Scattering of elastic and acoustic waves for applications in industry

Ultrasonic non-destructive evaluation (NDE) sends sound waves into a material (such as steel) to detect internal cracks or flaws, without damaging the structure. It is a highly valuable tool in the energy, power and aerospace engineering sectors since it is capable of inspecting safety-critical systems whilst saving both time and money. A key component of the design of industrial NDE inspections is mathematical modelling that provides insight for both the characteristic features of expected signals and how to interpret them physically.

One part of this project will consider the scattering of elastic shear waves by branched defects using a combination of analytical solutions (inverse problems, asymptotic analysis, stochastic methods), numerical simulation and machine learning to develop mathematical models. The work will be interdisciplinary including collaboration with mechanical engineers and physicists for experimental validations and industrial samples to inform the modelling. The research is in line with several key EPSRC themes: Mathematical Sciences, Energy, Engineering and Manufacturing for the Future. It is also a very timely piece of research since it has great potential for high impact in the nuclear energy sector which is part of the sustainable trinity of modern options that the UK is looking to replace traditional fossil fuel-powered methods with.

Another aspect of the work will focus on designing mathematical models to reduce vibrations around objects, such as sensitive machinery, with potential impact in industry. The techniques will use wave field expansions and active cloaking sources and devices to cancel out unwanted dominant wave propagation. More precisely, active sources have complex amplitudes that are chosen to cancel the main contribution to the scattered wave in the far field. These sources are represented by Green's functions and they describe the response to a point force. The approximate cloak leads to small analytical systems of linear algebraic equations for calculating the amplitudes of the sources, required for effective cloaking. Active devices are more complicated mathematical idealisations that take into account multipolar sources. We note that in either context both acoustic and elastic guided waves will be considered.