论文标题
几何精确的光束网络：适合和稳定
Networks of geometrically exact beams: well-posedness and stabilization
论文作者
论文摘要
在这项工作中，我们对在几何精确（GEB）的自由振动梁的树状网络感兴趣 - 从某种意义上说，除了剪切外，还考虑了大型运动（偏转，旋转） - 并通过刚性接头链接。对于固有的GEB公式，即，就速度和内部力量/力矩而言，我们得出了传输条件，并表明网络在经典意义上是在时间上良好的时间。在星形网络的外部节点上应用速度反馈控件，我们通过二次lyapunov功能显示，Bastin \＆Coron在\ cite {bc2016}中开发的理论表明，该网络的零稳态对于$ H^1 $和$ H^1 $ and $ H^2 $ norms非常稳定。在GEB网络的内在公式中要克服的主要障碍是，管理方程是半标准，包含二次非线性，而线性较低阶则不能忽略。
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.
