With the constant drive for better performance and efficiency, technological boundaries are being pushed to their limits. In mechanics, this often means that the dynamic behaviour of structures becomes increasingly nonlinear – the response of the structure is no longer proportional to the input. Nonlinearity can arise from a number of different sources as, for instance, the complex constitutive laws of new materials (composites, coatings), the large displacements and rotations of flexible components (as blades in wind turbines), or even the joints and gaps between components. Nonlinear systems exhibit a wide range of complicated behaviour that have no counterpart in linear systems and are very difficult to predict (modal interactions, bifurcations, etc.)
The overarching goal of my research is to develop tools and methods that can directly address the presence of nonlinearity and that, eventually, will allow to exploit it for improving design performance. My research focuses on three interlinked areas: Nonlinear Testing, Theoretical and Experimental Nonlinear Modal Analysis, Numerical Methods for Nonlinear Dynamic Systems.
Without the need for a mathematical model, control-based continuation (CBC) is a way of applying the concepts behind numerical continuation to a physical system. CBC combines stabilizing feedback control and path-following techniques in order to directly isolate the nonlinear behaviours of interest during experimental tests and track their evolution as parameters are varied. This allows the detection of boundaries between qualitatively different types of behaviours in a robust and systematic way as the experiment is running. The great deal of useful information generated can then be exploited for developing, updating and validating mathematical models.
The objective of my research in this area is to make CBC more robust and general, such that it can be applied to experiments across the breadth of engineering and the applied sciences. Learn more about my work
Nonlinear Modal Analysis
Modal analysis is based on the concept of linear normal modes (LNMs) and is routinely practised by structural dynamicist in industry. Thanks to some remarkable mathematical properties, LNMs are extensively used for linear model reduction and numerical simulations. Another remarkable feature of LNMs is that they can be determined either from a mathematical model or identified/measured by testing the physical system. This property is largely exploited in the context of model updating and validation.
Nonlinear Normal Modes (NNMs) represent the analogue of linear normal modes and allow to extend the concept of modal analysis to nonlinear systems. The objective of my research in this area is to 1) develop numerical algorithms to compute NNMs (in particular for large-scale systems); 2) to understand the role played by NNMs in the dynamics of nonlinear systems and how they can be exploited for design; and 3) to establish rigorous techniques to identify NNMs experimentally. Learn more about my work
Numerical Methods for Nonlinear Dynamic Systems
A number of methods to analyse the dynamics of nonlinear systems have been proposed in the scientific literature as, for instance, the popular numerical continuation techniques. Although these methods are rigorous mathematically and a priori broadly applicable, their application to high-dimensional systems such as those met in real-life engineering applications remains a challenge due to the (excessive) computational cost usually required.
My research in this domain aims to develop effective numerical algorithms and nonlinear model reduction techniques that can handle complex, real-life, nonlinear dynamic systems. Learn more about my work