Tugas Metodologi Penelitian Bedah Jurnal 1

 Tugas Metodologi Penelitian Bedah Jurnal 1

“Investigasi Eksperimental Deteksi Retak pada Balok Cantilever Menggunakan Frekuensi Alami sebagai Kriteria Dasar”

Nama : Iqbal Bayu Kurniawan

Kelas : 3IC05

NPM : 22417948

Experimental Investigation of Crack Detection in Cantilever Beam Using Natural Frequency as Basic Criterion

A.  A.V.Deokar, B.  V.D.Wakchaure A & B., Department of Mechanical Engineering, Amrutvahini College of Engineering, Sangamner.

Abstrak :

Retak mengubah perilaku dinamis struktur dan dengan memeriksa perubahan ini, ukuran dan posisi retak dapat diidentifikasi. Metode pengujian non destruktif (NDT) digunakan untuk mendeteksi retak yang sangat mahal dan memakan waktu. Saat ini penelitian telah difokuskan pada penggunaan parameter modal seperti frekuensi alami, bentuk mode dan redaman. untuk mendeteksi retakan pada balok. Dalam makalah ini disajikan metode untuk mendeteksi celah transversal terbuka pada balok Euler-Bernoulli yang ramping.

Eksperimental Modal Analysis (EMA) dilakukan pada balok yang retak dan balok yang sehat. Tiga frekuensi alami pertama dianggap sebagai kriteria dasar untuk deteksi keretakan. Untuk menemukan celah, grafik 3D frekuensi dinormalisasi dalam hal kedalaman retak dan lokasi diplot. Perpotongan ketiga kontur ini memberikan lokasi retakan dan kedalaman retakan. Dari beberapa studi kasus yang dilakukan, hasil dari salah satu studi kasus disajikan untuk menunjukkan penerapan dan efisiensi metode yang disarankan. Ketentuan Indeks— Retak, Euler – Bernoulli, bentuk mode, frekuensi alami.

 

Experimental Setup dan Prosedur :

Mild steel beams were used for this experimental investigation. The set consisted of 49 beam models with the fixed-free ends. Each beam model was of cross-sectional area 20mmX20mm with a length of 300 mm from fixed end. It had the following material properties: Young’s modulus, E= 2.06X10⁵MPa, density, ρ=7850Kg/m³, the Poisson ratio, µ=0.35.

Experimental Prosedur :

The fixed–free beam model was clamped at one end, between two thick rectangular steel plates, supported over a short and stiff steel I-section girder. The beam was excited with an impact hammer. The first three natural frequencies of the uncracked beam were measured. Then, 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 49 beam models were tested with cracks at different locations starting from a location near to fixed end. The crack depth varied from 1.5mm to 14mm 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.

Result Jurnal :

1.     Result

The FRFs obtained were curve-fitted using the B&K PULSE 14.1.1 software package. The experimental data from the curve-fitted results were tabulated, and plotted (in a

three dimensional plot) in the form of frequency ratio (ωc/ω) (ratio of the natural frequency of the cracked beam to that of the uncracked beam) versus the crack depth (a) for various crack location (X). Tables I–III show the variation of the frequency ratio as a function of the crack depth and crack location for beams with fixed-free ends.

2.     Changes in Natural Frequencies

Fig. 2 to 4 shows the plots of the first three frequency ratios as a function of crack depths for some of the crack positions. Fig.5 to Fig.7 shows the frequency ratio variation of three modes in terms of crack position for various crack depths respectively.

From Fig.2 it is observed that, for the cases considered, the fundamental natural frequency was least affected when the crack was located at 265mm from fixed end. The crack was mostly affected when the crack was located at 25mm from the fixed end. Hence for a cantilever beam, it could be inferred that the fundamental frequency decreases significantly as the crack location moves towards the fixed end of the beam. This could be explained by the fact that the decrease in frequencies is greatest for a crack located where the bending moment is greatest. It appears therefore that the change in frequencies is a function of crack location. From Fig.3 it is observed that the second natural frequency was mostly affected for a crack located at the center for all crack depths of a beam due to the fact that at that location the bending moment is having large value. The second natural frequency was least affected when the crack was located at 265mm from fixed end. From Fig.4 it is observed that the third natural frequency of beam changed rapidly for a crack located at 200 mm. The third natural frequency was almost unaffected for a crack located at the center of a cantilever beam; the reason for this zero influence was that the nodal point for the third mode was located at the center of beam.

From Fig.5 it is observed that, for the cases considered, the fundamental natural frequency was least affected when the crack depth was 4.5mm. The crack was mostly affected when the crack depth was 14mm. Hence for a cantilever beam, it could be inferred that the fundamental frequency decreases significantly as the crack depth increase to 70% of beam depth. This could be explained by the fact that the decrease in frequencies is greatest for a more crack depth because as more material gets removed the stiffness of the beam decrease and hence the natural frequency. It appears therefore that the change in frequencies is a function of crack depth also.

From Fig.6 it is observed that the second natural frequency was mostly affected for a crack depth of 14mm at the crack location 175mm. The second natural frequency was least affected when the crack depth was 2mm. From Fig.7 it is observed that the third natural frequency of beam changed rapidly for a crack depth of 14mm.Third natural frequency was remained unaffected when crack depth was 4.5mm. Third natural frequency was remained unchanged at crack locations 40mm, 200mm, and 265mm due to the presence of node point at that position.
Fig.8 to Fig.10 show the three dimensional plots of Normalized Frequency versus Crack Location and Crack Depth for first, second and third mode respectively for crack location of 100mm and crack depth of 7.5mm. To get these three dimensional plots program is written in MATLAB. In Fig.8 to Fig.10, the contour line are not present due to the presence of node points.

3) Crack Identification Technique Using Changes In Natural Frequencies

As stated earlier, both the crack location and the crack depth influence the changes in the natural frequencies of a cracked beam. Consequently, a particular frequency could correspond to different crack locations and crack depths. This can be observed from the three-dimensional plots of the first three natural frequencies of cantilever beams as shown in Fig.8 to Fig.10. On this basis, a contour line, which has the same normalized frequency change resulting from a combination of different crack depths and crack locations (for a particular mode) could be plotted in a curve with crack location and crack depth as its axes.

To identify the presence of crack in the beam, an essential step is to measure a sufficient number of natural frequencies of the beam, and then use the technique explained in this section to estimate the crack location, and depth. Measuring the first three natural frequencies will be sufficient to determine the crack location, and the crack depth for a beam with a single crack.

For a beam with a single crack with unknown parameters, the following steps are required to predict the crack location, and depth, namely, (1) measurements of the first three naturalfrequencies; (2) normalization of the measured frequencies; (3) plotting of contour lines from different modes on the same axes; and (4) location of the point(s) of intersection of the different contour lines. The point(s) of intersection, common to all the three modes, indicate(s) the crack location, and crack depth. This intersection will be unique due to the fact that any normalized crack frequency can be represented by a governing equation that is dependent on crack depth (a), crack location (X). Therefore a minimum of three curves is required to identify the two unknown parameters of crack location and crack depth.

From Tables I– III, it is observed that for a crack depth of 7.5mm located at a distance of 100mm from fixed end of the beam, the normalized frequencies are 0.9398 for the first mode, 0.9663 for the second mode and 0.9334 for the third mode. The contour lines with the values of 0.9398, 0.9663 and 0.9334 were retrieved from the first three modes with the help of MINITAB software as shown in Fig.11 to Fig.13 and plotted on the same axes as shown in Fig.14. From the Fig.14 it could be observed that there are two intersection points in the contour lines of the first and the second modes. Consequently the contour of the third mode is used to identify the crack location (X=100mm) and the crack depth (a=7.5mm), uniquely. The three contour lines gave just one common point of intersection, which indicates the crack location and the crack depth.

Since the frequencies depend on the crack depth and location, these values can be uniquely determined by the solution of a function having solutions one order higher (in this case, three) than the number of unknowns (in this case, two, namely crack depth and location) to be determined. This is the reason for the requirement of three modes. If there were more parameters that influence the response (besides the crack depth and location), then one will require more modes to identify the unknown crack depth and crack location.

CONCLUSIONS :

Detailed experimental investigations of the effects of crack on the first three modes of vibrating cantilever beams have been presented in this paper. From the results it is evident that the vibration behavior of the beams is very sensitive to the crack location, crack depth and mode number. A simple method for predicting the location and depth of the crack based on changes in the natural frequencies of the beam is also presented, and discussed. This procedure becomes feasible due to the fact that under robust test and measurement conditions, the measured parameters of frequencies are unique values, which will remain the same (within a tolerance level), wherever similar beams are tested and responses measured. The experimental identification of crack location and crack depth is very close to the actual crack size and location on the corresponding test specimen.

 

REFERENCES :

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[4] G.M. Owolabi, A.S.J. Swamidas, R. Seshadri, “Crack detection in beams using changes in frequencies and amplitudes of frequency response functions”, Journal of Sound and Vibration, vol. 265 (1), pp. 1–22, 2003. 

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