Engineers have spent decades pretending that bridges, wind turbines, and aircraft vibrate in simple, predictable ways—but they don't, and that assumption is now a bottleneck on performance. The problem is that nearly all structural design tools rely on linear mathematics, which assumes that a structure's response to forces can be neatly added up frequency by frequency. In reality, most real-world systems—from landing gear to medical robots to the International Space Station—behave nonlinearly: their response changes with amplitude, can jump between multiple states, and depends on the history of the forces applied. This makes current computer simulations unreliable for predicting dangerous vibrations, as seen in the Tacoma Narrows bridge collapse and the Millennium Bridge wobble. This project aims to build a new suite of modelling and control techniques that embrace nonlinearity rather than sidestepping it. If successful, engineers could design lighter, more efficient wind turbine blades, quieter cars, safer surgical robots, and more resilient civil infrastructure—without resorting to the crude approximations that currently limit performance. The work is applied and industry-facing, with experimental demonstrators planned across multiple sectors.
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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 approximations and 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.
Alan Champneys (Co-Investigator)David Wagg (Principal Investigator)Jonathan Edward Cooper (Co-Investigator)Keith Worden (Co-Investigator)Michael Ian Friswell (Co-Investigator)Robin Langley (Co-Investigator)Simon Neild (Co-Investigator)Steve Elliott (Co-Investigator)
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