PhD proposal in Applied Mathematics, Mechanical Engineering (dynamics/acoustics)

Reference

SCI2089

Closing Date

Friday, 30th September 2022

Department

Mathematical Sciences

Modeling vibroacoustic energy distributions in submerged structures at high frequencies 

Duration: 

3 years, earliest start date Sept 2022 

Locations: 

• University of Nottingham, United Kingdom 
• Naval Group, Ollioules, France 
• Matelys Research Lab, Vaulx-en-Velin, France 

Context: 

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) [1] 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 assumptions [4]. 

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 challenge [5]. 

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 external fluid; 
• 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. 

Profile 

• 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, gregor.tanner@nottingham.ac.uk 
• Valentin Meyer, Naval Group Research, valentin.meyer@naval-group.com 
• Fabien Chevillotte, Matelys Research Lab, fabien.chevillotte@matelys.com 

References: 

[1] N. Atalla, F. Sgard, Finite Element and Boundary Methods in Structural Acoustics and Vibration, CRC Press, 2015. 

[2] G. Tanner, Dynamical Energy Analysis –Determining wave energy distributions in vibro-acoustical structures in the high frequency regime, Journal of Sound and Vibration, 320:1023–1038, 2009. 

[3] 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.