Engineers typically design mechanical systems to perform through operating ranges, according to mathematical rules that are clearly established from the relatively narrow range of conditions it is possible to test in the laboratory or - in the case of aircraft - on the ground.
But while such linear design concepts have formed the basis for the aircraft and components underpinning today's aerospace industry, to make great leaps forward in such areas as aerodynamic efficiency and noise will require engineers to tackle the apparently chaotic non-linear design challenges that characterise much real-world performance.
To bridge the gap to that non-linear world, a team of University of Bristol and allied researchers is setting out to develop the a new set of mathematical tools for engineers, armed with a £4.2 million ($6.7 million), five-year grant from the UK government's Engineering and Physical Sciences Research Council.
The project leader and Bristol's professor of structural dynamics Dr David Wagg says non-linearity creeps in to a wide range of systems, ranging from compressor blades or the interaction between rotor blades and vibration in a helicopter's fuselage, to wind or wave power generation equipment and long bridges.
The Millennium footbridge over the Thames in London was one relatively recent example of a system which turned out to be so sensitive to vibration as to defy linear analysis - and thus requiring extensive re-engineering after construction to achieve stability. At a much smaller scale, even some medical devices are susceptible to non-linear performance variations - cochlear ear implants, for example are very sensitive to small vibrations.
Directly relevant to aerospace, modelling the dynamics of rotating components, Wagg says, "is still a big challenge".
The common factor linking all of these challenges, says Wagg, is that they operate in a dynamic environment. But while engineers have many mathematical tools for modelling linear systems, non-linear performance remains so difficult to model that the state-of-the-art design technique is, essentially, to avoid non-linearity.
To put it another way, says Wagg: "The complexity of modern designs has outstripped our ability to fully understand their dynamic behaviour." And that, he says, is no longer good enough if we hope to achieve some of the performance targets being set for next-generation aircraft.
So, to make it easier to introduce radical designs into aircraft Wagg - working with colleagues at Cambridge, Sheffield, Southampton and Swansea universities, and industrial partners including Airbus and AgustaWestland - want to develop better tools for engineers to model complex systems, and even exploit non-linear effects.
Without better models, says Wagg, some seemingly simple engineering problems are becoming difficult to resolve. How, for example, can an engineer know where or whether weight can be stripped from a component or a new material be introduced if the dynamic behaviour of the system cannot be accurately forecast?
To design a wind turbine structure that is safe, reliable and efficient, for example, is an increasingly urgent but far from simple task.
Wagg believes that in six months to two years the team may be able to realise some useful improvements in models already in use by their industrial partners. However, to develop the sort of non-linear system modelling tools the project is aiming for will take the full five years.
A commercially-valuable result, though, could be a five- to 10-year project.