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**Authors :**Y Seetha Rama Rao , A Durga Hari Prasad -
**Paper ID :**IJERTV7IS090057 -
**Volume & Issue :**Volume 07, Issue 09 (September – 2018) -
**Published (First Online):**05-01-2019 -
**ISSN (Online) :**2278-0181 -
**Publisher Name :**IJERT -
**License:**This work is licensed under a Creative Commons Attribution 4.0 International License

#### Vibration Analysis of CFRP Cantilever Beams due to Different Types of Notches Closed to Fixed End

Vibration Analysis of CFRP Cantilever Beams due to Different Types of Notches Closed to Fixed End

Y Seetha Rama Rao

Associate Professor, Department of Mechanical Engineering,

Gayatri Vidya Parishad

College of Engineering(A) Gandhi Nagar, Madhurawada,Visakhapatnam, Andhra Pradesh,India.

A Durga Hari Prasad PG Student,

Department of Mechanical Engineering, Gayatri Vidya Parishad

College of Engineering(A) Gandhi Nagar, Madhurawada,Visakhapatnam, Andhra Pradesh,India.

Abstract – The aim of experiment is to analyze the vibration of undamaged and damaged Carbon Fiber Reinforced Polymer (CFRP) beams. Experimental free vibration of CFRP cantilever beam will be investigated by dynamic tests. Total three different types of notches are made artificially on the beams closed to fixed end. A comparison will be made of the experimentally extracted frequencies at each damage level and in relation to the single positions of the accelerometer. A comparison between natural frequencies due to different types notches have been investigated. The present experiment illustrates the envelope of Frequency Response Functions (FRFs) obtained by the experimental dynamic tests and the changes of natural frequency values correlated to the damage degree of CFRP beam. Numerical data is found out and discussed in comparison to the experimental results.

Keywords – natural frequencies; frequency responses; damage analysis; CFRP cantilever beam;

INTRODUCTION

In recent decades fibre-reinforced composites have been extensively used for many applications because of their high strength-to-weight and stiffness-to-weight ratios [1]. Composite materials are similar to isotropic materials which are subjected to various damages that are cracks in fibres, matrix, and the interfaces of fibres and matrix is very common in the failure mode of composites [2]. In the present work, vibration analysis of the damaged CFRP cantilever beams can be done by experimental vibration tests by introducing changes of natural frequencies. The damaged condition may be correlated with the changes in frequency values, this decreased with the increasing of damaged condition [3-4]. The analysis demonstrated that the length of damage appears to have less influence as compared to width [5-6]. Experimental results are compared with theoretical results to confirm the availability of the vibration analysis method which is adopted for the analysis of undamaged and damaged CFRP beams. In order to compare the damage frequency values of beams with that of undamaged frequency values of the beams, the variation in natural frequencies of beams are required. A comparison of the values obtained during vibration values of rectangular notched beams with that of the vibration values of Curve notches and double rectangular notches to find out which notches of the beam have high strength capacity for same CFRP beams. Damages in FRP lamina may be represented by local reductions of section or/and loss of continuity of matrix or matrix and fibres [7-8]; these damages may occur for impact or high local stresses [9].

Damages reduce stiffness and lead to the development of diffused FRP cracking with a correlation on the frequency values [10].

EXPERIMENTAL INVESTIGATIONS

Tensile tests performed on CFRP specimen

Experimental tensile tests on specimens were carried out in the laboratory in order to evaluate the strength of CFRP laminas and Youngs modulus before vibration tests aimed at determining the frequency values of undamaged and damaged CFRP cantilever beam elements. Tensile test beam element dimensions are 250mm*20mm*2mm (thick) and 55mm aluminum pads for gripping purpose while testing at the end of the beams. Table 1 shows the tensile test results of CFRP Cantilever beam. Fig. 1 shows the test setup of CFRP cantilever beam. Fig. 2 shows the tensile test result of CFRP cantilever beam.

Fig. 1 Experimental setup for tensile test of a CFRP cantilever beam

Lengt h (mm)

Widt h (mm)

Thicknes s (mm)

Youngs Modulu s (N/mm2)

Poisson s Ratio

Density (Kg/m3

)

Ultimate Tensile Strength (N/mm2

)

250

19

2

70

0.43

1600

90

250

21

2

70

0.43

1600

97

Fig. 2 Experimental setup for tensile test of a CFRP cantilever beam Table no 1: Tensile test properties of CFRP cantilever beam

FFT analyzer and sensors

The Instrument used for determining the frequency values are crystal instruments Coco 80x, Impact Hammer and its Property is 0.9944mv/lbf, Sensor name is P20, weight is 3 grams, and its property is 10 mv/lbf. Fig. 3 shows the FFT analyzer. Fig. 4 shows the impact hammer and the sensor.

Fig. 3 FFT analyzer (Crystal Coco 80x)

Fig. 4 Impact Hammer and P20 sensor

Free vibration tests using FFT analyzer

Table no.2 the theoretical natural frequencies of an undamaged CFRP beam assumed as uniform slender beam. The hypothesis of rotary inertia, shear deformation and damping negligible are considered in the damage analysis of cantilever beam. A set of 10 hits was made for each position of the accelerometer a1 and the average value was acquired. The CFRP cantilever beam was initially tested in undamaged condition (D0). Frequency values were extracted by transformed signals in frequency domain using the Fast Fourier Transform (FFT) technique. The same procedure is repeated for all damaged conditions are Single rectangle notch damage (D1), single rectangle with curve notch damage (D2) and double rectangle notch damage (D3). Tables 3 6 shows the frequencies for each damage condition. Table 7 shows the average frequency

values for each damage level. Fig. 5 shows the accelerometer positions on the testing CFRP cantilever beam. Fig. 6 9 shows the CFRP Cantilever beams with different damage conditions as stated.

Table no 2: Experimental CFRP cantilever beam parameters

Lengt h (mm)

Widt h (mm)

Thicknes s (mm)

Young s Modulu s (N/mm2

)

Poisson s Ratio

Densit y (Kg/m3

)

Ultimat e Tensile Strengt h (N/mm2

)

250

21

2

70

0.43

1600

97

Fig. 5 Accelerometer positions on CFRP cantilever beam for

vibration test

Fig. 6 CFRP cantilever beam in undamaged condition

Fig. 7 CFRP cantilever beam in a single rectangle notch damage condition

Fig. 8 CFRP cantilever beam in a single rectangle with notch damage condition

Fig. 9 CFRP cantilever beam in double rectangle notch damage condition

Free vibration frequency test values using FFT analyzer

Undamaged

1

2

3

4

a1

33.7500

127.5000

357.5000

737.5000

a2

32.7500

125.0000

386.2500

741.7500

a3

32.5000

121.2500

381.2500

715.0000

a4

33.7500

116.2500

351.2500

697.5000

Average

33.1875

122.5000

369.0625

722.3119

Table no 3: CFRP cantilever beam in undamaged condition frequency values

Damaged

1

2

3

4

a1

31.7500

101.2500

353.7500

727.0000

a2

31.2500

112.2500

359.0000

729.2500

a3

29.5000

105.7500

346.5000

706.5000

a4

27.5000

103.5000

342.2500

691.2500

Average

30.0000

105.6875

350.375

713.5000

Table no 4: CFRP cantilever beam in single rectangle notch damage condition frequency values

Damaged

1

2

3

4

a1

30.2500

100.2500

338.7500

714.7500

a2

30.7500

99.7500

341.2500

721.2500

a3

29.5000

97.2500

321.7500

701.7500

a4

29.2500

96.7500

301.2500

698.2500

Average

29.9375

98.5000

325.7500

709.000

Table no 5: CFRP cantilever beam in a single rectangle with notch damage condition frequency values

Damaged

1

2

3

4

a1

28.5000

86.2500

246.2500

710.7500

a2

27.7500

85.0000

253.7500

695.7500

a3

26.5000

84.2500

247.5000

702.2500

a4

24.2500

83.7500

245.7500

689.7500

Average

26.7500

84.8125

248.3125

699.6250

Table no 6: CFRP cantilever beam in double rectangle notch damage condition frequency values

Free vibration frequency spectrums of CFRP cantilever beam

Frequency spectrum with respect to accelerometer positions All graphs are frequency vs DB. Fig. 10 shows the frequency spectrums of CFRP undamaged condition. Fig. 11 shows the frequency spectrums of CFRP single rectangle notch damaged condition. Fig. 12 shows the frequency spectrums of CFRP single rectangle with curve notch damaged condition. Fig. 13 shows the frequency spectrums of CFRP single rectangle notch damaged condition.

Fig. 10 Frequency spectrums of CFRP undamaged condition

Fig. 11 Frequency spectrums of CFRP single rectangle notch damaged condition.

Frequencies (Hz)

Fig. 12 Frequency spectrums of CFRP single rectangle with curve notch damaged condition

Fig. 13 Frequency spectrums of CFRP double rectangle notch damaged condition

THEORETICAL CALCULATIONS Theoretical natural frequencies in the case of the damaged condition of the CFRP cantilever beam has been analyzed solving Eq. 1 and Eq.2) for non-dimensional stiffness values, k, of the spring capable of describing the damages in a limited zone of the beam.

The equations are taken from [1] for theoretical calculations Eigen values () are 1.875, 4.694, 7.855

The Theoretical frequency values obtained from solving above equation was are shown in Table 8.

RESULTS AND DISCUSSION

A series of experiments are conducted to determine the natural frequencies of a CFRP cantilever beam. The frequency near to the notch at accelerometer position (a1) for undamaged condition is 33.1875, for single rectangular notch damage condition is 30.0000, for single rectangle with curve notch condition is 29.9375, and for double rectangle notch condition is 26.7500. As a result of conducting two types of analysis, it can be found that the frequency decreases with the increase in damage condition.

The frequency values obtained by theoretical calculations for undamaged condition is 36.4, for single rectangular notch damage condition is 33.7, for single rectangle with curve notch condition is 31.81, and for double rectangle notch condition is 27.29.

Tables 7 and 8 shows the experimental and theoretical natural frequencies. Fig.14 shows the varaiation of natural frequencies by experimental investigations.

Damage Condition

1

2

3

4

Undamaged

33.1875

122.5000

369.0625

722.3119

Single Rectangular Notch

30.0000

105.6875

350.375

713.5000

Combination of Single Rectangle & Arc

Notch

29.9375

98.5000

325.7500

709.000

Double Rectangular Notch

26.7500

84.8125

305.3125

699.625

Table no 7: Average frequency values in all damaged conditions by experimental investigations

Damage Condition

1

2

3

Undamaged

36.4

130.14

390.42

Single Rectangular Notch

33.7

115.26

375.26

Combination of

Single Rectangle & Arc Notch

31.81

108.8

360.27

Double Rectangular Notch

27.29

90.12

331.35

Table 8 Average frequency values in all damaged conditions by theoretical calculations

Different modes damage

Fig. 14 Variation of natural frequencies for experimental investigations

CONCLUSIONS

An experimental dynamic research on the damage behaviour of CFRP cantilever beams was developed both in the undamaged condition and in three types of damage due to notches close to the fixed end. The damaged condition may be correlated with the changes in frequency values; these decrease with the increasing of damage condition. Both experimental and theoretical methods results are demonstrated. The error is found between experimental and analytical frequency calculation methods and it is observed that it varies from 5% – 10%. In this experimentation, there is not much frequency difference between single rectangle notch and single rectangle with a curved cross-section. By using curved notches in place of rectangle notches to avoid sharp corners so that better performance of beams can be achieved.

REFERENCES

[1]. R. Copuzzuco , The vibration of CFRP cantilever beam with damage, Composite Structures, vol. 116, pp. 211-222, 2014. [2]. C. Soutis, Failure of Notched CFRP Laminates due to Fiber Micro Buckling: A Review, Journal of the Mechanical Behavior of Materials, vol. 6, Issue. 4, pp. 309-330, 1996. [3]. P. D. Chi nd S. Xiushan, Experimental and Computational Studies on Progressive Failure Analysis of Notched Cross-ply CFRP Composite, International Journal Computational Materials, vol. 1, 1250023 pp. 1-15, 2012. [4]. P. Cawley and R. D. Adams, The location of defects in structures from measurements of natural frequencies, Journal of Strain Analytical Engineering, vol. 14, pp. 4957, 1979. [5]. O. S. Salawu, Detection of structural damage through changes in frequency: A Review, Engineering Structures, vol. 19, pp.718-723, 1997. [6]. W. M. Ostachowics and M. Krawczuk, Analysis of the effect of cracks on the natural frequencies of a cantilever beams. Journal of Sound Vibrations, vol. 150, pp. 191-201, 1991. [7]. Jun Deng, M. Curveus and M. K. Lee, Behaviour under Static Loading of Metallic Beams Reinforced with a Bonded CFRP Plate. Composite Structures, vol. 78, pp. 232242, 2007 [8]. Shravan H.Gawande, Rudesh R. More. Effect of Notch Depth& Location on Modal Natural Frequency of Cantilever Beam, Article: Sep 2016.

[9]. Ahmed N. Ouyed. Free Vibration Analysis of Notched Composite Laminated Cantilever Beams, Journal of Engineering, vol. 17, Dec 2011. [10].A. L . Gawali, and Sanjay C Kumawat. Vibration Analysis of Beams, Journal of Civil Engineering, vol. 1, pp. 15-29, 2011.