Theoretical and Numerical Vibration Investigation Study of Orthotropic Hyper Composite Plate Structure

International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:14 No:06 1 Theoretical and Numerical Vibration Investigation Study of Orthotropic Hyper Composite Plate Structure Dr. Mohsin Abdullah Al-Shammari and Dr. Muhannad Al-Waily Abstract In this research the reinforcement of the resin materials is done with two type's, as powder reinforcement and unidirectional or woven reinforcement fiber to produce an orthotropic hyper composite materials composed of three materials, resin materials and two reinforcement fibers powder and unidirectional or woven fiber). The composite structure is studied to estimate the natural frequency and mode shape. The effect of volume fraction of powder reinforcement and the direction of woven reinforcement fiber on the natural frequency of hyper orthotropic composite plate with different aspect ratios of plate supported as simply supported plate were studied. The methods used to evaluate the natural frequency of composite plate are theoretical method and numerical method. The theoretical method includes the solution of the general equation of motion of orthotropic composite plate. The numerical study includes the estimation of the natural frequency of the plate using finite element method by Ansys program Ver. 14. The results got by theoretical and numerical studies are the natural frequency of orthotropic hyper composite simply supported plate with various volume fractions of reinforcement powder and unidirectional or woven fiber. Also, a comparison is made between the results of theoretical solution of general equation of motion of plate and numerical solution by ANSYS. The maximum discrepancy was about 3.2 %). Index Term-- Vibration Plate, Composite Plate, Hyper Composite Materials, Theoretical Analysis of Plate, Theoretical Analysis of Orthotropic Composite Plate, Dynamic Analysis of Plate. I. INTRODUCTION Composite materials consist of two or more materials which together produce desirable properties that cannot be achieved with any of the constituents alone. Fiber-reinforced composite materials, for example, contain high strength and high modulus fibers in a matrix material, 4]. Composite material reveals a material that is different from common heterogeneous materials. A currently composite material refers to materials having strong fibers, continuous or non-continuous, surrounded by a weaker matrix material. The matrix serves to distribute the fibers and also to transmit the load to the fibers. The mixture of reinforcement/resin does not really become a composite material until the last phase of the Dr. Mohsin Abdullah Al-Shammari Mechanical Engineering Department/College of Engineering/Baghdad University/Iraq dr.alshammari@uobaghdad.edu.iq mohsinabdullah@yahoo.com Dr. Muhannad Al-Waily Mechanical Engineering Department/Faculty of Engineering/Al-Kufa University/Iraq muhanedl.alwaeli@uokufa.edu.iq muhannad_al_waily@yahoo.com fabrication, that is, when the matrix is hardened. After this phase, it would be impossible to modify the material, as in the way one would like to modify the structure of a metal alloy using heat treatment, 1]. Many studies were performed to examine the vibration and dynamic of plate, as, Muhannad Al-Waily 3], presented a suggested analytical solution for dynamic analysis of hyper composite plate combined from two reinforcement fiber, mat and powder or short and powder reinforcement fiber, with resin matrix, as polyester or epoxy resin. The theoretical study of hyper composite plate evaluated the natural frequency of plate with different volume fraction of reinforcement fiber and resin matrix effect and evaluated the effect of reinforcement fiber and resin types on the natural frequency of plate. The a suggested analytical solution included evaluated the mechanical properties of isotropic hyper composite material plate, combine from powder reinforcement and mat or short reinforcement fiber with polyester or epoxy resin matrix, as modulus of elasticity and modulus of rigidity in addition to Poisson s ratio of hyper composite plate. And, solution for the general equation of motion for an isotropic hyper composite plate with effect of the volume fraction and types of reinforcement fiber and matrix resin. KanakKalita et al 5], presented different mode frequencies for free vibration of isotropic plates are studied using the ANSYS computer package. Several different boundary condition cases involving clamped, simply-supported and free edge conditions are considered. The analysis for isotropic plate is carried out for uniform thickness and different aspect ratios. The Square plate is analyzed for different boundary conditions with different thickness ratio. Anil Kumar Dash 11], in the presented investigation, large amplitude free vibration analyses of composite Mindlin s plates have been carried out using a C 0 eight nodded Langragian element by finite element method. The formulation is based on First order shear deformation theory. The large deformation effect on plate structures has been taken care by the dynamic version of von Karman s field equation. The effects of variations in the Poisson s ratio, amplitude ratio, thickness parameter & plate aspect ratio on the non-linear frequency ratio has also been included in the research. Gururaja M. N. et al 13], the investigation of the novel applications of hybrid composites has been of deep interest to the researchers for many years as evident from reports. This paper presents a review of the current status of hybrid composite materials technology, in terms of materials

International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:14 No:06 2 available and properties, and an outline of some of the trends, obvious and speculative, with emphasis on various applications including some details of smart hybrid composites. ParsuramNayak 14], this work presented a combined experimental and numerical study of free vibration of woven fiber Glass/Epoxy composite plates. Experimental setup and procedure of the modal testing method is described. Fabrication procedure of the plate is described. Geometrical properties are determined. Elastic parameters of the plate are determined experimentally by tensile testing of specimens. A computer program based on FEM has been developed to perform all necessary computations. The program results compared with other existing literature. The natural frequency and mode shape of the plate has been determined using ANSYS package. The presented experimental value and program result compared with ANSYS package. In this research a suggested analytical solution of orthotropic hyper composite materials plate combined from composite matrix combined from resin and powder reinforcement) and unidirectional or woven reinforcement fiber, with evaluated the general equation of hyper composite materials properties and drive the general equation of motion of orthotropic composite plate with mechanical properties of hyper composite materials effect to getting the natural frequency of orthotropic hyper composite plate with volume fraction of powder, unidirectional or woven reinforcement and resin materials effect. And, compare the theoretical results evaluated by solution of general equation of motion of orthotropic hyper composite plate with numerical results evaluated with finite element methods, by using Ansys program Ver. 14. II. A SUGGESTED THEORETICAL STUDY The suggested solution of orthotropic composite plate divided to two parts, as, 1. Evaluated mechanical properties of hyper composite plate, combined from resin materials and reinforcement fibers by powder and unidirectional or woven reinforcement fiber. 2. Evaluated of the natural frequency of simply supported plate with various volume fraction of reinforcement powder and unidirectional or woven fiber. 1. Mechanical Properties of Hyper Composite Plate Structural The mechanical properties of hyper composite materials evaluated by assuming the matrix of composite materials is composite materials combined from resin materials and powder reinforcement, and then evaluated the mechanical properties of composite materials combined from composite matrix resin and powder reinforcement) and unidirectional or woven reinforcement fiber to giving hyper composite materials, as, Mechanical Properties of Composite Matrix, Spherical fillers are reinforcements associated with polymer matrices. They are in the form of micro-balls, either solid or hollow, with diameters between 10 and 150 m. They are made of glass, carbon, or polystyrene. The composite matrix + filler) is isotropic, with elastic properties E, G, given by the following relations, 1], ) ) * ) + ) * ) + ) ) * ) + ) * ) + ) ) * ) + ) * ) + ) ) * ) + ) * ) + )] 1) Where, are modulus of elasticity and Poisson's ratio of resin materials matrix, and, are volume fractions of powder and resin materials matrix. Then the mechanical properties of composite matrix are,,, 2) And, the volume fraction of resin and powder composite matrix can be evaluated as, 3) Hyper Composite Plate, Composite Matrix and Unidirectional or Woven Reinforcement Fiber), The mechanical properties of orthotropic composite material evaluated for two types of reinforcement fiber, first, unidirectional and composite matrix composite materials, second, woven and composite matrix materials as, A. Unidirectional Reinforcement of Composite Materials The mechanical characteristics of the fiber/matrix composite mixture can be obtained based on the characteristics of each of the constituents. With the definitions in the previous paragraph, one can use the following relations to characterize the unidirectional ply,1], ) * ) + * ) + 4)

International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:14 No:06 3 Where, modulus of elasticity of long fiber, shear modulus of long fiber, Poisson ratio of long fiber, E 1, modulus of elasticity along the direction of the fiber, E 2, modulus of elasticity in the transverse direction to the fiber axis, G 12, shear modulus, 12, Poisson coefficient and volume fraction of long fiber. And, the density of hyper composite materials can be evaluated as, 5) Where,, density of unidirectional, resin and powder materials, respectively. Then, by substitution Eq. 2 into Eq. 4, get, the mechanical properties of unidirectional hyper composite materials properties, as, * * ) + ) * ) ) * ) + +) ) * ) + ) * ) + ) ) * ) + ) * ) + )] 6) ) ) * ) + ) ) * ) + ) * ) + ) ] ) )] B. Woven Fabrics Reinforcement of Composite Materials The fabric layer is replaced by one single anisotropic layer, x being along the warp direction and y along the fill direction. One can therefore obtain, 1], ) ), ) ) 7) Where,, number of warp yarns per meter, number of fill yarns per meter. And,,,, and are mechanical properties of woven fabrics in 1 and 2- directions; and,,, and as in Eq. 6, Then, substation Eq. 6 into Eq. 7, get the mechanical properties of woven composite, as, * * ) + ) ) * ) ++ ] ) * ) + ) * ) +) ) * ) * ) + ) * ) + ) * ) * ) + + ) * ) +) ], ] * ) * ) + ) ) * ) ++ ] ) * ) + ) * ) +) ) * ) * ) + ) * ) + * ) * ) + + ) * ) +) ], ]

International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:14 No:06 4 ) ) ] * ) ) * ) + +) ) ) ] ) ) ] ] 8) ) ) ) ) ] * ] * ) ) ] * ) ) ] ) ) ] ) ) ] ) ] ) And, the density of composite materials combined from woven reinforcement and composite matrix materials can be evaluated as, 9) Where,,,, and are mechanical properties and density of woven reinforcement fiber, respectively, And is volume fraction of woven reinforcement fiber. 2. Vibration of Hyper Composite Plate Special Orthotropic Plate Equation) The vibration analysis of orthotropic hyper composite plate included solution the general equation for orthotropic plate by using special orthotropic plate equation, 2], 10) Where, are the bending moments per unit length) of orthotropic plate, can be determined as, 2], 11) And, are stresses of orthotropic plate can be written as the following, 2], 12) And, are strains fields determine with the displacement fields as in the following equations, 2],,,, 13) Where, w deflection of plate in z-direction. Then, by substituting the strain fields in Eq. 13 in to stress of plate in Eq. 12, get the stresses-strain relation of orthotropic plate as a faction of plate defection w, as, * * 14) And then, with substituting the stress in terms of plate defection, Eq. 14, into the bending moments, and, get, Where, ) ) ) ) ), ), 15) ), 16) Where, h thickness of plate in z-direction. And. Then, by substituting for the bending and twisting moments from Eq. 15 into general equation of orthotropic plate Eq. 10, get the general equation of motion for orthotropic hyper composite plate, as,

International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:14 No:06 5 ) ) ) Or, * ) ] + ) 17) For free vibration plate, the general equation of plate Eq. 17 can be rewritten as the general equation of motion of orthotropic composite plate as, 2], * ), + 18) To evaluated the natural frequency of composite plate from Eq. 18, solve Eq. 18 by using separation of variable method to evaluated the general deflection of plate in x and y-direction with substation the boundary condition of plate, depended on the types of plate supported, as, for simply supported boundary condition plate 2], On the edge, ) on the edge ) 19) Then, with substituting the boundary conditions in Eq. 19 into general equation of motion Eq. 18, and solve the equation for time dependent, get, 2], 20) Where and are integers and constant. are length and width of plate, respectively. Then, by substitute the general behavior of plate Eq. 20), as a faction of x, y-direction and time t), into the general equation of motion Eq. 18) of plate, get, * ) ) ) + 21) Therefore, the natural frequency equation of orthotropic hyper composite plate will be, * ) + 22) ) ) Where, for unidirectional reinforcement fiber, and for woven reinforcement fiber. for unidirectional reinforcement fiber, and for woven reinforcement fiber. for unidirectional reinforcement fiber, and for woven reinforcement fiber. for unidirectional reinforcement fiber, and for woven reinforcement fiber. Then, by substitute for composite materials into Eq. 16 and substitution the results equation and density of composite plate into Eq. 22, get, By substitute Eq. 6 into Eq. 16 and substitute the results and density of composite plate Eq. 5) into Eq. 22, get the natural frequency of unidirectional hyper composite plate, as shown in Eq. 23. By substitute Eq. 8 into Eq. 16 and substitute the results and density of composite plate Eq. 9) into Eq. 22, the natural frequency of woven hyper composite plate, as shown in Eq. 24. The computer program building by using Fortran power station Ver. 4, to evaluated the natural frequency for unidirectional, Eq. 23, and woven, Eq. 24, reinforcement hyper composite simply supported plate. The program requirement input data as, the mechanical properties of reinforcement powder and unidirectional or woven fiber) and resin materials, and dimensions of plate length, width and thickness of plate). And, the program output include the natural frequency of unidirectional and woven hyper composite plate with different volume fraction of reinforcement, in addition to, the mechanical properties of hyper composite materials. The flow chart of computer program shown in the Fig. 1, show the steps of the solution to evaluated the natural frequency of hyper composite plate with different volume fraction of reinforcement and different plate materials types and different plate dimensions. The first step was the input of mechanical properties of reinforcement powder and fiber) and resin materials. Also in the same step the dimensions of composite plates were input. In the second step a do-loop process of variation of the volume fraction of the reinforcement powder and fiber) from the value of 30% to 50%) in steps of 5%). Then the reinforcement fiber will vary from 15%) volume fraction to 30%) volume fraction in steps of also 5%). From those percent of volume fraction, the mechanical properties will be calculated for only two types of hyper composite materials. The mechanical properties will be calculated for the first type which is reinforcement with unidirectional fiber using Eq. 6 as shown in the flow chart, but, the mechanical properties of the second type which is reinforcement with woven fiber will be estimated using Eq. 8 as shown in Fig. 1. After that the natural frequency for the two types of composite materials will be calculated using Eq. 23 and 24 for the first and second type respectively. At the last step, the program will show the results of mechanical properties and natural frequency for different values of reinforcement powder and fiber) volume fraction.

International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:14 No:06 6 ) ) ] ) ) ] ) * ) ) ] ) ) ] ] ) ) * ) ] ) ) ) ] ) ) ] ] ) ) ] ) ) ) ] ] ) ) * ) ] ) ) ] ) ) ) ] ] ) ) ) ] ] ) * ]) * + )] 23)

International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:14 No:06 7 ) ] ) ) * ) ] ) ) * ) ] ) ) ) ) ] ) ] ) ) ] ) ) * ) ] ) ) * ) ] ) ) ) ) ] ) ] ) ) ] ) ) * ) ] ) ) * ) ] ) ) ) ) ] ) ] ) ) ) * )] )] * + 24)

International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:14 No:06 8 Start Input Mechanical Properties of Reinforcement and Resin Materials Input Dimensions of Composite Plate, Thickness, Length, and Width of Plate Evaluated Mechanical Properties of Unidirectional Reinforcement Composite Plate, Eq. 6 Evaluated Mechanical Properties of Woven Reinforcement Composite Plate, Eq. 8 Evaluated Natural Frequency of Unidirectional Reinforcement Composite Plate, Eq. 23 Evaluated Natural Frequency of Woven Reinforcement Composite Plate, Eq. 24 Output Written Mechanical properties with Different Reinforcement Volume Fraction of Different Unidirectional and Woven Reinforcement Materials Types and Resin Materials Types Output Written, Natural Frequency with Different Reinforcement Volume Fraction of Different Unidirectional and Woven Reinforcement Material Types, Resin Materials Types, and Aspect Ratio of Plate End Fig. 1. Flow Chart Program to Evaluating Mechanical Properties and Natural frequency of Orthotropic Unidirectional and Woven Hyper Composite Simply Supported Plate.

International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:14 No:06 9 III. NUMERICAL STUDY The finite element method is a powerful computational technique for the solution of differential and integral equations that arise in various fields of engineering and applied science. The basic idea of the finite element method is to view a given domain as an assemblage of simple geometric shapes, called finite elements, for which it is possible to systematically generate the approximation functions needed in the solution of differential equations by any of the variational and weightedresidual methods. The ability to represent domains with irregular geometries by a collection of finite elements makes the method a valuable practical tool for the solution of boundary, initial, and eigenvalue problems arising in various fields of engineering, 4]. The numerical study of natural frequency for different orthotropic hyper composite plate evaluated by using the finite elements method was applied by using the ANSYS program ver. 14). The three dimensional model were built and the element SHELL 8 node 281) were used. Shell 281 is suitable for analyzing thin to moderately-thick shell structures. The element has eight nodes with six degrees of freedom at each node: translations in the x, y, and z axes, and rotations about the x, y, and z-axes. When using the membrane option, the element has translational degrees of freedom only.). Shell 281 is well-suited for linear, large rotation, and/or large strain nonlinear applications. The Fig. 2 shows the geometry, node locations, and the element coordinate system for this element. The element is defined by shell section information and by eight nodes I, J, K, L, M, N, O and P). Shell 281 can be associated with linear elastic, elasto-plastic, creep, or hyper-elastic material properties. Only isotropic, anisotropic, and orthotropic linear elastic properties can be input for elasticity. Hyper-elastic material properties can be used with this element. IV. RESULTS AND DISCUSSION The results of orthotropic hyper composite plate included the evaluation of the effect of the added powder reinforcement on the natural frequency of unidirectional or woven simply supported hyper composite plate. In addition to, a study of the effect of the powder reinforcement types on the natural frequency of hyper simply supported composite plate is done. And, study of the effect of thy aspect ratio and other parameters of plate on natural frequency of hyper unidirectional and woven composite plate is done also. The natural frequency of orthotropic hyper composite plate is evaluated using theoretical analysis solution of the general equation of motion of orthotropic composite plate with different volume fraction mechanical properties) of powder reinforcement, unidirectional or woven fiber, and resin materials. A comparison between the theoretical and numerical results is done. The mechanical properties of different powder materials, unidirectional and woven fiber, and resin materials used to combine the orthotropic hyper composite plate are shown in Table 1. And, the mechanical properties of orthotropic hyper composite plate types studied are shown in the Tables 2 and 3, for different combined and reinforcement types of unidirectional and woven hyper composite materials, respectively. The dimensions length, width and thickness of plate) of orthotropic unidirectional and woven hyper composite plate studied with different aspect ratio of plate are Length of plate with different aspect ratio are, Table I Mechanical Properties of Different Reinforcement Fiber and Resin Materials, 1]. Materials kg/m 3 ) E Gpa) G Gpa) Glass Fibers 2066 74 30 0.25 Boron Fiber 2600 400 / / Polyester 1200 4 1.4 0.4 Epoxy 1200 4.5 1.6 0.4 Fig. 2. Shell 281 Geometry. The comparison between theoretical and numerical results of the estimated natural frequency of hyper unidirectional and woven composite plate with different aspect ratio AR=0.5, 1, 2) and various volume fractions of various reinforcement types unidirectional and woven reinforcement types,, for glass and boron reinforcement powder) and different resin materials types polyester and epoxy resin materials) are shown in Figs. 3 to 6. The figures show that the

International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:14 No:06 10 suggested analytical solution of natural frequency for orthotropic hyper composite plate evaluated with solution of general equation of motion of hyper unidirectional and woven composite plate is a powerful tool for natural frequency calculation of hyper orthotropic plate with different mechanical properties of plate materials and various types of reinforcement fiber, with maximum error between theoretical and numerical results evaluated with finite element method, by using Ansys Ver. 14., is 3.2%). Figs. 7 to 12 show the effect of volume fraction of reinforcements as powder reinforcement and unidirectional fiber on the natural frequency of hyper composite plate for various aspect ratio of plate AR=0.5, 1, 2) and different resin materials polyester and epoxy resin materials). The figures show that the natural frequency is increased with the increasing of volume fraction of reinforcement powder and unidirectional fiber) for different aspect ratio, and, the natural frequency of composite plate is increased with the increasing of the volume fraction of unidirectional reinforcement fiber with aspect ratio AR=0.5 and1), and the natural frequency is decreasing with increasing of unidirectional reinforcement fiber with aspect ratio of plate AR=2. Since, the increasing of powder reinforcement cases increases the modulus of elasticity of composite matrix materials, and then increasing of the modulus of elasticity of composite and increases the stiffness of composite plate, then increasing of the natural frequency of plate. In addition to, the natural frequency of plate composed of epoxy resin is more than the natural frequency of the plate composed of polyester resin, since the stiffness of epoxy resin is more than stiffness of polyester resin, and then the stiffness of composite plate with epoxy resin is more than the stiffness of polyester resin, and then the natural frequency is higher. Figs. 13 to 18 show the effect of volume fraction of powder reinforcement and woven fiber on the natural frequency of hyper composite plate for various aspect ratios of plate AR=0.5, 1, 2) and different resin materials polyester and epoxy resin materials). These figures show that the natural frequency is increasing with increasing of the volume fraction of reinforcement powder and woven reinforcement fiber). Since, the increasing of powder reinforcement increases the modulus of elasticity of composite matrix, and then increases the modulus of elasticity of composite and increases the stiffness of the composite plate, then increases the natural frequency of plate. In addition to, the natural frequency of the plate composed of the epoxy resin is more than the natural frequency of the plate composed of polyester resin, since the stiffness of epoxy resin is more than the stiffness of polyester resin, and then the stiffness of composite plate with epoxy resin is more than the stiffness of the plate with polyester resin, and then the natural frequency is higher. Figs. 19 and 20 show the natural frequency of unidirectional and woven hyper composite plate, respectively, with different aspect ratios effect, for polyester resin and volume fraction of reinforcement and with different volume fraction of powder reinforcement. these figures show that the natural frequency is increases with the increasing of unidirectional and woven volume fraction with different aspect ratios of unidirectional AR=0.5, and 1) and woven AR=0.5, 1, 2). But, the natural frequency of unidirectional composite plate is decreased with the increasing of the volume fraction of unidirectional composite plate with aspect ratio of plate AR=2, since the increasing in the value of density is more than the increasing in the value of stiffness of the plate. Figs. 21 and 22 show the effect of the used powder reinforcement types glass or boron powder reinforcement) on the natural frequency of hyper unidirectional and woven composite plate, with polyester resin, volume fraction for reinforcement with different unidirectional and woven reinforcement fiber) and aspect ratio of plate AR=0.5. These figures showed that the value of natural frequency of unidirectional and woven composite plate is not affected by the variation of reinforcement powder for same density of powder types), since the different modulus of elasticity of reinforcement powder did not affect the modulus of elasticity of the composite materials. Figs. 23 and 24 show the effect of the used resin materials types polyester and epoxy resin materials) on the value of the natural frequency of unidirectional and woven hyper composite plate with different values of volume fraction of unidirectional and woven fiber with volume fraction of reinforcement and aspect ratio of composite plate AR=0.5). These figures showed that the value of natural frequency of unidirectional or woven hyper composite plate with epoxy resin is more than the value of the natural frequency of hyper composite plate with polyester resin. Since, the value of the modulus of elasticity of epoxy is greater than the value of the modulus of elasticity of the polyester resin materials, and then, the value of the stiffness of plate composed of epoxy resin is greater than the value of the stiffness of plate composed of polyester resin. Figs. 25 to 30 show the difference between the effect of unidirectional and woven reinforcement types on the natural frequency of hyper composite plate with different aspect ratios of plate AR=0.5, 1, 2), different resin materials polyester and epoxy resin materials) and various volume fractions of unidirectional and woven fiber, for volume fraction of reinforcement powder and unidirectional or woven reinforcement fiber). These figures show that the value of the natural frequency of unidirectional hyper composite plate is more than the value of the natural frequency of woven hyper composite plate for aspect ratio of plate AR=0.5 and 1), since, the effect of unidirectional reinforcement on the value of the stiffness of plate with aspect ratio AR=0.5 and 1) is more than the effect of woven reinforcement fiber on the value of the stiffness of plate. And, the natural frequency of composite plate with woven reinforcement of aspect ratio AR=2 is more than the natural frequency of composite plate with unidirectional reinforcement fiber, since the effect of woven reinforcement is more than the effect of unidirectional reinforcement on the stiffness of plate with AR=2, and then on the natural frequency of plate.

Volume Fraction of Resin Volume Fraction of Reinforcement Volume Fraction of Long Fiber Volume Fraction of Powder Fiber kg/m 3 ) Volume Fraction of Resin Volume Fraction of Reinforcement Volume Fraction of Long Fiber Volume Fraction of Powder Fiber kg/m 3 ) International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:14 No:06 11 Table II Mechanical Properties of Unidirectional Hyper Composite Plate Combined of Different Reinforcement Fiber and Different Resin Matrix. Unidirectional Glass Fiber, Glass or Boron Reinforcement Powder, and Polyester Resin Unidirectional Glass Fiber, Glass or Boron Reinforcement Powder, and Epoxy Resin E 1 Gpa) E 2 Gpa) G 12 Gpa) 12 E 1 Gpa) E 2 Gpa) G 12 Gpa) 12 70 30 65 35 60 40 55 45 50 50 15 15 16.09 6.81 2.46 0.36 16.71 7.64 2.76 0.36 1620 20 10 19.00 6.44 2.32 0.36 19.52 7.23 2.61 0.36 1620 25 5 21.97 6.04 2.17 0.36 22.40 6.78 2.44 0.36 1620 30 0 25.00 5.58 2.00 0.36 25.35 6.27 2.24 0.36 1620 15 20 16.77 7.73 2.80 0.36 17.48 8.68 3.15 0.36 1690 20 15 19.61 7.36 2.66 0.36 20.21 8.26 2.99 0.36 1690 25 10 22.51 6.95 2.51 0.35 23.01 7.80 2.82 0.35 1690 30 5 25.47 6.50 2.34 0.35 25.88 7.29 2.62 0.35 1690 15 25 17.57 8.80 3.20 0.36 18.38 9.88 3.60 0.36 1760 20 20 20.32 8.42 3.06 0.35 21.01 9.45 3.44 0.35 1760 25 15 23.13 8.01 2.90 0.35 23.71 8.98 3.26 0.35 1760 30 10 26.02 7.55 2.73 0.35 26.49 8.46 3.06 0.35 1760 15 30 18.52 10.06 3.67 0.35 19.45 11.29 4.12 0.35 1830 20 25 21.16 9.67 3.53 0.35 21.95 10.84 3.96 0.35 1830 25 20 23.87 9.25 3.37 0.35 24.54 10.36 3.77 0.35 1830 30 15 26.66 8.78 3.19 0.34 27.22 9.83 3.57 0.34 1830 15 35 19.65 11.56 4.24 0.35 20.72 12.97 4.75 0.35 1900 20 30 22.16 11.15 4.08 0.35 23.08 12.50 4.58 0.35 1900 25 25 24.75 10.71 3.92 0.34 25.53 12.00 4.39 0.34 1900 30 20 27.43 10.23 3.73 0.34 28.09 11.45 4.18 0.34 1900 Table III Mechanical Properties of Woven Hyper Composite Plate Combined of Different Reinforcement Fiber and Different Resin Matrix. Woven Glass Fiber, Glass or Boron Reinforcement Powder, and Polyester Resin Woven Glass Fiber, Glass or Boron Reinforcement Powder, and Epoxy Resin E 1 Gpa) E 2 Gpa) G 12 Gpa) 12 E 1 Gpa) E 2 Gpa) G 12 Gpa) 12 70 30 65 35 60 40 55 45 50 50 15 15 11.45 11.45 2.46 0.22 12.18 12.18 2.76 0.23 1620 20 10 12.72 12.72 2.32 0.18 13.38 13.38 2.61 0.20 1620 25 5 14.00 14.00 2.17 0.15 14.59 14.59 2.44 0.17 1620 30 0 15.29 15.29 2.00 0.13 15.81 15.81 2.24 0.14 1620 15 20 12.25 12.25 2.80 0.23 13.08 13.08 3.15 0.24 1690 20 15 13.48 13.48 2.66 0.20 14.23 14.23 2.99 0.21 1690 25 10 14.73 14.73 2.51 0.17 15.40 15.40 2.82 0.18 1690 30 5 15.98 15.98 2.34 0.14 16.58 16.58 2.62 0.15 1690 15 25 13.19 13.19 3.20 0.24 14.13 14.13 3.60 0.25 1760 20 20 14.37 14.37 3.06 0.21 15.23 15.23 3.44 0.22 1760 25 15 15.57 15.57 2.90 0.18 16.35 16.35 3.26 0.19 1760 30 10 16.78 16.78 2.73 0.16 17.48 17.48 3.06 0.17 1760 15 30 14.29 14.29 3.67 0.25 15.37 15.37 4.12 0.26 1830 20 25 15.41 15.41 3.53 0.22 16.40 16.40 3.96 0.23 1830 25 20 16.56 16.56 3.37 0.19 17.45 17.45 3.77 0.21 1830 30 15 17.72 17.72 3.19 0.17 18.53 18.53 3.57 0.18 1830 15 35 15.61 15.61 4.24 0.26 16.84 16.84 4.75 0.27 1900 20 30 16.66 16.66 4.08 0.23 17.79 17.79 4.58 0.24 1900 25 25 17.73 17.73 3.92 0.21 18.77 18.77 4.39 0.22 1900 30 20 18.83 18.83 3.73 0.18 19.77 19.77 4.18 0.20 1900

f=50% f=45% f=40% f=35% f=30% International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:14 No:06 12 AR=0.5 AR=1 AR=2 Fig. 3. Compare Between Theoretical and Numerical Study for Glass UnidirectionalFiber, with Glass or Boron Powder and Polyester Resin, for Different Aspect Ratio and Volume Fraction Fiber.

f=50% f=45% f=40% f=35% f=30% International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:14 No:06 13 AR=0.5 AR=1 AR=2 Fig. 4. Compare Between Theoretical and Numerical Study for Glass Unidirectional Fiber, with Glass or Boron Powder and Epoxy Resin, for Different Aspect Ratio and Volume Fraction Fiber.

f=50% f=45% f=40% f=35% f=30% International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:14 No:06 14 AR=0.5 AR=1 AR=2 Fig. 5. Compare Between Theoretical and Numerical Study for Glass Woven Fiber, with Glass or Boron Powder and Polyester Resin, for Different Aspect Ratio and Volume Fraction Fiber.

f=50% f=45% f=40% f=35% f=30% International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:14 No:06 15 AR=0.5 AR=1 AR=2 Fig. 6. Compare Between Theoretical and Numerical Study for Glass Woven Fiber, with Glass or Boron Powder and Epoxy Resin, for Different Aspect Ratio and Volume Fraction Fiber.

International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:14 No:06 16 Fig. 7. Natural Frequency of Unidirectional Composite Plate with Different Volume Fraction of Reinforcement Powder and Fiber, for Polyester Resin and AR=0.5. Fig. 10. Natural Frequency of Unidirectional Composite Plate with Different Volume Fraction of Reinforcement Powder and Fiber, for Epoxy Resin and AR=0.5. Fig. 8. Natural Frequency of Unidirectional Composite Plate with Different Volume Fraction of Reinforcement Powder and Fiber, for Polyester Resin and AR=1. Fig. 11. Natural Frequency of Unidirectional Composite Plate with Different Volume Fraction of Reinforcement Powder and Fiber, for Epoxy Resin and AR=1. Fig. 9. Natural Frequency of Unidirectional Composite Plate with Different Volume Fraction of Reinforcement Powder and Fiber, for Polyester Resin and AR=2. Fig. 12. Natural Frequency of Unidirectional Composite Plate with Different Volume Fraction of Reinforcement Powder and Fiber, for Epoxy Resin and AR=2.

International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:14 No:06 17 Fig. 13. Natural Frequency of Woven Composite Plate with Different Volume Fraction of Reinforcement Powder and Fiber, for Polyester Resin and AR=0.5. Fig. 16. Natural Frequency of Woven Composite Plate with Different Volume Fraction of Reinforcement Powder and Fiber, for Epoxy Resin and AR=0.5. Fig. 14. Natural Frequency of Woven Composite Plate with Different Volume Fraction of Reinforcement Powder and Fiber, for Polyester Resin and AR=1. Fig. 17. Natural Frequency of Woven Composite Plate with Different Volume Fraction of Reinforcement Powder and Fiber, for Epoxy Resin and AR=1. Fig. 15. Natural Frequency of Woven Composite Plate with Different Volume Fraction of Reinforcement Powder and Fiber, for Polyester Resin and AR=2. Fig. 18. Natural Frequency of Woven Composite Plate with Different Volume Fraction of Reinforcement Powder and Fiber, for Epoxy Resin and AR=2.

International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:14 No:06 18 Fig. 19. Natural Frequency of Unidirectional Composite Plate with Different Fiber Volume Fraction and Various Aspect Ratio of Plate, for Polyester Resin and f=50%. Fig. 22. Natural Frequency of Woven Composite Plate with Different Fiber Volume Fraction for Various Powder Types, for Polyester Resin, AR=0.5, f=50%. Fig. 20. Natural Frequency of Woven Composite Plate with Different Fiber Volume Fraction and Various Aspect Ratio of Plate, for Polyester Resin and f=50%. Fig. 23. Natural Frequency of Unidirectional Composite Plate with Different Fiber Volume Fraction and Various Resin Materials Types, for AR=0.5 and f=50%. Fig. 21. Natural Frequency of Unidirectional Composite Plate with Different Fiber Volume Fraction and Various Powder Types, for Polyester Resin, AR=0.5, f=50%. Fig. 24. Natural Frequency of Woven Composite Plate with Different Fiber Volume Fraction and Various Resin Materials Types, for AR=0.5 and f=50%.

International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:14 No:06 19 Fig. 25. Natural Frequency of Unidirectional and Woven Composite Plate with Different Fiber Volume Fraction, for Polyester Resin, AR=0.5, f=50%. Fig. 28. Natural Frequency of Unidirectional and Woven Composite Plate with Different Fiber Volume Fraction, for Epoxy Resin Material, AR=0.5, f=50%. Fig. 26. Natural Frequency of Unidirectional and Woven Composite Plate with Different Fiber Volume Fraction, for Polyester Resin Material, AR=1, f=50%. Fig. 29. Natural Frequency of Unidirectional and Woven Composite Plate with Different Fiber Volume Fraction, for Epoxy Resin Material, AR=1, f=50%. Fig. 27. Natural Frequency of Unidirectional and Woven Composite Plate with Different Fiber Volume Fraction, for Polyester Resin Material, AR=2, f=50%. Fig. 30. Natural Frequency of Unidirectional and Woven Composite Plate with Different Fiber Volume Fraction, for Epoxy Resin Material, AR=2, f=50%.

International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:14 No:06 20 V. CONCLUSION Some concluding observations from the investigation of analytical and numerical study of natural frequency of orthotropic hyper composite plate are given below, 1. The suggested analytical solution is a powerful tool for natural frequency analysis study of unidirectional and woven hyper composite plate combined from three materials as powder reinforcement, unidirectional or woven reinforcement and resin materials, with different volume fractions of reinforcement powder and unidirectional or woven fiber effect. 2. A comparison is made between the suggested analytical solutions results from solved of general equation of motion for natural frequency of orthotropic hyper composite plate with numerical results from finite element methods, by using Ansys program Ver. 14. It shows a good agreement with a maximum discrepancy between the theoretical and numerical results of about 3.2%). 3. The reinforcement using powder increases the modulus of elasticity of matrix materials, and then increases the value of the stiffness of hyper composite materials plate. Then, the value of the natural frequency of the hyper composite plate is increased with the increasing of the powder reinforcement. And, then natural frequency of hyper composite plate is increased with the increasing of the value of the modulus of elasticity of the resin materials types. 4. The variation of type of the reinforcement powder do not affect the value of the modulus of elasticity of hyper composite materials plate, and then, do not affect the value of the natural frequency of hyper composite plate, with same density of reinforcement powder. Therefore, the natural frequency of hyper composite plate is increased with the decreasing of the density of reinforcement powder. 5. The value of the natural frequency of hyper composite plate reinforcement with unidirectional fiber is more than the value of the natural frequency of plate reinforcement with woven fiber for aspect ratio of plate less than 1, and, it's more than with aspect ratio greater than 1. 6. For the values of the aspect ratio less than 1, the value of the natural frequency of hyper composite plate is increased with the increasing of volume fraction of the unidirectional or woven reinforcement fiber. This Increment in the value of the natural frequency is less for the increasing of volume fraction of the hyper composite plate composed of powder. But, the value of the natural frequency of composite plate is decreased with the increasing the volume fraction of unidirectional reinforcement fiber with the aspect ratio AR) of composite plate more than 1. REFERENCES 1. Daniel Gay, Suong V. Hoa and Stephen W. Tsai 'Composite Materials Design and Applications' Book, CRC Press LLC, 2003. 2. J. S. Rao 'Dynamics of Plates' Narosa Publishing House, 1999. 3. Muhannad Al-Waily Theoretical and Numerical Analysis Vibration Study of Isotropic Hyper Composite Plate Structural International Journal of Mechanical and Production Engineering Research and Development IJMPERD), TJPRC), Vol. 3, No. 5, 2013. 4. J. N. Reddy 'Mechanics of Laminated Composite Plates and Shells, Second Edition' Book, CRC Press LLC, 2004. 5. KanakKalita and AbirDutta 'Free vibration Analysis of Isotropic and Composite Rectangular Plates' International Journal of Mechanical Engineering and Research, Vol. 3, No. 4, PP. 301-308, 2013. 6. R.K. Misra 'Free Vibration Analysis of Isotropic Plate Using Multi- Quadric Radial Basis Function' International Journal of Science, Environment and Technology, Vol. 1, No. 2, pp. 99-107, 2012. 7. A. Ergin, B. Ugurlu 'Linear vibration analysis of cantilever plates partially submerged in fluid' Journal of Fluids and Structures, Vol. 17, pp. 927 939, 2003. 8. Avadesh K. Sharma and N. D. Mittal 'Review on Stress and Vibration Analysis of Composite Plate' Journal of Applied Sciences, Vol. 10, No. 23, pp. 3156-3166, 2010. 9. Muhsin J. Jweeg and Muhannad Al-Waily 'Dynamic Analysis of Stiffened and Unstiffened Composite Plates' The Iraqi Journal For Mechanical And Material Engineering, Vol. 13, No. 4, 2013. 10. D. J. Gorman ' Accurate Free Vibration Analysis of Point Supported Mindlin Plates by the Superposition Method' Journal of Sound and Vibration, Vol. 219, No. 2, pp. 265-277, 1999. 11. Anil Kumar Dash 'Large Amplitude Free Vibration Analysis of Composite Plates by Finite Element Method' M. Sc. Thesis of Technology in Structural Engineering, Department of Civil Engineering National Institute of Technology, 2010. 12. R.C.L. Dutra, B.G. Soares, E.A. Campos, J.L.G. Silva ' Hybrid Composites Based on Polypropylene and Carbon Fiber and Epoxy Matrix' Elsevier, Polymer, Vol. 41, pp. 3841 3849, 2000. 13. Gururaja M N, A N HariRao 'A Review on Recent Applications and Future Prospectus of Hybrid Composites' International Journal of Soft Computing and Engineering IJSCE), Vol. 1, No. 6, 2012. 14. ParsuramNayak 'Vibration Analysis of Woven Fiber Glass/Epoxy Composite Plates' M. Sc. Thesis of Technology in Civil Engineering Structural Engineering), Department of Civil Engineering National Institute of Technology Rourkela, 2008. 15. Timothy W. Taylor, Adnan H. Nayfeh ' Natural Frequencies of Thick, Layered Composite Plates' Composites Engineering, Vol. 4, No. 10, pp. 1011-1021, 1994 16. Muhannad Al-Waily 'Experimental and Numerical Vibration Study of Woven Reinforcement Composite Laminated Plate with Delamination Effect' International Journal of Mechanical Engineering IJME- IASET), Vol. 2, No. 5, 2013. 17. Y.B. Zhao, G.W. Wei, Y. Xiang 'Plate Vibration Under Irregular Internal Supports' International Journal of Solids and Structures, Vol. 39, pp. 1361 1383, 2002. 18. JunaidKameran Ahmed, V.C. Agarwal, P.Pal, VikasSrivastav ' Static and Dynamic Analysis of Composite Laminated Plate' International Journal of Innovative Technology and Exploring Engineering IJITEE), Vol. 3, No. 6, 2013. 19. Y.X. Zhang, C.H. Yang 'Recent Developments in Finite Element Analysis for Laminated Composite Plates' Composite Structures, Vol. 88, pp. 147 157, 2009. 20. Parikshit Mehta 'Vibrations of Thin Plate with Piezoelectric Actuator: Theory and Experiments' M. Sc. Thesis to the Graduate School of Clemson University, Mechanical Engineering, 2009. 21. Muhsin J. Jweeg and Muhannad Al-Waily 'Analytical Investigation of Time Dependent Tensional Loading of Stiffened and Un-Stiffened Composite Laminated Plates' International Journal of Mechanical and Production Engineering Research and Development IJMPERD), TJPRC), Vol. 3, No. 4, 2013. 22. Itishree Mishra and Shishir Kumar Sahu 'An Experimental Approach to Free Vibration Response of Woven Fiber Composite Plates under Free- Free Boundary Condition' International Journal of Advanced Technology in Civil Engineering, Vol. 1, No. 2, 2012. 23. Mansour Nikkhah-Bahrami, MasihLoghmani, and MostafaPooyanfar ' Analytical Solution for Free Vibration of Rectangular Kirchhoff Plate from Wave Approach' World Academy of Science, Engineering and Technology, Vol. 39, 2008.

International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:14 No:06 21 24. R.C. Batra, S. Aimmanee ' Vibrations of Thick Isotropic Plates with Higher Order Shear and Normal Deformable Plate Theories' Computers and Structures, Vol. 83, pp. 934 955, 2005. 25. Muhsin J. Jweeg and Muhannad Al-Waily 'Determination of Inter- Laminar Shearing Stresses Using a Suggested Analytical Solution in the Composite Laminated Plates' International Journal of Mechanical Engineering IJME), IASET, Vol. 2, No. 5, 2013. 26. F. Zhang, T. Lisle, W.A. Curtin, Z. Xia 'Multiscale Modeling of Ductile-Fiber-Reinforced Composites' Composites Science and Technology, Vol. 69, pp. 1887 1895, 2009. 27. Werner Soedel ' Vibrations of Shells and Plates, Third Edition, Revised and Expanded' Marcel Dekker, Inc., 2004. 28. Rudolph Szilard ' Theories and Applications of Plate Analysis: Classical, Numerical and Engineering Methods' John Wiley & Sons, Inc., 2004. 29. Eduard Ventsel and Theodor Krauthammer Thin Plates and Shells, Theory, Analysis, and Applications Book, Marcel Dekker, Inc., 2001. 30. Valery V. Vasiliev, Evgeny V. Morozov ' Mechanics and Analysis of Composite Materials' Elsevier Science Ltd, 2001. 31. Valery V. Vasiliev, Evgeny V. Morozov ' Advanced Mechanics of Composite Materials' Elsevier Ltd, 2007. Dr. Mohsin A. Al-Shammari, Lecture in University of Baghdad- Faculty of Engineering - Mechanical Engineering Department. Ph.D. In Mechanical Engineering/ University of Technology/ Iraq. Specialization: Applied Mechanics- Vibration Analysis Study and Composite Material Study-Crack Study,Graduation Date: 2010. M.Sc. In Mechanical Engineering/ College of Engineering/University of Baghdad/Iraq Specialization: Applied Mechanics- Tribology, Graduation Date: 1997. B.Sc. In Mechanical Engineering/ College of Engineering/University of Baghdad /Iraq Specialization: General Mechanics, Graduation Date: 1992. Research Interests, Vibration Analysis Study, Stress Analysis Study under Static and Dynamic Loading, Composite Materials Study, Fatigue and Creep Analysis Study of Engineering Materials, Mechanical Properties of Engineering Materials Study, Damage Study Crack and Delamination Study), Hydrodynamic Lubrication and other mechanical researches. dr.alshammari@uobaghdad.edu.iq, mohsinabdullah@yahoo.com Dr. Muhannad Al-Waily, Lecture in Kufa University- Faculty of Engineering- Mechanical Engineering Department. Ph.D. In Mechanical Engineering/ College of Engineering/ Alnahrain University/Iraq. Specialization: Applied Mechanics- Vibration Analysis Study, Composite Material Study- Crack Study, Health Monitoring, Graduation Date: 2012. M.Sc. In Mechanical Engineering/ College of Engineering/University of Kufa/Iraq Specialization: Applied Mechanics- Vibration Analysis Study, Composite Material Study-Stress Analysis Study, Graduation Date: 2005. B.Sc. In Mechanical Engineering/ College of Engineering/University of Kufa /Iraq Specialization: General Mechanics, Graduation Date: 2002. Research Interests, Vibration Analysis Study, Stress Analysis Study under Static and Dynamic Loading, Composite Materials Study, Fatigue and Creep Analysis Study of Engineering Materials, Mechanical Properties of Engineering Materials Study, Control and Stability of Mechanical Application Study, Damage Study Crack and Delamination Study) and other mechanical researches. muhanedl.alwaeli@uokufa.edu.iq, muhannad_al_waily@yahoo.com