PhD Studentship: Analysis and Design of Nonlinear Dynamic Structures: Numerical and Experimental Methods

University of Bristol - Engineering Mathematics

The project:

With the constant drive for better performance and efficiency, mechanical structures such as aircraft, satellites and rotating machines are becoming increasingly nonlinear. Whether anticipated or discovered at the end of product design, the presence of nonlinearity often leads to untimely delays and additional development costs because nonlinear systems can exhibit a wide range of complicated dynamic behaviours that are difficult to predict and have no counterpart in linear systems (bifurcations, quasi-periodic oscillations, chaos). As such, there is a clear and urgent need for rigorous tools that fully encompass nonlinear effects, which existing methods cannot.

Further Particulars

Depending on the interest of the candidate, the PhD project can focus on different topics in this area, ranging from the development of numerical algorithms to the establishment of nonlinear testing techniques. For instance, the project could address:

  • The development of effective algorithms for the bifurcation analysis of large-scale systems as those met in industry. Algorithm performance will be demonstrated on real-life aerospace structures including a full-scale aircraft and a satellite. Developed tools will eventually be exploited to establish innovative bifurcation-based optimization and design methodologies for nonlinear structures. 
  • The further development of nonlinear model reduction techniques enabling the fast and accurate dynamic analysis of structures with distributed (geometric) nonlinearities. The reduction methods will be demonstrated on geometrically-nonlinear finite element models of academic (beams, shells) and real-life (aircraft wings) structures. Developed methods will then be extended to the case where sensitivity to physical parameters is needed.
  • The development of robust testing approaches for nonlinear systems based on feedback control techniques. In particular, the adaption of phase-locked loop techniques (extensively used in electronics) will be considered. Experimental demonstration will be performed on a series of benchmark structures available in our Dynamics Lab.

The successful candidate will be part of the University of Bristol’s Dynamics and Control research group and have the opportunity to collaborate with other researchers from the Faculty. The candidate will also benefit from the momentum created by other research activities in the group addressing the analysis and design of nonlinear systems, such as the Engineering Nonlinearity and Agile Wing Integration projects.

URL for further information (if applicable):

How to apply:

Please make an online application for this project at Please select < Engineering Mathematics> on the Programme Choice page and enter details of the studentship when prompted in the Funding and Research Details sections of the form with the name of the supervisor

Candidate requirements: 

We are looking for an enthusiastic student with either a first or high 2:1 honours degree in Engineering or a recognised taught Masters’ degree.


Scholarship covers full UK/EU (EU applicants who have been resident in the UK for 3 years prior to application) PhD tuition fees and a tax-free stipend at the current RCUK rate (£14,553 in 2017/18).  EU nationals resident in the EU may also apply but will only qualify for PhD tuition fees.


Please contact Dr Ludovic Renson, with your up-to-date CV for informal enquiries.

For general enquiries, please email

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South West England