Continuum Mechanics Research Group
The department has an active and thriving group of applied mathematicians that considers various aspects of acoustic, elastic, electro-magnetic, and water wave propagation phenomena. Dynamic responses are analysed for both continua and solid structures, in particular for thin elastic shells characterised by the presence of natural small geometric parameter. Many of these investigations are motivated by important practical problems and require advanced mathematical techniques, such as, the Wiener-Hopf technique, transform methods, asymptotic methods, and perturbation techniques. This also involves numerical methods and symbolic computation.
Specific applications in acoustics and electromagnetism include noise-reduction by novel duct design and the use of absorbent linings, the optimum placing of mobile phone masts. In water waves we consider violent free-surface deformations due to water entry/exit and wave impact on marine structures. Thin shell theory, in addition to the applications in mechanical, aerospace, naval and civil engineering, has more recently been found to be useful for the design and non-destructive testing of nanostructures, thin coatings and interfaces, micromechanical electronic systems, and biomedicine.
Current projects of the group include
- Matrix Wiener-Hopf technique
- The dielectric wedge problem
- Comparison methods for absorbing structures
- Acoustic flow structure interaction
- Wave propagation in ducts
- Asymptotic analysis of boundary and initial conditions for thin structures
- Localised waves and vibrations in linear elasticity
- Classification of quasi-fronts in anisotropic media with weak dispersion.
