1 research outputs found
Networks of geometrically exact beams: well-posedness and stabilization
In this work, we are interested in tree-shaped networks of freely vibrating
beams which are geometrically exact (GEB) -- in the sense that large motions
(deflections, rotations) are accounted for in addition to shearing -- and
linked by rigid joints. For the intrinsic GEB formulation, namely that in terms
of velocities and internal forces/moments, we derive transmission conditions
and show that the network is locally in time well-posed in the classical sense.
Applying velocity feedback controls at the external nodes of a star-shaped
network, we show by means of a quadratic Lyapunov functional and the theory
developed by Bastin \& Coron in \cite{BC2016} that the zero steady state of
this network is exponentially stable for the and norms. The major
obstacles to overcome in the intrinsic formulation of the GEB network, are that
the governing equations are semilinar, containing a quadratic nonlinearity, and
that linear lower order terms cannot be neglected.Comment: 36 pages, 6 figures, preprin