosome, which coded the damage state, then the objective function equation (5) is evaluated for these chromosomes. Only best chromosomes are selected to continue, and reproduction and mutation operator are applied on the chromosomes except the

Vibration Analysis of Laminated Composites
Using Experimental and Genetic Algorithms Optimization Technique 3202 best chromosome. After mutation operator one generation is completed and in the next generation the new population is used for calculating the natural frequencies and cost evaluation. The best cost value is checked in every generation and if the cost reaches a certain level. The convergence plot for the GA for plate and simply support boundary condition for all side are shown in Figure (28), it is seen that convergence occurs at a round (3) for delamination case, (6) for crack case and (8) for hole. The convergence plot for the GA for plate and clamp boundary condition for all side are shown in Figure (29), it is seen that convergence occurs at a round (12) for delamination case, (10) for crack case and (7) for hole. The convergence plot for the GA for cylindrical and clamp-free-clamp-free boundary condition each side respectively are shown in Figure (30), it is seen that convergence occurs at a round (3) for delamination case, (8) for crack case and (5) for hole.

CONCLUSIONS
The main conclusions that can be draw from this investigation are: • Results show that Genetic Algorithm is an efficient method in damage identification for different boundary condition of structure with high precision and capable of detecting small damage with small errors. • The length of the run (in term of generation number) and results depends on the initial randomly generated population and GA parameters and the test point. • When the plate or shell containing some defect such as delamination, crack or hole this causes a decreasing in natural frequency, this properties used to detecte the damage in structure. • Single and multiple damages can be detected in plate or in shell by using the genetic algorithms.