Summary
The aim of this project is to validate the 1D theoretical directivity functions obtained analytically and numerically with experimental directivity function measured using direct contact and immersion techniques. Numerical theoretical directivity functions consist of the finite length, Gaussian and Sinc shape theoretical directivity functions.
1D linear phased array transducers were used to investigate directivity function. For direct contact, the experiment was conducted using aluminium as solid specimen and coupled with a coupling gel. Immersion wise, the experiment was conducted using water as coupling medium. The data was captured using Full Matrix Capture technique. The experiment was carried out with different specimen thicknesses (for direct contact) and distances between array and specimen (for immersion) using two types of array transducer; small and big element size.
The data was post-processed to compute the experimental and theoretical directivity functions. The experimental directivity was calculated in frequency and time domain using fast Fourier transform and Hilbert transform to provide a better comparison.
All the experiments in direct contact and immersion yielded a close agreement to either type of the theoretical directivity functions.
In general, immersion method is better as it provides a better coupling. Also, there is a stronger correlation (correlation coefficient value more than 0.9) between the experimental and theoretical directivity for immersion. For direct contact, the larger array follows the analytical theoretical directivity function. While for the smaller array, the experimental directivity yielded a closer agreement to the Sinc theoretical directivity function.
Table of Contents
1 | Introduction…………………………………………………………………………. | 7 |
2 | Experimental Method……………………………………………………………….. | 7 |
2.1 Phased Array Transducer……………………………………………………… | 7 | |
2.2 Full Matrix Capture…………………………………………………………… | 8 | |
2.3 Experimental Setup…………………………………………………………… | 8 | |
2.3.1 Direct Contact………………………………………………………… | 8 | |
2.3.2 Immersion…………………………………………………………….. | 9 | |
3 | Measurement of Experimental Directivity Function……………………………….. | 10 |
3.1 Calculation of Propagation Distance…………………………………………. | 10 | |
3.2 Wave Propagation Speed and Density………………………………………… | 11 | |
3.3 Calculation of Longitudinal and Shear Wave Angles………………………… | 11 | |
3.3.1 Direct Contact…………………………………………………………… | 12 | |
3.3.2 Immersion………………………………………………………………. | 12 | |
3.4 Calculation of Time of Arrival………………………………………………… | 12 | |
3.5 Removal of Unwanted Signals………………………………………………… | 12 | |
3.6 Calculation of Reflection Coefficients………………………………………… | 13 | |
3.7 Amplitude Extraction Method…………………………………………………. | 13 | |
3.7.1 Type 1: Frequency Domain Signal – Fast Fourier Transform………… | 13 | |
3.7.2 Type 2: Time Domain Signal – Hilbert Transform…………………….. | 13 | |
3.8 Calculation of Normalised Experimental Directivity Function………………. | 14 | |
4 | Calculation of Theoretical Directivity Function…………………………………… | 15 |
4.1 Analytical Theoretical Directivity Function…………………………………… | 15 | |
4.2 Numerical Theoretical Directivity Function………………………………….. | 16 | |
4.2.1 Finite Element Length………………………………………………… | 16 | |
4.2.2 Varying Signal Shape…………………………………………………. | 18 | |
5 | Results………………………………………………………………………………. | 21 |
5.1 Direct Contact…………………………………………………………………. | 21 | |
5.2 Immersion…………………………………………………………………….. | 23 | |
6 | Discussion…………………………………………………………………………… | 25 |
6.1 Direct Contact………………………………………………………………… | 26 | |
6.2 Immersion…………………………………………………………………….. | 28 | |
7 | Conclusion and Future Work……………………………………………………….. | 29 |
8 | References…………………………………………………………………………… | 30 |
List of Figures | |
Figure 1: Geometry of a phased 1D array transducer (Reproduced from [1])…….. | 8 |
Figure 2: Illustration of full matrix capture (Reproduced from [2])………………. | 8 |
Figure 3: (a) Direct contact experiment setup where the transducer and specimen were clamped (b) Immersion experiment setup with a spacer (circled in red) between the transducer and specimen………………………………………………………………….. | 9 |
Figure 4: Graph of amplitude vs time for all 64 pulse echo signals.……………… | 100 |
Figure 5: (a) Direct contact and (b) Immersion propagation distance of wave from one transmitter to another receiver …………………………………………………. | 10 |
Figure 6: Model illustrating the angles for (a) direct contact and (b) immersion calculated using Snell’s Law (5eproduced from [8])…………………………………… | 11 |
Figure 7: Amplitude vs time graph (a) before applying filter and (b) after applying filter….……………………………………………………..……………………. | 12 |
Figure 8: Graph showing envelope of signal over original signal after Hilbert transform …………..………….…………………………………………………………… | 14 |
Figure 9: Directivity function before averaging over similar longitudinal angle…. | 15 |
Figure 10: 1D array transducer sectioned into |
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