Topological Imaging of Tubular Structures using Ultrasonic guided waves

Tubular structures are widely used in a variety of industries such as Aerospace, Oil and Gas, Nuclear, etc. Non Destructive Evaluation (NDE) of these structures plays a crucial role during it’s life cycle. In order to test large structures with limited accessibility, guided wave testing was developed as a viable solution. Due to the nature of these waves, they are able to propagate over large distances without losing much of their energy. However, they are also complex in that their velocity is frequency dependent i.e. they are dispersive. Conventionally, guided wave testing require costly finite element simulations. This thesis offers an alternative to such simulations with a quick and robust method to simulate guided wave propagation in tubular structures.Based on these calculations, the aim of this work is to obtain the 3d topological image of multilayered isotropic tubular structures using ultrasonic guided waves to locate defects. A mathematical model has been proposed where the wave equation is converted to an ordinary differential equation with respect to radius 'r' using the Fourier and Laplace transforms for the spatial and temporal variables respectively. The partial wave solution, expressed as a combination of Bessel’s functions, allows for the creation of a fast robust semi-analytical algorithm to compute the Green function in tubular structures. A model to approximate numerical defects is then developed. The defect response is considered as the cumulative response of secondary sources, aiming to negate the incident and diffracted stress field present within it. Next, the numerical model is validated with experimental measurements.Finally, the technique of Topological Imaging is introduced. This method of imaging is based on the idea of performing a correlation between two wave fields for defect localization. The versatility and flexibility of the numerical tool in conjunction with the method of imaging is then successfully demonstrated by localising and imaging a multitude of numerical and experimental defects with dimensions as low as 1=40th of the wavelength.