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Modelling high-frequency vibrations of complex built-up structures using transport theory

  • School: School of Science and Technology
  • Study mode(s): Full-time / Part-time
  • Starting: 2023
  • Funding: UK student / EU student (non-UK) / International student (non-EU) / Fully-funded


NTU's Fully-funded PhD Studentship Scheme 2023

Project ID: S&T26

This project will develop a new high-frequency vibroacoustic simulation tool inspired by mathematical modelling techniques that have been developed in the context of optical tomography and climate science. Working in collaboration with industrial partner, Far UK, you will develop a new approach for simulating high-frequency vibrations in complex built-up structures, such as cars, trains or aircraft. Predicting the vibrational energy throughout these structures is important for minimising noise pollution, structural fatigue, and for passenger comfort.

Developing simulation tools capable of modelling complex three-dimensional structures is highly challenging. For low frequencies, manufacturers typically perform vibroacoustic simulations using commercial software based on numerical solutions of the corresponding equations of motion. The finite element method is widely used here and typically provides reliable estimates of the lower natural frequencies. For higher frequencies, finite element simulations require larger computational models to retain their accuracy, which can easily tip the balance and make the simulations unviable. In addition, uncertainties introduced during manufacturing mean that apparently identical structures from the same production line may have very different vibroacoustic responses at high frequencies. Consequently, finite elements are often abandoned for a highly efficient statistical approach called Statistical Energy Analysis. However, Statistical Energy Analysis is only a coarse tool based on a very limiting set of simplifying assumptions.

The development of improved high-frequency vibroacoustic simulation methods has been an active area of research during the last twenty years. One approach that has been pioneered in Nottingham is Dynamical Energy Analysis, which improves on Statistical Energy Analysis by incorporating wave directionality and local spatial variability of the vibration levels, but with greater computational overheads. Our new high-frequency vibroacoustic simulation tool will contain all the functionality of Dynamical Energy Analysis, but at reduced computational costs. The method will include Statistical Energy Analysis as a coarse mesh implementation, allowing for improvement of the spatial resolution through using finite volume meshes and capturing directionality through Monte-Carlo simulations. One advantage of this approach is to minimise the effect of dimensionality, making complex 3D vectorial elasticity models tractable for the first time!

The project would suit a highly motivated candidate with a passion for using mathematical modelling to help design more products based on lightweight and multi-material structures, such as those designed by our award-winning project collaborator Far UK Ltd. A good background in partial differential equations and a willingness to develop your skills in scientific computing would also be beneficial.

Supervisory Team: 

DoS: Dr David Chappell 


Dr Mark Wilkinson (early career) 

Dr Golnaz Shahtamassebi

Industrial advisor (informal): Thomas Dutton (Far UK)

Entry qualifications

For the eligibility criteria, visit our studentship application page.

How to apply

To make an application, please visit our studentship application page.

Fees and funding

This is part of NTU's 2023 fully-funded PhD Studentship Scheme.

Guidance and support

Application guidance can be found on our studentship application page.

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