Engineering Nonlinearity

本提案的目的是通过缓解当前将设计限制在线性动态状态的实践所造成的瓶颈，来改变结构系统的设计和制造。我们的目标不仅是解决处理非线性的挑战，而且要释放利用其积极属性可以获得的巨大潜力。产出将是一套新颖的建模和控制技术，可以直接用于结构系统的设计过程，我们将在一系列基于工业的实验演示中进行演示。这些设计工具将使工程结构系统的性能在技术、经济和环境压力下迅速增长的需求下发生转变。工程结构和系统的性能取决于它们在操作环境中的表现。对于许多工程部门，如风力发电、汽车、医疗机器人、航空航天和大型民用基础设施，动态效应主导着运行机制。因此，了解结构动力学对于确保我们拥有安全、可靠和高效的结构至关重要。事实上，相关的数学问题延伸到系统生物学、生理建模和信息技术等其他重要研究领域中遇到的其他建模问题。那么，我们在这项提案中寻求解决的问题究竟是什么？通常，当一个工程系统的行为是线性的，计算机模拟可以用来对其动态行为做出非常准确的预测。端到端仿真和虚拟原型、验证和测试的概念已经成为许多领域的关键范例。这种基于模拟的方法的问题在于，它是建立在可重复性和线性的隐含假设之上的。例如，许多结构分析方法是基于频域表征的概念，它假设系统的响应可以通过对每个频率的响应的线性叠加来表征。但是，已知非线性系统的响应显示振幅依赖性，对强迫中的瞬态效应的敏感性，以及相同输入频率的潜在双稳性或多重性结果。因此，当系统是非线性的（对于大量重要的工业问题几乎总是如此），如果不引入非常有限的近似和简化，几乎不可能进行动态预测。例如，在最近的历史中，有许多不必要的振动的例子；塔科马海峡大桥的失败（1940年）；洞庭湖大桥索-桥面耦合振动（1999）；千年大桥的人为振动（2000）；NASA太阳神号失败（2003年）；国际空间站柔性结构推进器与固有频率耦合研究（2009）起落架摇摆。在许多情况下，现代设计的复杂性已经超出了我们详细了解其动态行为的能力。即使有高功率计算的好处，这使得工程师能够进行详细的模拟，从这些模拟中解释结果是一个基本的瓶颈，而且我们匹配实验结果的能力似乎没有提高，主要是由于随机和不确定效应的结合以及线性叠加方法的失败。因此，迫切需要一种完全包含非线性的新型结构动力学，以实现下一代工程结构的最有效设计和制造。

The aim of this proposal is to transform the design and manufacture of structural systems by relieving the bottleneck caused by the current practice of restricting designs to a linear dynamic regime. Our ambition is to not only address the challenge of dealing with nonlinearity, but to unlock the huge potential which can be gained from exploiting its positive attributes. The outputs will be a suite of novel modelling and control techniques which can be used directly in the design processes for structural systems, which we will demonstrate on a series of industry based experimental demonstrators. These design tools will enable a transformation in the performance of engineering structural systems which are under rapidly increasing demands from technological, economic and environmental pressures. The performance of engineering structures and systems is governed by how well they behave in their operating environment. For a significant number of engineering sectors, such as wind power generation, automotive, medical robotics, aerospace and large civil infrastructure, dynamic effects dominate the operational regime. As a result, understanding structural dynamics is crucial for ensuring that we have safe, reliable and efficient structures. In fact, the related mathematical problems extend to other modelling problems encountered in other important research areas such as systems biology, physiological modelling and information technology.So what exactly is the problem we are seeking to address in this proposal? Typically, when the behaviour of an engineering system is linear, computer simulations can be used to make very accurate predictions of its dynamic behaviour. The concept of end-to-end simulation and virtual prototyping, verification and testing has become a key paradigm across many sectors. The problem with this simulation based approach is that it is built on implicit assumptions of repeatability and linearity. For example, many structural analysis methods are based on the concept of a frequency domain charaterisation, which assumes that response of the system can be characterised by linear superposition of the response to each frequency seperately. But, the response of nonlinear systems is known to display amplitude dependence, sensitivity to transient effects in the forcing, and potential bistability or multiplicity of outcome for the same input frequency. As a result, when the system is nonlinear (which is nearly always the case for a large number of important industrial problems) it is almost impossible to make dynamic predictions without introducing very limiting approximationsand simplifications. For example, throughout recent history, there have been many examples of unwanted vibrations; Failure of the Tacoma Narrows bridge (1940); cable-deck coupled vibrations on the DongTing Lake Bridge (1999); human induced vibration on the Millennium Bridge (2000); NASA Helios failure (2003); Coupling between thrusters and natural frequencies of the flexible structure on the International Space Station (2009); Landing gear shimmy.In many cases, the complexity of modern designs has outstripped our ability to understand their dynamic behaviour in detail. Even with the benefit of high power computing, which has enabled engineers to carry out detailed simulations, interpreting results from these simulations is a fundamental bottleneck, and it would seem that our ability to match experimental results is not improving, due primarily to the combination of random and uncertain effects and the failure of the linear superposition approach. As a result a new type of structural dynamics, which fully embraces nonlinearity, is urgently needed to enable the most efficient design and manufacture of the next generation of engineering structures.