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

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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;

  1. 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].

  2. EXPERIMENTAL INVESTIGATIONS

    1. 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

    2. 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

    3. 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

    4. 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

    5. 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

  3. 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.

  4. 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

  5. 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.

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