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Optimal Energy Transfer in Nonlinear Systems


   Faculty of Engineering and Physical Sciences

   Tuesday, November 01, 2022  Competition Funded PhD Project (UK Students Only)

About the Project

Supervisory Team:   Daniil Yurchenko and Tim Waters

This is a unique project to study how energy transfer can be optimally performed between subsystems of a nonlinear system. The project output will have significant impacts in the area of vibration mitigation, vibration isolation and vibration energy harvesting. 

Project description

Design and understanding of nonlinear models is required for optimal performance and for accurate reproduction of dynamical behavior. One of the intriguing phenomenon in nonlinear systems is Targeted Energy Transfer (TET), where the goal is to transfer energy within a nonlinear system between subsystems. The theory of linear dynamical systems is well-developed in the context tuned mass dampers, in contrast to nonlinear systems, where often individual nonlinear mechanisms are considered with a model-specific. A majority of these approaches rely on perturbation theory, which is valid, strictly speaking, for weak nonlinearities over finite time. TET is a nonlinear alternative that can also be generalized to multi-degree-of-freedom systems. In the traditional TET formulation, the nonlinearities are given for all degrees of freedom (for instance of cubic order), and the energy-transfer subsystem is tuned to an optimal set of parameters (coefficients) to mitigate undesirable dynamics of the primary system.

Based on the existing publications this leaves the following gaps in the TET’s state-of-the-art.

1.   The typical approximate methods used to analyse TET are not applicable to fully nonlinear effects and are infeasible for necessary multi-degree-of-freedom (MDOF) systems.

2.   A given nonlinearity in the system may not be optimal, and traditional methods do not scale to exploring the full range of potential nonlinear mechanisms.

3.   There is no established framework for fast identification of the optimal nonlinear system for efficient TET from purely experimental data.

To address these gaps the project will combine machine learning optimization algorithms, such as Surrogate Optimization (SO) and methods in nonlinear dynamics.

This project will require a student with:

Mechanical Engineering or Applied Mathematics degree;

Excellent programming skills in one of the Engineering languages (Matlab, Python, Julia, etc) to explore nonlinear dynamical systems and optimisation algorithms; Great mathematical skills; Excellent communication skills;

If you wish to discuss any details of the project informally, please contact Daniil Yurchenko, Dynamics Research Group, Email: , Tel: +44 (0) 2380 59406.

Entry Requirements

A very good undergraduate degree (at least a UK 2:1 honours degree, or its international equivalent).

Closing date: applications should be received no later than 1 November 2022 for standard admissions, but later applications may be considered depending on the funds remaining in place.

Funding: For UK students, Tuition Fees and a stipend of £16,062 tax-free per annum for up to 3.5 years.

How To Apply

Applications should be made online. Select programme type (Research), 2022/23, Faculty of Physical Sciences and Engineering, next page select “PhD Engineering & Environment (Full time)”. In Section 2 of the application form you should insert the name of the supervisor Daniil Yurchenko

Applications should include:

Research Proposal

Curriculum Vitae

Two reference letters

Degree Transcripts to date

Apply online: https://www.southampton.ac.uk/courses/how-to-apply/postgraduate-applications.page

For further information please contact:


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