Engineering Nonlinearity

Lead Research Organisation: University of Bristol
Department Name: Mechanical Engineering


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.

Planned Impact

This highly ambitious, multi-disciplinary, and innovative programme is aimed at transforming the design and manufacture of structural systems. The goal is not only to improve performance and reduce cost, but to exploit new aspects of nonlinearity for positive effect. Relevant sectors include, energy, aerospace, offshore, renewables, and medical engineering, but will extend to conventional automotive and other ground transport and civil engineering. A range of stakeholders will benefit:

Companies with a high dependence on structural dynamic expertise for the design and manufacture of their products will gain access to new technology, either through directly licensing intellectual property developed during the programme, or through subsequent co-development projects. Technology transfer will be facilitated by specialist teams at the five partner institutions, coordinated by Research & Enterprise Development Department at Bristol, who have extensive experience in balancing the need to protect inventions while encouraging commercial exploitation. Industrial partners will thus gain new capabilities allowing them to develop new products, leading to a competitive advantage, and ultimately, UK wealth creation.

In addition, there are a variety of smaller, specialist manufacturing and consulting companies, for example, in civil/structural engineering and the automotive sectors, who also require structural dynamic expertise. These companies will benefit from new software products developed as a direct impact from this proposed programme. Faster, more efficient design tools and techniques will enable such companies to be more competitive in an era where economic and environmental pressures are rapidly increasing the demands on the performance of all civil, mechanical and aerospace systems.


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Agrawal DK (2013) Modeling nonlinearities in MEMS oscillators. in IEEE transactions on ultrasonics, ferroelectrics, and frequency control

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Arrieta A (2012) Dynamic control for morphing of bi-stable composites in Journal of Intelligent Material Systems and Structures

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Arrieta A (2012) Passive load alleviation bi-stable morphing concept in AIP Advances

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Becker W (2013) Bayesian sensitivity analysis of bifurcating nonlinear models in Mechanical Systems and Signal Processing

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Ben Abdessalem A (2018) Model selection and parameter estimation in structural dynamics using approximate Bayesian computation in Mechanical Systems and Signal Processing

Related Projects

Project Reference Relationship Related To Start End Award Value
EP/K003836/1 07/09/2012 06/09/2013 £4,214,087
EP/K003836/2 Transfer EP/K003836/1 06/12/2013 06/09/2017 £3,768,933
Description This grant was transferred between University of Bristol and University of Sheffield. The findings will be given in data for EP/K003836/2
Exploitation Route See data for EP/K003836/2
Sectors Aerospace, Defence and Marine

Title Research data supporting Validation of a constitutive law for friction-induced vibration under different wear conditions 
Description The experimental data, simulation results and associated Matlab files are all included in this dataset. They are organised according to the figure numbers in the paper. 
Type Of Material Database/Collection of data 
Year Produced 2017 
Provided To Others? Yes