WP 3: Analysis and Control of nD flexible systems.
Organization:
Funded by: | |
PhD: |  |
Supervisors: | Promotor & daily supervisor:  Daily Supervisor:  |
Collaboration: |
Description:
ModConFlex network:
The ModConFlex project is centered around the interaction between flexible structures and fluids, specifically air and water. The main applications are off-shore wind turbines, which are a powerful source of renewable energy, and highly flexible aircrafts, which have better rates of fuel consumption compared to most of the operating fleet today.
The network involves 6 universities and many industrial partners, with researchers being both mathematicians and engineers. More information can be found at https://modconflex.uni-wuppertal.de/en/
WP3 our project:
We are working on the well-posedness of linear homogeneous models of n-dimensional systems. We aim to generalize existing criteria for well-posedness of linear port-Hamiltonian systems, using the language of exterior calculus and differential forms. Such criteria exist for one-dimensional domains and consist of classifying the boundary conditions for which the Hamiltonian operator defining the system generates a contraction semigroup.
The prime object of study is the wave equation, in its formulation with the Hodge Laplacian, on a generic n-dimensional compact manifold. The advantages of studying such a problem using differential forms are multiple: coordinate independence, which has the added bonus of making any notion of curvature intrinsic, the ability to tackle the scalar and vectorial wave equations at the same time, and the global nature of the method, which accounts for the geometry of the manifold, in contrast with the classical approach of breaking down the object via charts.