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- W3086576413 abstract "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 $H^1$ and $H^2$ 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." @default.
- W3086576413 created "2020-09-21" @default.
- W3086576413 creator A5041678387 @default.
- W3086576413 date "2020-09-17" @default.
- W3086576413 modified "2023-09-25" @default.
- W3086576413 title "Networks of geometrically exact beams: well-posedness and stabilization" @default.
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