3 years, earliest start date Sept 2022
• University of Nottingham, United Kingdom
• Naval Group, Ollioules, France
• Matelys Research Lab, Vaulx-en-Velin, France
Predicting the vibro-acoustic behavior of structures in contact with water is of primary interest for the
naval industry: the noise level on-board must satisfy regulations and should be kept low for comfort
of crew and passengers. The radiated noise into water must be controlled to reduce the impact on the
marine fauna. Prediction methods typically used in the industry such as the Finite Element Method
(FEM)  require a mesh to discretize the dynamical equations. To properly describe the physical
phenomena, this mesh needs to be refined as frequency increases, leading to prohibitive calculation
cost above several hundreds of Hertz for a full-scale surface ship. Over the last decades, novel methods
have been developed to propose an alternative at high frequencies. Among those methods, the
Dynamical Energy Analysis (DEA) has been successfully applied to various model and full-scale
industrial structures [2,3]. The method calculates the vibrational energy flow within structures and is
based on a reformulation of ray-tracing algorithms, where boundary operators describe the energy
transfer between elements of the structure. Compared to more classical high frequency methods such
as Statistical Energy Analysis (SEA), the DEA has a wider range of applications due to less limiting
Objectives of the PhD:
The DEA has so far only been applied to the description of energy propagation within structures in-
vacuo. In the naval industry, the coupling with surrounding water must be modeled: it has an important
impact on the response of the structure and there is interest in understanding and predicting the
radiated energy into the water.
The DEA is so far limited to mechanical excitation, meaning that energy is directly injected into the
structure. Internal machinery (engines for instance) produces noise that can be transmitted through air-borne propagation to the hull, and then tends to radiate noise into water. The energy flow from an
internal acoustic source needs thus to be modeled.
Finally, to reduce the underwater radiated noise (URN), decoupling materials can be introduced
between the structure and the fluid. These materials, classically made of viscoelastic with micro-voids
or cavities, have the ability to isolate the structure from the surrounding fluid or reduce the scattering
from incoming waves. The modeling of these materials in the high frequency range is still a
The main tasks of the PhD consist in extending the DEA formulation by:
• modeling the energy exchanges between the structure and the internal and external fluid;
• adding the possibility to excite the structure by an acoustic source, located in the internal or
• accounting for external coatings. The coatings can be applied on the hull (air on one side,
water on the other side) or on a light structure (water on both sides).
The developments will be implemented into an additional module of the existing DEA software.
Results will be validated through comparison to analytical, numerical and if possible experimental results.
• Holding a MsC in Acoustics, Mechanical Engineering, Physics or Applied Mathematics
• Experience in programming (preferably Python and C++)
• Working independently and as a member of the team
• Good command of the English language
How to apply:
Send a resume, a cover letter and MsC transcripts to:
• Prof Gregor Tanner, University of Nottingham, email@example.com
• Valentin Meyer, Naval Group Research, firstname.lastname@example.org
• Fabien Chevillotte, Matelys Research Lab, email@example.com
 N. Atalla, F. Sgard, Finite Element and Boundary Methods in Structural Acoustics and
Vibration, CRC Press, 2015.
 G. Tanner, Dynamical Energy Analysis –Determining wave energy distributions in vibro-
acoustical structures in the high frequency regime, Journal of Sound and Vibration,
 T. Hartmann, S. Morita, G. Tanner and D. J. Chappell, High-frequency structure- and air-
borne sound transmission for a tractor model using Dynamical Energy Analysis,
Wave Motion 87:132-150, 2019.
 T. Lafont, N. Totaro, A. Le Bot. Review of statistical energy analysis hypotheses in
vibroacoustics. Proceedings of the Royal Society A: Mathematical, Physical and Engineering
Sciences, 470(2162):20130515, 2014.
 L. Roux. Acoustic metamaterials for underwater acoustic applications: homogenisation
theory, design optimisation and experimental characterisation. PhD thesis, Institut
d’Electronique, de Microélectronique et de nanotechnologie, 2021.