 Open Access
 Total Downloads : 0
 Authors : Y Seetha Rama Rao , A Durga Hari Prasad
 Paper ID : IJERTV7IS090057
 Volume & Issue : Volume 07, Issue 09 (September – 2018)
 Published (First Online): 05012019
 ISSN (Online) : 22780181
 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 fibrereinforced composites have been extensively used for many applications because of their high strengthtoweight and stiffnesstoweight 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 [34]. The analysis demonstrated that the length of damage appears to have less influence as compared to width [56]. 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 [78]; 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 nondimensional 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 crosssection. By using curved notches in place of rectangle notches to avoid sharp corners so that better performance of beams can be achieved.
REFERENCES
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