Scattering of elastic and acoustic waves for applications in industry

超声波无损检测（NDE）将声波发送到材料（如钢）中，以检测内部裂纹或缺陷，而不会损坏结构。它在能源、电力和航空航天工程领域是一种非常有价值的工具，因为它能够检测安全关键系统，同时节省时间和金钱。工业无损检测设计的一个关键组成部分是数学建模，它提供了对预期信号的特征和如何物理解释它们的洞察力。该项目的一部分将考虑分支缺陷的弹性剪切波散射，使用分析解决方案（反问题，渐近分析，随机方法），数值模拟和机器学习的组合来开发数学模型。这项工作将是跨学科的，包括与机械工程师和物理学家合作进行实验验证和工业样品，以告知建模。该研究符合EPSRC的几个关键主题：未来的数学科学，能源，工程和制造。这也是一项非常及时的研究，因为它在核能领域具有巨大的潜力，这是英国正在寻求取代传统化石燃料动力方法的可持续Trinity位一体现代选择的一部分。这项工作的另一个方面将集中在设计数学模型，以减少物体周围的振动，如敏感机械，对工业有潜在的影响。该技术将使用波场扩展和主动隐身源和设备来抵消不需要的主导波传播。更准确地说，有源源具有复振幅，选择复振幅以抵消对远场中的散射波的主要贡献。这些源由绿色函数表示，它们描述了对点力的响应。近似的隐形导致小的线性代数方程组的分析系统，用于计算有效隐形所需的源的振幅。有源器件是考虑多极源的更复杂的数学理想化。我们注意到，在这两种情况下，声波和弹性导波都将被考虑。

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.