Document Type : Research Paper
Authors
^{1} Professor, Department of Mechanical Engineering, University College of Engineering Kakinada (A), Kakinada, 533003, India.
^{2} M.Tech Student in University College of Engineering Kakinada (A) Kakinada, 533003, India.
^{3} DAssistant Professor, Department of Mechanical Engineering, University College of Engineering, JNTUK Kakinada, Kakinada, India.
Abstract
Keywords
Main Subjects
Free Vibration Analysis of Graphene Reinforced Laminated Composite Plates using Experimental Modal Testing
^{a} Professor, Department of Mechanical Engineering, University College of Engineering Kakinada (A), Kakinada, 533003, India.
^{b} M.Tech Student in University College of Engineering Kakinada (A) Kakinada, 533003, India.
^{c} Assistant Professor, Department of Mechanical Engineering, University College of Engineering, JNTUK Kakinada, Kakinada, India.
KEYWORDS 

ABSTRACT 
HalpinTsai model; Finite element method; Stacking sequence; Experimental modal analysis; Fast Fourier transform. 
Graphene has become a significant and handy nanomaterial due to its excellent tensile strength, electrical conductivity, and stiffness, and is the thinnest material. It could be utilized to reinforce the polymer matrix of composites, increasing their strength and stiffness. In this study, the vibration behaviour of carbon fiber graphenereinforced hybrid polymer plate, graphenereinforced polymer plate, and carbon fiberreinforced polymer plate (CFRP), is examined in the context of developing laminated composite plates. The material properties of the graphenereinforced matrix are estimated using the applicable HalpinTsai models. Following that, the orthotropic mechanical properties of a composite carbon fiber and hybrid matrix lamina are evaluated. Plates are modeled using finite element modeling methods while taking into account a specific stacking order and geometric layouts. The impact hammer modal testing method is used to document the plates' reaction to vibration. In order to see the intrinsic frequencies and mode shapes of the plate, the recorded time domain responses are translated to the frequency domain using the Fast Fourier transform (FFT). The ME Scope software is used for postprocessing. The modes of vibration response are assessed by applying various boundary conditions. Results indicate that natural frequencies increase with increasing graphene volume fraction. The larger the volume percentage, the higher the plate’s frequency for all transverse modes, as seen. By incorporating 1% graphene into the polymer matrix, the first, second, third, and fourth mode forms increase by up to 32.35%, 48.96%, 22.17%, and 30.08%, respectively. Adding graphene to the composite raises the frequency of higher modes relative to the basic mode. 
Polymer matrix composites offer great strength and stiffness while being lightweight, making them a viable choice for Aerospace, Automotive, Medical, and other technical applications. Graphene's high mechanical performance allows it to be utilized to strengthen polymer matrix composites, increasing strength and stiffness.
Carbon fiber reinforced polymers have high strength and stiffness as well as good corrosive resistance which can be extensively used for marine applications as well as aerospace applications. Graphene is a carbon allotrope, which is 200 times stronger than steel. Nowadays, Graphene nanoplatelets are used as fillers in composite materials which enhances the mechanical properties of the composite structures.
Premixing nanoparticles into the polymer matrix may improve throughthickness or matrixdominant characteristics. Combining spray coating with vacuumassisted resin infusion resulted in a process for producing CFRP hybrid composites with the desirable inplane aligned graphene nanoplatelets, according to Yao [1] findings.
The tensile, flexural, and CO_{2} gas permeability of the material was assessed. It was demonstrated that under relatively modest GNP loadings (0.2 vol %), both tensile and flexural properties performed better, however, the gas barrier property improved dramatically as GNP loadings increased.
Firstorder shear deformation plate theory is used to create the theoretical formulation, and thermoelastic equilibrium equations are solved to get the initial thermal stresses. To assess the effective material properties of each layer of the composite plates reinforced graphene nanoparticles, the HalpinTsai micromechanical model is applied. Qaderi [2] concluded that as the Graphene platelets' weight fraction rises; the dimensionless frequency of graphenereinforced composite plates gets better. Regardless of the Graphene platelet distribution pattern, the dimensional less natural frequency rises when graphene platelets are introduced into an epoxy matrix. Soykok [3] used two distinct ways to theoretically establish the engineering constants of CNT and carbon fiberreinforced composite laminates. They employed the finite element approach to model and investigate the behaviour of a certain stacking sequence and composite plate design under static loadings. Their findings show a considerable enhancement in plate stiffness due to the presence of nanotubes. Hulun et al. [4] used the elementfree Improved Moving Least SquaresRitz approach to examine the free vibration response of graphenereinforced composite quadrilateral plates. They came to the conclusion that raising the weight percentage of GPLs can increase the natural frequency of a quadrilateral plate.
Mishra et al. [18] performed the vibration analysis of the composite plates both analytically and numerically. The research was done on the UD fiber GFRP woven fabric composite plates at free–free test conditions. The authors mentioned that the analysis was performed using modern testing methods and analysis was done using computerized software. Results indicate that the natural frequency of the composite plate with the CL condition is very less when compared with the SS condition.
Patel et al. [19] conducted a study on the experimental and numerical analysis of the free vibrations of MWCNTRCP. The authors studied the effects of different percentages of MWCNT on the NFs of FRP by varying the thickness, aspect ratios, and boundary conditions. The manufacturing technique used to fabricate the composite plate was the Manual Hand layup technique. The authors also stated that the elastic properties were determined using experimental techniques. In this research, an advanced simulation, known as ABAQUS, was used to determine the modal response of the composites and compared them with the experimental ones. Results indicate that there is an increase in the elastic properties and NF’s up to 0.3 wt. % of MWCNT and thereafter decreases gradually due to agglomeration of CNT in a polymer matrix.
Prasad et al. [20] research has been carried out on the experimental and numerical study of the vibration analysis of the woven FML plates. The authors stated that they initiated the work using the firstorder Reissner–Mindlin theory with the FE formulations for both fibers and metals. The NFs were obtained by performing the experimental analysis using B & K FFT analyzer. Results also include that as the thickness ratio is decreased the NF of the FML increased. It is also declared that the type of boundary condition may affect the NF of the FML plate.
Prasad et al. [21] performed experimental work on the fatigue characteristics of the FML with the effect of the Nano alumina. In this article, the authors stated that the addition of Nanofillers to the composite material increases the binding strength of the composite. The experimental test such as the low cycle fatigue test indicated that as the percentage of the Nanofillers are increasing so as the fatigue characteristics of the composite also increase. Maximum UTS of about 70% was found at 94% of FBL.
Sahu et al. [22] conducted numerical prediction and experimental validation of free vibration responses of the hybrid composite curved panel structure. The authors used a mathematical formulation with 5 modal responses by considering different parameters. Results indicate that the experimental data is correlated with the ANSYS FE data through a static structural module. Also, it indicated that the number of layers and type of fiber affect the frequency due to the stiffness variation.
Sahu. P et al. [23] performed a generic computer code generated via the higherorder mathematical model to calculate the variation in modal responses with temperature increments. The numerical frequency values are compared to the experimental results and the numerical results from other publications.
Using the variation approach [24], the weak form of the governing equation is established by constructing a higherorder kinematic model that takes into account the effect of single and double curvatures, respectively on the shell panel.
Mehar et al. [25] conducted experimental verification on the thermomechanical transient flexure on the GCKRHCC shell panels. To perform the numerical research, HOKM is prepared considering the effect of the curvature of the shell panel. The transient vibrations are found using the governing equations derived from MATLAB and computed through FEM. The validation of the numerical results is then compared with the experimental results.
In this journal [26] thermal free vibration behavior of the nanotubereinforced SMA bonded composite structural model has been formulated mathematically using the HSDT kind of displacement theory including the nonlinearity due to the embedded functional material. A mathematical model for the thermal free vibration behavior of nanotube–reinforced SMA bonded composite structures has been formulated using the displacement theory including nonlinearity caused by embedded functional materials [27].
The novelty of this [28] work lies in developing a finite component model integrated with the HDMR tool, for a laminated plate with curving fiber, and incorporation of PNN into the model for sensitivity and random analysis, severally. The finite component code developed in MATLAB surroundings is valid completely with the sooner printed literature.
Sharma et al. [29] conducted a stochastic RBFN test and found three completely different fiber distribution patterns and a spread of boundary conditions. For the thermal buckling analysis, uncertainty within the material properties and thermal parameters is taken into consideration. The variancebased world sensitivity analysis is employed to estimate the contribution of every input parameter. In [30] authors performed the aeroelastic analysis of composite laminates with different fiber spacings.
In [31], Sharma et al. performed static and free vibration analysis of LCP with delamination and found that the delamination is an associated degree of inevitable development in composite structures encountered typically in world operative conditions. The presence of delamination among the structure might considerably affect the dynamic response thanks to the reduction of stiffness of the structure.
For aeroelastic analysis, the metal model is as well as a master's degree. Varied constant studies area units were performed to seek out the foremost essential location of the delamination that severely affects vibration and flutter characteristics [3234]. The results showed that the delamination close to the vanguard that faces free stream wind is found to be the foremost essential for the dynamic aeroelastic failure of structures [35].
In [36] two kinds of sandwich plate sandwiches with FGM face sheets and uniform core and sandwiches with uniform face sheets and FGM core are thought of for gratis vibration analysis with nonlinear temperature variation over the thickness direction. The higherorder layerwise theory is adopted with an associate in nursing eightnoded rectangular component to make a finite component model for gratis vibration analysis.
In this study, the vibration behavior of carbon fiber graphenereinforced hybrid polymer plate, graphenereinforced polymer plate, and carbon fiber reinforced polymer plate (CFRP), are examined in the context of developing laminated composite plates. The material properties of the graphenereinforced matrix are estimated using the applicable HalpinTsai models. Following that, the orthotropic elastic constants of a composite carbon fiber and hybrid matrix lamina are evaluated. Plates are modeled using finite element modeling methods (ANSYS APDL Software) while taking into account specific stacking order and geometric layouts. The impact hammer modal testing method is used to document the plates' reaction to vibration.
Materials used for the carbon fiber reinforced plate (CFRP) are carbon fiber as reinforcement, and polyester resin as the matrix. For Graphene reinforced polymer plate (GRP), Graphene Nanoplatelets as reinforcement and Polyester resin as the matrix. For carbon fiber graphene reinforced hybrid plate, Carbon, Graphene nanoplatelets as reinforcement, and Polyester resin as the matrix. The Quasielastic lamination Sequence of both eightlayered unidirectional fibers of the CFRP plate and Hybrid plate is [0/45/45/90/90/45/45/0]. The GRP plate is a singlelayered plate with a 3 mm thickness.
Fig. 1. Numerical modeling of Composite plates
The ASTM D7264 standard specifies that plates are modeled and fabricated using a hand layup process with dimensions of W, L, and T (W, L, and T) greater than or equal to 10 T.
Table 1. Dimensions of plate
Dimension 
CFRP Plate 
GRP Plate 
Hybrid Plate 
Length (L) 
250mm 
245mm 
250mm 
Width (W) 
250mm 
245mm 
250mm 
Thickness (T) 
3mm 
3mm 
3mm 
Table 2 below provides the measurements of all three plates.
According to the HalpinTsai model, Young's modulus of the graphene and polymer matrix may be estimated using the following equation [8].

(1) 
where

(2) 

(3) 

(4) 
where V_{gpl} and T_{gpl} represent the graphene volume fraction and thickness of graphene, respectively. Furthermore, E_{m} is the Polymer matrix’s Young’s modulus, whereas ξ_{T}, ξ_{L}, η_{L}, and η_{T} are HalpinTsai parameters that depend on the shape of the reinforcement. Assuming that Poisson’s ratio _{m}, Shear modulus , Density are

(5) 

(6) 

(7) 
When considering a unidirectional lamina, the standard rule of a mixture can be used to obtain its modulus of elasticity in the longitudinal direction, E_{1}, and Poisson’s ratio, _{12} of Hybrid plate,

(8) 

(9) 
where E_{f1}, V_{f}, _{f,} and V_{mgpl }are longitudinal Young’s modulus and volume fraction of ﬁber, Poisson’s ratio of ﬁber and volume fraction of the hybrid plate, severally.
The material properties of Plates by adding 1% by weight (V_{gr} = 0.005) of Graphene Nanoplatelets into the matrix are listed in
Table 3. Values in Table 3 are obtained by equations 1  9.
Table 2. Properties of components of the composite material
Carbon fiber[5] 
Polyester resin[6] 
Graphene[7] 

Ef_{1 }(GPa) 
230 
E_{m} (GPa) 
3 
E_{gpl} (GPa) 
735 
Ef_{2}(_{ }GPa) 
15.4 
_{m} 
0.316 
W_{gpl }(nm) 
10.02 
f_{23 } 
0.46 
G_{m }(GPa) 
1.139 
L_{gpl }(nm) 
9.97 
f_{12} 
0.29 
ρ_{m} (Kg/m^{3}) 
1200 
ρ_{gpl} (Kg/m^{3}) 
2260 
Gf_{12 }(GPa) 
10 




Gf_{23 }(GPa) 
5.28 




ρf (Kg/m^{3}) 
1800 




Table 3. Material properties of Composite plates
Material Property 
CFRP Plate 
GRP plate 
Hybrid Plate 
E_{11 } (GPa) 
139.20 
3.197 
139.28 
E_{22 } (GPa) 
7.799 
3.199 
10.52 
E_{33 } (GPa) 
7.799 
3.199 
10.52 
_{12} 
0.3 
0.315 
0.3 
_{23} 
0.397 
0.315 
0.397 
_{13} 
0.3 
0.315 
0.3 
G_{12 }(GPa) 
4.924 
1.215 
6.51 
G_{23 }(GPa) 
3.493 
1.216 
3.65 
G_{13 }(GPa) 
4.924 
1.215 
6.51 
ρ_{C }(Kg/m^{3}) 
1560 
1205 
1562 
In ANSYS 19.2 Mechanical APDL Software, the plates are modeled as a plane region, and eightnoded quadrilateral shell elements are used for meshing (SHELL281). For evaluating thin to moderately thick shell structures, use the SHELL281 element. The element has eight nodes, each of which has six degrees of freedom: translations along the x, y, and z axes, as well as rotations about these axes. The firstorder shear deformation theory (FSDT), which assumes that the transverse shear strain is constant throughout the thickness of the shell, governs the accuracy of modeling composite shells employing these elements [9].
Fig. 2. 8 Layered composite laminate plate in ANSYS
Three plates with two end conditions, such as Clamped  Free  Clamped  Free (CFCF) and Simply Supported  Free  Simply Supported  Free (SFSF), are subjected to experimental modal analysis (EMA) to determine the vibration behavior and dynamic features. The experimental setup for modal analysis illustrates how a free vibration test performs a modal analysis. By converting the vibration motion into electrical signals, an accelerometer may measure the sample response and vibration levels at various locations on a structure. Using beeswax, (commercial) the accelerometer was attached to the sample.
An exciting shock is delivered using an impact hammer with a quartz tip to establish the initial input frequency and magnitude for the modal setup. To obtain the sample I/O data, a unit with eight input channels was used. To take measurements, two input channels are chosen, the first of which is coupled to an accelerometer, and the second of which is attached to an impact hammer. To ascertain the dynamic characteristics and modal characteristics, including natural frequencies and mode shapes, a data acquisition system (DAQ) is employed. Using the SAMURAI software tool, these data were retrieved from frequency response function curves (FRF).
The ME'Scope Software is used for postprocessing. The natural frequencies will be extracted from the FRFs obtained from the testing throughout this module, and they will be assigned to the ME Scope structure along with the FRFs in order to produce the animation of Mode shapes.
The following apparatus will be used to perform the experiment:
The experimental setup with various boundary conditions was shown in Figures
3 to 9.
Fig. 3. Experimental Setup
Fig. 4. CFRP square plate with CFCF Boundary condition
Fig. 5. Hybrid square plate with SFSF Boundary condition
Fig. 6. GRP square plate with SFSF boundary condition
Fig. 7. CFRP square Plate with SFSF Boundary condition
Fig. 8. GRP square plate with CFCF Boundary condition
Fig. 9. Hybrid square plate with CFCF Boundary condition
The results for Natural frequencies and mode shapes of all three plates are discussed in this section. The ANSYS results for natural frequencies and mode shapes are evaluated and compared with the experiment results.
4.1 Carbon Fiber Reinforced Plate (CFRP)
Tables 4 and 5 show the natural frequencies of carbon fiber reinforced plates with SFSF and CFCF boundary conditions compared with ANSYS and experimentation.
Table 4. Natural frequencies of CFRP square plate
with SFSF boundary condition
Mode Number 
EMA 
ANSYS (Hz) 
Percentage 
1 
87.5 
97.4 
10.16 
2 
125 
134 
6.71 
3 
241 
247 
2.42 
Table 5. Natural frequencies of CFRP square plate
with CFCF boundary condition
Mode Number 
EMA 
ANSYS (Hz) 
Percentage 
1 
322 
332 
3.01 
2 
366 
365 
0.27 
3 
497 
494 
0.60 
Fig. 10. Natural frequencies of CFRP square plate
with SFSF boundary condition
Fig. 11. Natural frequencies of CFRP square plate
with CFCF boundary condition
EMA ANSYS
First Mode
Second Mode
Third Mode
Fig. 12. Variation of mode shapes for SFSF CFRP square plate with experimental modal testing and ANSYS
EMA ANSYS
First Mode
Second Mode
Third Mode
Fig. 13. Variation of mode shapes for CFCF CFRP square plate with experimental modal testing and ANSYS
As observed from the above values of natural frequencies for both SFSF and CFCF conditions, CFCF has higher natural frequencies than SFSF. as the stiffness of clamped condition is more than the supported condition.
The results obtained from experimental modal testing agreed well with ANSYS results. Visual representation of mode shapes was given in Figures 12 and 13.
Graphene nanoplatelets are uniformly and randomly oriented all over the plate with a single layer thickness of 3mm.
Tables 6 and 7 show the natural frequencies of the graphenereinforced plate with SFSF and CFCF boundary conditions compared with ANSYS and experimentation.
Table 6. Natural frequencies of GRP square plate
with SFSF boundary condition
Mode Number 
EMA 
ANSYS (Hz) 
Percentage 
1 
43.8 
37.8 
13.69 
2 
75 
62.6 
16.53 
3 
134 
143 
5.59 
Table 7. Natural frequencies of GRP square plate
with CFCF boundary condition
Mode Number 
EMA 
ANSYS (Hz) 
Percentage 
1 
119 
116 
2.52 
2 
156 
137 
12.17 
3 
238 
226 
5.04 
Fig. 14. Natural frequencies of GRP square plate
with SFSF boundary condition
Fig. 15. Natural frequencies of GRP square plate with CFCF boundary condition
EMA ANSYS
First Mode
Second Mode
Third Mode
Fig. 16. Variation of mode shapes for SFSF GRP square plate with experimental modal testing and ANSYS
EMA ANSYS
First Mode
Second Mode
Third Mode
Fig. 17. Variation of mode shapes for CFCF GRP square plate with Experimental modal testing and ANSYS
As observed from the above values of natural frequencies for both SFSF and CFCF conditions, CFCF has high natural frequencies than SFSF. As the stiffness of clamped condition is more than the supported condition.
The results obtained from experimental modal testing agreed well with ANSYS results. Visual representation of mode shapes was given in Figures 16 and 17.
Tables 8 and 9 show the natural frequencies of the graphenereinforced plate with SFSF and CFCF boundary conditions compared with ANSYS and experimentation.
Table 8. Natural frequencies of Hybrid square plate
with SFSF boundary condition
Mode Number 
EMA (Hz) 
ANSYS (Hz) 
Percentage 
1 
90.6 
97.4 
6.98 
2 
128 
134.4 
4.76 
3 
244 
247 
1.21 
Table 9. Natural frequencies of Hybrid square plate
with CFCF boundary condition
Mode Number 
EMA 
ANSYS (Hz) 
Percentage 
1 
328 
333 
1.50 
2 
369 
366 
0.81 
3 
475 
497 
4.42 
As observed from the above values of natural frequencies for both SFSF and CFCF conditions, CFCF has high natural frequencies than SFSF, as the stiffness of clamped condition is more than supported condition.
Fig. 18. Natural frequencies of Hybrid square plate
with SFSF boundary condition
The results obtained from the Experimental modal testing very well agreed with ANSYS results. Visual representation of mode shapes was given in Figures 19 and 20.
EMA ANSYS
First Mode
Second Mode
Third Mode
Fig. 19. Variation of mode shapes for SFSF hybrid square plate with experimental modal testing and ANSYS
Fig. 20. Natural frequencies of Hybrid square plate
with CFCF boundary condition
EMA ANSYS
First Mode
Second Mode
Third Mode
Fig. 21. Variation of mode shapes for CFCF hybrid square plate with experimental modal testing and ANSYS
Table 10. Material properties of carbon fiber graphene reinforced hybrid composite plate
V_{gpl} 
E_{11 }(GPa) 
E_{22 }(GPa) 
_{12} 
_{23} 
G_{12} (GPa) 
G_{23 }(GPa) 
ρ_{c} (Kg/m^{3}) 
0 
139.20 
7.799 
0.30 
0.397 
4.924 
3.493 
1560 
0.1 
145.47 
16.673 
0.30 
0.397 
10.589 
7.466 
1602 
0.2 
152.95 
23.073 
0.30 
0.397 
14.559 
11.124 
1645 
0.3 
162.00 
30.305 
0.30 
0.397 
19.010 
15.445 
1687 
0.4 
173.20 
39.064 
0.30 
0.397 
24.388 
20.752 
1730 
0.5 
187.42 
50.094 
0.30 
0.397 
31.154 
27.473 
1772 
Fig. 22. Effect of Graphene volume fraction on natural frequencies with corresponding mode shapes
for all edges simplysupported (SSSS) plate boundary condition
From the results, one can clearly observe that the hybrid plate has higher natural frequencies when compared to the CFRP plate and
GRP plate and the lower Natural frequencies were observed at the GRP plate. This indicates that by adding Graphene nanoplatelets into polymer composite plates, the natural frequencies of plates get increased which implies stiffness of the plate is also increased, and further dynamic characteristics of the plate get enhanced.
4.4. Effect of Graphene Volume Fraction on Carbon Fiber – Graphene – Reinforced Hybrid Plate Assuming SSSS Boundary Condition
The graphene volume fraction is evaluated to find the influence of graphene inclusion on the vibration response of a carbon fibergraphenereinforced hybrid plate under SSSS boundary conditions on ANSYS.
To carry out the method, five distinct situations are considered: V_{gpl} = 0.1, 0.2, 0.3, 0.4, and 0.5. The influence of graphene volume percentage on the first, second, third, and fourth mode forms of transverse vibrations are shown in Fig. 22. The larger the volume percentage, the higher the plate’s frequency for all transverse modes, as seen. By incorporating 50% graphene into the polymer matrix, the first, second, third, and fourth mode forms increase by up to 32.35%, 48.96%, 22.17%, and 30.08%, respectively.
Table 11. Effect of Graphene volume fraction on natural frequencies with corresponding mode shapes for SSSS boundary condition
Mode number 

V_{gpl} 
1 
2 
3 
4 
0 
170 
337 
514 
688 
0.1 
182 
379 
537 
746 
0.2 
193 
409 
559 
795 
0.3 
201 
434 
575 
805 
0.4 
212 
465 
599 
839 
0.5 
225 
502 
628 
895 
Unlike traditional experiments that use resin to bind two layers together, combined properties of resin and fiber were imparted to a single layer in order to account for resin's effect, followed by the other layers modeled the same way and simulations were performed. If the boundary conditions were not aligned properly with the support structure, it may cause not detect the natural frequencies and have lower bound values.
Laminated composite hybrid plates’ free vibration behavior has been examined in order to find out natural frequencies and mode shapes for various end conditions. An indepth analysis is done on the impact of graphene volume fraction on the dynamic properties of the hybrid plate reinforced with carbon fiber and graphene.
Acknowledgments
The Authors are thankful to the University College of Engineering (A) Kakinada for providing space and utilizing software and hardware facilities for this research work.
Conflicts of Interest
The author confirms that there are no conflicts of interest with the publication of this article.
References