Rodriguez C (2020)
Publication Type: Journal article
Publication year: 2020
DOI: 10.3934/mcrf.2021002
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 [2] 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.
APA:
Rodriguez, C. (2020). NETWORKS OF GEOMETRICALLY EXACT BEAMS: WELL-POSEDNESS AND STABILIZATION. Mathematical Control and Related Fields. https://doi.org/10.3934/mcrf.2021002
MLA:
Rodriguez, Charlotte. "NETWORKS OF GEOMETRICALLY EXACT BEAMS: WELL-POSEDNESS AND STABILIZATION." Mathematical Control and Related Fields (2020).
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