 Open Access
 Total Downloads : 2043
 Authors : Yogesh D. Shinde, Prof. S. D. Katekar
 Paper ID : IJERTV3IS051696
 Volume & Issue : Volume 03, Issue 05 (May 2014)
 Published (First Online): 31052014
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Vibration Analysis of Cantilever beam with Single Crack using Experimental Method
Yogesh D. Shinde
Department of ME, Mechanical Engineering Dept., SKN Sinhgad College of Engg College, Pandharpur,413304,India
Prof. S. D. Katekar
Department of ME, Mechanical Engineering Dept., SKN Sinhgad College of Engg College, Pandharpur,413304,India
Abstract In the present study, vibration analysis of a cantilever beam with single open transverse crack for different crack depth and different crack locations is done using experimental method. For this analysis two cases are considered, first is without load and second case is with transverse load. For transverse load condition a spherical object is taken and dropped on free end of cantilever beam from certain height. This analysis is done to study the response characteristics (i.e. frequency and amplitude) of cracked cantilever beam and to find effect of crack on these response characteristics. From the modal test data, it is found that, as crack depth increases natural frequency decreases and as crack position shifted towards fixed end natural frequency decreases.
Keywordscantilever beam, crack, crack depth, crack location, natural frequency.

INTRODUCTION
Structural health monitoring and analysis of structures like cantilever beam with cracks is of great importance from safety as well as system performance point of view. When a structure suffers from damages like cracks, its dynamic properties can change. Crack damage leads to reduction in stiffness also with an inherent reduction in natural frequency [3]. Kaushar H. Barad et. al. [1] presented a method for detection of crack in cantilever beam which is based on frequency measurement. Experimental method and finite element method is used to analyze modal parameters of the cracked cantilever beam by D.K. Agarwalla and D.R. Parhi [2].Irshad A Khan and Dayal R Parhi [3] studied the vibration characteristics of cantilever beam with two cracks. Two types of beams are considered for study i.e. cantilevers beam and fixedfixed beam. Dong Wei et. al. [4] proposed analytical method for solving the free vibration of cracked functionally graded material (FGM) beams with axial loading, rotary inertia and shear deformation.
Celalettin Karaagac et. al. [7] studied the effects of crack ratios and positions on the fundamental frequencies and buckling loads of slender cantilever Euler beams with a single edge crack are investigated both experimentally and numerically using the finite element method, based on energy approach. SadettinOrhan [12] analyzed cracked cantilever beam under free and forced condition numerically by FEM. Samer Masoud AlSaid [13] proposed a simple algorithm based on a mathematical model to identify crack location and depth in a stepped cantilever EulerBernoulli beam carrying a
rigid disk at its tip. The proposed identification algorithm utilizes the first three natural frequencies shift of the beam caused by a crack to estimate its location and depth. To identify the crack, contours of the normalized frequency in terms of the normalized crack depth and location are plotted. The intersection of contours with the constant modal natural frequency planes is used to relate the crack location and depth.
G.M. Owolabi et. al. [14] investigated the effect of crack on vibration characteristics by experimental method. For damage detection, change in first three natural frequencies and corresponding amplitudes is measured. S. P. Lele et. al. [15] proposed a method of detection of location of crack in beams based on frequency measurements. This method is based on measurement of change in first natural frequency.

EXPERIMENTAL SETUP AND PROCEDURE

Experimental Setup Description
Mild steel beams were used for this experimental investigation. The set consisted of 13 beam models with the fixedfree ends. Each beam model was of crosssectional area 30mm X 20mm with a length of 500 mm from fixed end. It has the following properties:
TABLE I. GEOMETRIC AND MATERIAL PROPERTES
Material
Mild Steel
Length
500 mm
Width
20 mm
Height
30 mm
Modulus of elasticity
200 GPa
Density
7850 kg/m3
Poissons ratio
0.3
Fig.1 shows that, two heavy plates are used to clamp the one end of cantilever beam with the help of fasteners. Accelerometer is kept on beam at a distance of 50mm from fixed end for both the cases i.e. for no load condition and for loading condition. Accelerometer is connected to FFT analyzer for data acquisition. For no load condition Modal test is conducted. For vibration analysis under loading condition impact hammer is not required. To apply load, a spherical object is dropped from different heights. In this paper spherical object is dropped from 400mm height.

Experimental Procedure
The fixedfree beam model was clamped at one end, in a fixture supported over a stiff steel Isection beam. In modal test, the accelerometer is kept at 50mm distance from
Fig.1Block diagram of Experimental Setup
fixed end and impact is given by impact hammer at different points on beam to extract natural frequency values. By using modal test first three natural frequencies are extracted. Cracks were generated to the desired depth using a wire cut EDM (around 0.35mm thick); the crack always remained open during dynamic testing Total 12 beam models were tested with cracks at different locations starting from a location near to fixed end and 1 beam model was tested without crack. The crack depth varied from 4mm to 12mm at each crack position. Each model was excited by an impact hammer. This served as the input to the system. It is to be noted that the model was excited at a point, which was a few millimeters away from the center of the model. This was done to avoid exciting the beam at a nodal point (of a mode), since the beam would not respond for that mode at that point. The dynamic responses of the beam model were measured by using light accelerometer placed on the model as indicated in Fig. 1. The response measurements were acquired, one at a time, using the FFT analyzer.
For vibration analysis under loading condition, spherical object is dropped at a distance of 50mm from free end, from height of 400mm for all the cases i.e. 12 beams with crack and 1 beam without crack. Data acquisition is done using accelerometer and FFT analyzer.


RESULT AND DISCUSSIONS

For no load condition ( Modal test)
Results obtained from Modal test using FFT analyzer are given in following Table II. Results consist of first three natural frequencies for different beam specimens which are made of different crack depth and different crack locations. From following Table 1 it observed that, crack causes decrease in natural frequency of cantilever beam. The decreasing trend of natural frequency is not found for third natural frequency for all cases. Results obtained from modal test can be use to find the effect of crack depth and crack location on natural frequency.
TABLE II. RESULTS OF MODAL TEST
Crack Location from Fixed
End (mm)
Crack depth (mm)
Natural frequency (Hz)
1st
2nd
3rd
Uncrac
Nill
66.827
96.718
416.35
100
4
66.868
99.45
417.79
8
66.386
97.019
417.63
12
65.642
92.646
417.4
200
4
66.979
100.05
416.97
8
66.789
99.067
415.22
12
66.496
97.19
412.54
300
4
67.048
100.3
416.98
8
67.009
100.09
414.58
12
66.941
99.593
410.78
400
4
67.075
100.42
417.71
8
67.091
100.42
417.23
12
67.102
100.41
416.3
Following Fig. 2, Fig.3, Fig. 4 and Fig.5 shows the variation of second natural frequency with crack depth, for crack location at 100mm, 200mm, 300mm and 400mm distance from fixed end respectively.
Fig. 2 Crack depth Vs. first Natural frequency for crack at
100mm distance
Fig. 3 Crack depth Vs. first Natural frequency for crack at
200mm distance
Fig. 4 Crack depth Vs. first Natural frequency for crack at
300mm distance
Fig. 5 Crack depth Vs. first Natural frequency for crack at 400mm distance
From above Fig. 2, Fig. 3 and Fig. 4, it is observed that, as crack depth increases natural frequency decreases but from Fig. 5 it is observed that, natural frequency increases as crack depth increases.
Following Fig 6, Fig.7 and Fig. 8 shows the variation of second natural frequency with crack location for crack depth 4mm, 8mm and 12mm respectively.
Fig.6 Natural frequency Vs. Crack location for 4mm crack depth
Fig.7 Natural frequency Vs. Crack location for 8mm crack depth
Fig.8 Natural frequency Vs. Crack location for 12mm crack depth
From above Fig. 6, Fig. 7 and Fig. 8, it is observed that, as crack location moves away from fixed end, natural frequency increases gradually.

For loading codition
For the analysis of cracked cantilever beam under loading condition, Root Mean Square (RMS) values, Crest factor and Peak values of acceleration are calculated from the time domain data obtained from FFT analyzer.
Formulae used for calculation of Peak values, Root Mean Square (RMS) values and Crest factor are given in following equations,
(1)
(2)
(3)
Where,
max(x(t)) = maximum acceleration min(x(t)) = minimum acceleration
N = total number of data
x(i) = instantaneous acceleration = average acceleration
Following Table III shows the values of Peak, Root mean square and crest factor calculated using equation (1), equation
(2) and equation (3) respectively.
TABLE III. RESULTS OF CRACKED BEAM UNDER LOADING
Crack location
(mm)
Crack depth
(mm)
Peak
RMS
Crest Factor
Healthy
Nill
516.653
339.120
1.52
4
663.555
339.489
1.95
100
8
781.085
339.882
2.30
12
769.376
340.051
2.26
4
525.955
310.663
1.69
200
8
526.250
323.561
1.44
12
526.834
339.139
1.55
4
515.002
339.007
1.51
300
8
676.975
339.416
1.99
12
826.387
339.583
2.43
4
866.112
347.394
2.49
400
8
707.763
340.218
2.08
12
658.608
339.777
1.93
Following Fig. 9, Fig. 10, Fig 11 and Fig. 12 shows the variation of Root Mean Square (RMS) of acceleration with crack depth for crack located at 100mm, 200mm, 300mm and 400mm distance from fixed end respectively.
Fig. 9 RMS Vs Crack depth for crack at 100 mm distance
Fig.10 RMS Vs Crack depth for crack at 200 mm distance
Fig.11 RMS Vs Crack depth for crack at 300 mm distance
Fig.12 RMS Vs Crack depth for crack at 400 mm distance
From above Fig. 9, Fig. 10, Fig. 11, it is observed that, as crack depth increases Root Mean Square of acceleration increases for crack located at 100mm, 200mm and 300mm distance respectively. But for crack located at 400mm distance from fixed end, as crack depth increases Root Mean Square of acceleration decreases up to approximate crack depth of 9mm and beyond that crack depth it increases slightly, as shown in Fig.12.


CONCLUSIONS
Detailed experimental investigations of the effects of cracks on the first three modes of vibrating cantilever beams have been presented in this paper. The vibration behavior of the beams is shown to be very sensitive to the crack location, crack depth.
From experimental measures of cracked cantilever under no load, it is found that, as crack depth increases natural frequency decreases. Also, when crack location moves away from fix end the natural frequency increases.
From experimental measures of cracked cantilever under load of spherical object (which is dropped from a 400 mm height), it is found that, as crack depth increases the Root Mean Square of acceleration also increases for crack locations of 100mm, 200mm and 300mm. But for crack location of
400mm, as crack depth increases the Root Mean Square of acceleration decreases.
ACKNOWLEDGMENT
The authors would like to acknowledge the Excel Engineers Ltd. Sangali (India) for providing the test samples of Cantilever beam required for the experimentation. The gratitude is also extended to SKN Sinhgad College of Engineering, Pandharpur for providing facilities during experimentation.
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