A fractional Fourier transform analysis of the scattering of ultrasonic waves

Proceedings. Mathematical, Physical, and Engineering Sciences
Katherine M M TantAnthony Gachagan

Abstract

Many safety critical structures, such as those found in nuclear plants, oil pipelines and in the aerospace industry, rely on key components that are constructed from heterogeneous materials. Ultrasonic non-destructive testing (NDT) uses high-frequency mechanical waves to inspect these parts, ensuring they operate reliably without compromising their integrity. It is possible to employ mathematical models to develop a deeper understanding of the acquired ultrasonic data and enhance defect imaging algorithms. In this paper, a model for the scattering of ultrasonic waves by a crack is derived in the time-frequency domain. The fractional Fourier transform (FrFT) is applied to an inhomogeneous wave equation where the forcing function is prescribed as a linear chirp, modulated by a Gaussian envelope. The homogeneous solution is found via the Born approximation which encapsulates information regarding the flaw geometry. The inhomogeneous solution is obtained via the inverse Fourier transform of a Gaussian-windowed linear chirp excitation. It is observed that, although the scattering profile of the flaw does not change, it is amplified. Thus, the theory demonstrates the enhanced signal-to-noise ratio permitted by the use of coded excita...Continue Reading

References

Feb 1, 1988·The Journal of the Acoustical Society of America·W W AuD A Pawloski
Apr 2, 2005·IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control·Richard Y Chiao, Xiaohui Hao
Jan 1, 1992·IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control·M O'Donnell
Jul 9, 2014·IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control· Jie ZhangP D Wilcox

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Citations

Jun 9, 2016·Proceedings. Mathematical, Physical, and Engineering Sciences·Laura J CunninghamColin Bird

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