Networks of geometrically exact beams: Well-posedness and stabilization

In this work, we are interested in tree-shaped networks of freely vibrating beams which geometrically exact (GEB) – the sense that large motions (deflections, rotations) accounted for addition to shearing and linked by rigid joints. For intrinsic GEB formulation, namely terms velocities internal forces/moments, derive transmission conditions show network is locally time well-posed classical sense. Applying velocity feedback controls at external nodes a star-shaped network, means quadratic Lyapunov functional theory developed Bastin & Coron [2] zero steady state exponentially stable \begin{document}$ H^1 $\end{document} id="M2">\begin{document}$ H^2 norms. The major obstacles overcome formulation governing equations semilinar, containing nonlinearity, linear lower order cannot be neglected.