Vibration Analysis of Natural Fiber Composite Beam under Various End Conditions

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Vibration Analysis of Natural Fiber Composite Beam under Various End Conditions

Manan Shah 1, Haresh Patolia 3,

Ketul Brahmbhatt 4

1 Research Scholar, 3 Associated Professor,

4 Assistant Professor

1, 3, 4 Mechanical Engineering Department, BVM Engineering College,

  1. V. Nagar, Anand, India

    Jay Khatri 2

    2 Assistant Professor,

    2 Mechanical Engineering Department, Aditya Silver Oak Institute of Technology, Ahmedabad, India

    Abstract The todays research trend in composite is for the development of composite with natural fibre instead of synthetic fibre. It is because of Properties like light weight, low cost, bio- degradability, low environmental impact and ease to manufacture. It becomes necessary to study the vibrational behavior of composite in addition to mechanical strength and chemical properties for effective utilization in real world applications as they subjected to many types of loading condition and different types of vibration with different configurations. In present work a natural fibre composite beam is manufactured with unidirectional orientation for measurement of transverse vibration with different end configurations results obtained from analytical method and modal analysis in ANSYS are compared. The mechanical properties are considered by performing tensile, flexural and impact test on the beam according to ASTM standards. Hemp and sisal fiber are taken as fiber component and ARSONOL IP 1005 P, unsaturated polyester resin is as matrix material. The vibration test is performed using LabVIEW software, which gives data based on time and measures the acceleration. To convert time domain data into frequency domain, Fast Fourier Transformation (FFT) is done in MATLAB and natural frequencies are found out. Those results are also compared with analytical results, with the results obtained by modal analysis in ANSYS and with the results obtained by Neural Network Tool of MATLAB.

    Keywords Free Vibration, Natural Fiber, Composite Material, Properties Of Composite, FEA, Neural Network.

    1. INTRODUCTION

      Natural fiber composites are attracting the researcher because of advantages that these fibers make available over conventional reinforcing synthetic fiber. Natural fibers possess properties like light weight, low environmental impact, biodegradability and non-abrasive characteristics. In fact, certain drawbacks like poor moisture resistance, lower stability, hydrophilic nature, lower life cycle and poor fire resistance properties create the resistance in use of natural fiber composite. However nowadays new surface treatments are developed which increases mechanical properties of natural fibers makes them available for certain industrial applications. In the light of mechanical and economical properties, there are different type of natural available from different species and different origin. Mechanical properties of various fibers are compared with synthetic fibers. Since glass fiber has occupied more than 90% of market for reinforcement in composite industry, lower mechanical properties and improper (poor) bonding characteristics of fiber with matrix material limited the use of natural fiber. With the development of improved technology mechanical properties of this natural fiber are started improving.

      Despite that natural fibers are currently facing the problem of poor fire resistance, lack of dimensional stability and hydrophilic nature, which tends to affect the mechanical properties.

      The researchers also studied effect of volume fraction of fiber on mechanical properties, which shows increasing trend in mechanical properties of composite as volume fraction of fiber increased up to 50%. After that the mechanical properties of composite shows decreasing trend due to poor adhesion of fiber with matrix material [1].Despite of having lower life cycle compared to synthetic fiber, natural fiber composites are looking like to be superior to glass fiber as they required larger fraction of fiber which tends to reduce the overall weight and also they have less environmental impact compared to glass fiber composites. [2]. The reduction in overall weight improves the fuel efficiency which in turns results in fuel saving [3] and also reduction of cost.

      Effect of layering pattern is carried out by different researchers [4, 5]. Various combinations has been studied and compared with glass fiber composite to replace synthetic fibers in as many as possible ways and to promote use of natural fiber composites. Effect of addition of Nano clay is also studied with different layering pattern of glass and coconut sheath to reduce the fraction of glass fiber [6] The research is also on going to study the vibrational behavior of natural fiber composite beam in addition to other mechanical properties [7]. Different researcher studied or examined free vibration characteristics of natural fiber composite beam with different fiber length [8] , with different weightage fraction [9] and analysis of mechanical properties are carried out for various composites [10] to find effect of such parameters. The short length fiber shows better results as they have less surface damage as compared to long fibers and 50% weight shows the higher mechanical properties while better damping properties are achieved with 35% w/w ratio of fiber to matrix. There is some functional relationship between damping and temperature, but there is inverse relationship between first natural frequency and temperature as increased in temperature reduce the natural frequency as increase in temperature will decrease the young modulus and there is a relation between natural frequency and youngs modulus [11]. As composite is anisotropic material increase in weightage fraction of fiber initially increase in the transverse, compressive and shear strength but then it start decreasing [12]. The effect of cut off on the centre of the composite plate has been studied as cut out is commonly used as an access port to connect other appliances [13].

      Effect of orientation of fiber in composite also studied and it shows that composite with (00) fiber orientation shows maximum mechanical properties and it start decreasing as fiber orientation increases towards (900) [14]. Effect of various end conditions are also studied which shows maximum natural frequency for clamped-clamped condition while cantilever condition shows minimum value of natural frequency [15].

      However, for varied shaped structures or system may be analyzed with soft computing techniques more effectively. Soft Computing techniques constitute artificial neural networks (ANN), fuzzy logic, machine learning and genetic algorithm [16]. Soft computing methods are different from classical computing method , unlike classical computing method it is tolerant of imprecision, an uncertainty, a partial truth to achieve tractability, an approximation, robustness, decreases solution cost and a better relation with reality [17].On over all, ANN has a benefits of parallelism, high speed evaluation, less time consumption, optimization to problem, well suited to constrained problem, easy to design, understandable. So, ANN is one of the beneficial method for soft computing technique and also an optional method used to obtain solutions of mathematical form of dynamic systems, represented with the help of ordinary differential equations. [18, 19].

    2. EXPERIMENTAL WORK

      For testing of mechanical properties, the standard specimens of Hemp fiber, Sisal fiber and Hemp-Sisal fiber with 10 w/w ratio of fiber to matrix weight have prepared. To investigate mechanical properties tensile, impact and flexural test ae performed.

      1. Tensile test

        Tensile test is performed using ASTM standard on UTM machine. The beam is prepared according to ASTM D368. The Figure 1 shows the standard specimen and the dimensions are given in Table 1.The specimen before and after tensile test shown in Figure 2.

        Fig. 1. Dimensions of dumbbell shape

        TABLE I. DIMENSIONS OF DUMBBELL SHAPE

        Notation

        Meaning

        Thickness up to 7 mm (mm)

        W

        Width of narrow section

        13

        L

        Length of narrow section

        57

        WO

        Width overall

        19

        LO

        Length overall

        165

        G

        Gauge length

        50

        D

        Distance between grips

        115

        R

        Radius of fillet

        76

        1. Before (b) After

          Fig. 2. Test specimen before and after tensile test

          In Table 2, the results of tensile test are shown. The hemp- sisal FRPC shows the grater tensile strength compared to Hemp and Sisal FRPC.

      2. Flexural test

        The flexural test is also performed on UTM machine. The specimens are prepared with standard ASTM D790. The beam prepared with the dimensions of 12.7×127×5 mm3. The Figure 3 shows test specimen before test and after test while Table 3 shows the results of test

        TABLE II. TABLE 1: RESULT OF TENSILE TEST

        Beam

        Max. Load (N)

        Max. Extension (mm)

        Elongation (%)

        Tensile strength (MPa)

        Modulus of Elasticity (MPa)

        Hemp FRPC

        1660

        1.28

        2.44

        25.6

        1140

        Sisal FRPC

        1420

        1.76

        3.56

        21.9

        797

        Hemp- sisal FRPC

        1810

        2.04

        4.15

        27.8

        682

        Fig. 3. Test specimen before test and after flexural test

        TABLE III. FLEXURAL TEST RESULTS

        Specimen

        Width (mm)

        Thickness (mm)

        Max. force (N)

        Flexural strength (MPa)

        Flexural strain (%)

        Modulus (MPa)

        Hemp FRPC

        12.7

        5

        167

        63.3

        1.58

        4530

        Sisal FRPC

        12.7

        5

        134

        50.7

        1.91

        2910

        Hemp-

        sisal FRPC

        12.7

        5

        146

        55.1

        2.18

        2820

      3. Impact test

        Charpy test is used to measure the impact strength of the composite beam are shown in Figure 4 shows the test specimen before test and after impact test while Table 4 shows the result of test.

        Beam

        Impact strength (J)

        Hemp FRPC

        2.50

        Sisal FRPC

        2.15

        Hemp-sisal FRPC

        2.34

        Fig. 4. Test Specimen before test and after impact test TABLE IV. IMPACT TEST RESULTS

      4. Vibration test

      Vibration analysis is performed with different end conditions and LabVIEW is used for measuring the acceleration. This software gives data of time and acceleration. To find out natural frequency Fast Fourier Transformation (FFT) is performed in MATLAB and natural frequencies are plotted and measured. Figure 5 shows test set up for doing experimental work while Table 5 shows the results of vibration analysis and Figure 6 shows frequency response curve.

      Fig. 5. Set up for vibration measurement

      TABLE V. EXPERIMENTAL RESULT OF NATURAL FREQUENCY FOR DIFFERENT FRPC FOR VARIOUS END CONDITIONS

      Beam

      Mode no

      Natural frequency (Hz)

      End configuration

      Cantilever

      Clamped- Clamped

      Clamped- Supported

      Supported- Supported

      Hemp- FRPC

      1

      16.8

      109.8

      76.17

      48.44

      2

      106.2

      302.7

      241.8

      193.8

      3

      297.3

      590.6

      503.9

      427.7

      Sisal- FRPC

      1

      14.06

      91.8

      62.5

      40.23

      2

      87.5

      248.4

      203.9

      161.3

      3

      245.7

      498

      418

      353.5

      Hemp- Sisal FRPC

      1

      13.67

      89.06

      61.33

      39.84

      2

      87.11

      246.5

      198.8

      156.3

      3

      241.4

      493

      409

      344.9

      Fig. 6. Frequency response curve

    3. THEORETICAL ANALYSIS

      For theoretical analysis, considering the beam as continuous and free undamped system. Since the beam is made of composite material, so data regarding the physical properties of matrix material and resin like density, youngs modulus and poisons ratio of individual material and by weightage or volume fraction of matrix material used for making the composite are to be theoretically calculated and subsequently the natural frequency for respective END condition by theoretical analysis. For analyzing natural frequency, requires properties like youngs modulus, density and poisons ratio of beam can be calculated by equations (1), (2) and (3). By results of equations (1), (2) and (3), frequency is theoretically obtained by equation (4).

      1. Youngs modulus (Ec)

        1. In case of axial loading,

          c f V f mVm

          Ec Em Vm E f

          V f

          4) Natural frequency ( f )

        2. For transverse loading,

          w 2

          EI l 2

          A

          EI

          Al 4

          1 V f

          Ec E f

          • Vm

            Em

            w = 2f

      2. Poisons ratio ( c)

        Where,

        W and V

        are weightage fraction and volume

        c t

        l

        f V f

        • mVm

          fraction respectively. There is many possible type of beam configuration. Following Table 6 shows the governing equation for some of different beam configuration. Satisfying equation

          3.4 of Natural Frequency we get different values of for known

      3. Density ( c)

      length of beam and from these values of natural frequency at different mode can be found out.

      1 W f

      c f

      • Wm

      m

      TABLE VI. GOVERNING EQUATION FOR DIFFERENT BEAM CONFIGURATION

      Beam configuration

      Frequency equation

      Value of lfor

      1st natural frequency

      2nd natural frequency

      3rd natural frequency

      Clamped-free

      coshl cosl 1 0

      1.875104

      4.694091

      p>7.854757

      Clamped-clamped

      coshl cosl 1 0

      4.730041

      7.853205

      10.995608

      Clamped -supported

      tanl tanhl 0

      3.926602

      7.068583

      10.210176

      Supported-supported

      sinl 0

    4. FINITE ELEMENT MODELING

      ANSYS 15.0 is used for analysis purpose. Model analysis module is used for the model analysis. Beam is modelled in ANSYS and various end conditions are configured and analysis done to find out natural frequencies of different beam with different end conditions. Figure 7 shows visual interpretation of different mode of vibration and Table 7 shows the results of ANSYS analysis.

      1. mode 1 (b) mode 2

        (c) mode 3

        Fig. 7. Vibrating pattern of beam at different mode for Cantilever beam

    5. NEURAL NETWORK ANALYSIS

      Neural Network Tool of MATLAB R2017a for analysis purpose. Neural Network is prepared consisting of Hidden Layer Size of 10 with 3 input variables and 1 output. Training, Validation and Testing of Network is done and analysis results are obtained. Figure 8 shows Neural Network while Figure 9 shows regression pattern of network at different mode for Cantilever beam and Table 8 shows the results of ANN analysis.

      TABLE VII. ANSYS RESULTS OF NATURAL FREQUENCY AT VARIOUS MODES

      beam

      Mode no

      Natural frequency (Hz)

      End configuration

      Cantilever

      Clamped- Clamped

      Clamped- Supported

      Supported- supported

      Hemp- FRPC

      1

      18.622

      119.76

      81.832

      51.94

      2

      116.31

      328.48

      264.49

      207.78

      3

      324.6

      640.59

      550.06

      466.33

      Sisal- FRPC

      1

      15.339

      98.649

      67.407

      42.785

      2

      95.81

      270.58

      217.87

      171.15

      3

      267.38

      527.67

      453.1

      384.13

      Hemp- Sisal

      FRPC

      1

      14.777

      95.029

      64.934

      41.215

      2

      92.294

      260.65

      209.87

      164.87

      3

      257.57

      508.42

      436.47

      370.04

      Fig. 8. Neural Network (Inputs: l, E and and Output: Frequency)

    6. RESULT AND DISCUSSION

      Table 9 shows the comparison of natural frequency obtained by different method namely experiment, analytical and ANSYS.

      From Table 9, it is clear that cantilever beam configuration have minimum natural frequency for same mode compared to other end configuration, while natural frequencies are maximum for clamped-clamped condition followed by clamped-supported and supported-supported configuration. Among all hemp FRPC have maximum natural frequency for same mode followed by sisal FRPC and hemp-sisal FRPC.

      TABLE VIII. ANN RESULTS OF NATURAL FREQUENCY AT VARIOUS MODES

      beam

      Mode no

      Natural frequency (Hz)

      End configuration

      cantilever

      Clamped- clamped

      Clamped- supported

      Supported- supported

      Hemp- FRPC

      1

      18.22

      119.18

      81.26

      51.28

      2

      115.21

      335.36

      262.78

      204.33

      3

      321.87

      637.14

      544.86

      424.02

      Sisal- FRPC

      1

      15.026

      98.17

      67.06

      42.18

      2

      94.87

      252.06

      214.16

      169.34

      3

      262.19

      524.07

      447.91

      378.64

      Hemp- Sisal FRPC

      1

      14.61

      95.04

      62.07

      40.89

      2

      92.08

      265.28

      204.56

      168.52

      3

      253.34

      496.36

      407.19

      363.92

      Hemp-sisal FRPC possess maximum tensile strength of 27.8 MPa with maximum elongation of 4.15% (2.04 mm), followed by hemp FRPC with tensile strength of 25.6 MPa and maximum elongation of 2.44% (1.28 mm) and sisal FRPC with maximum tensile strength of 21.9 MPa and maximum elongation of 3.56% (1.76 mm).

      1. Hemp (b) Sisal

        (c) Sisal-Hemp

        Fig. 9. Regression pattern of network at different mode for Cantilever beam

    7. CONCLUSION

Due to comparative properties like light weight, low cost, good mechanical properties, low environmental impact, less energy requirement, safety in manufacturing and bio- degradability natural fibres are now become the major area for research in composites to replace the synthetic fiber. So now it is necessary to study the vibrational characteristics of composite beam with the study of mechanical properties. Here analytical modelling is presented considering the transverse isotropy, which gives an idea about nature frequency of composite beam. Mathematical modelling is also done in ANSYS 15.0 to verify the validity of mathematical modelling. Natural frequency obtained by mathematical modelling is supported by ANSYS result and Neural Network Analysis result. It also gives an idea about natural frequency of beam.

Results shows that hemp FRPC possess higher tensile strength, modulus of elasticity higher impact strength and comparative flexural strength which enable it to available for various applications

Despite of having slightly less impact strength, hemp-sisal FRPC can be used for various application due to its higher tensile strength and comparative flexural strength. In the hemp-sisal FRPC hemp fiber provides strength to composite while addition of sisal fiber improves the flexibility of composite.

END

Configuration

Cantilever

Clamped- Clamped

Clamped- Supported

Supported- Supported

Mode

1

2

3

1

2

3

1

2

3

1

2

3

Natural frequency (Hz)

Hemp-Sisal FRPC

ANSYS

14.777

92.294

257.57

95.029

260.65

508.42

64.934

209.87

436.47

41.215

164.87

370.04

Analytica l

14.21

91.68

254.89

94.87

256.78

502.88

64.34

206.22

429.65

40.89

161.37

363.96

Experime nt

13.67

87.11

241.4

89.06

246.5

493

61.33

198.8

409

39.84

156.3

344.9

Neural Network

14.61

92.08

253.34

95.04

265.28

496.36

62.07

204.56

407.19

40.89

168.52

363.92

Sisal FRPC

ANSYS

15.339

95.81

267.38

98.649

270.58

527.67

67.407

217.87

453.1

42.785

171.15

384.13

Analytical

15.04

94.67

262.19

98.17

267.88

524.07

67.06

214.16

447.91

42.18

167.34

378.64

Experiment

14.06

87.5

245.7

91.8

248.4

498

62.5

203.9

418

40.23

161.3

353.5

Neural Network

15.026

94.87

262.19

98.17

252.06

524.07

67.06

214.16

447.91

42.18

169.34

378.64

Hemp FRPC

ANSYS

18.622

116.31

324.6

119.76

328.48

640.59

81.832

264.49

550.06

51.94

207.78

466.33

Analytical

18.22

115.21

321.87

119.18

326.62

637.14

81.26

262.78

544.86

51.29

204.27

459.39

Experiment

16.8

106.2

297.3

109.8

302.7

590.6

76.17

241.8

503.9

48.44

193.8

427.7

Neural Network

18.22

115.2

321.8

119.1

335.36

637.1

81.26

262.78

544.86

51.28

204.33

424.02

These composites are preferably used in household applications aerospace structure application, high speed turbine machinery and in automobile applications such as bumper of car, side panel back panel of door, roof and dash board in place of glass fiber composite.

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