School of Mathematical Sciences

Modelling the vibro-acoustic response of complex structures

Project description

The vibro-acoustic response of mechanical structures (cars, airplanes...) can in general be well approximated in terms of linear wave equations. Standard numerical solution methods comprise the finite or boundary element method (FEM, BEM) in the low frequency regime and so-called Statistical Energy Analysis (SEA) in the high-frequency limit. Major computational challenges are posed by so-called mid-frequency problems - that is, composite structures where the local wave length may vary by orders of magnitude across the components.

Recently, I propsed a set of new methods based on ideas from wave chaos (also known as quantum chaos) theory.  Starting from the phase space flow of the underlying - generally chaotic - ray dynamics, the new method called Dynamical Energy Analysis (DEA) interpolates between SEA and ray tracing containing both these methods as limiting cases. Within the new theory SEA is identified as a low resolution ray tracing algorithm and typical SEA assumptions can be quantified in terms of the properties of the ray dynamics. I have furthermore developed a hybrid SEA/FEM method based on random wave model assumptions for the short-wavelength components. This makes it possible to tackle mid-frequency problems under certain constraints on the geometry of the structure.

The PhD project wil deal with extending these techniques towards a DEA/FEM hybrid method as well as  considering FEM formulations of the method. The work will comprise a mix of analytic and numerical skills and will be conducted in close collaboration with our industrial partners CDH AG, Germany and Jaguar/Landrover, Gaydon, UK.

Supervisor contacts

 

Related research centre or theme

Wave Modelling

 
 

 

 

Project published references

Wave chaos in acoustics and elasticity, G. Tanner and N. Soendergaard, J. Phys. A 40, R443 - R509 (2007).

Dynamical Energy Analysis - determining wave energy distributions in complex vibro-acoustical structures, G. Tanner, Journal of Sound and Vibration 320, 1023 (2009).

More information

Full details of our Maths PhD

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School of Mathematical Sciences

The University of Nottingham
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Nottingham, NG7 2RD

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