论文标题
亚音速流中结构抑制面板的大偏转
Large Deflections of A Structurally Damped Panel in A Subsonic Flow
论文作者
论文摘要
考虑了亚音速流中面板的大偏转。具体而言，考虑了板丝中旋转的旋转惯性和平方根类型的结构阻尼的完全夹紧的von karman板。该面板被视为嵌入在$ \ Mathbb r^3 $中的正线性势流的边界中。尽管缺乏与线性动力学的发电机相关的自然耗散性，但通过半群方法构建了溶液。然后通过明确的neumann to-dirichlet（向下冲洗到压力）求解器来减少流动板动力学 - 用于流动的求解器 - 到板的内存类型动力学系统。对于非保守板动力学，通过Lyapunov和准稳定性方法明确构建了全局吸引子。最后，结果表明，通过吸引子的紧凑性和耗散积分的有限性，所有轨迹都会强烈收敛于一组固定状态。
The large deflections of panels in subsonic flow are considered. Specifically, a fully clamped von Karman plate accounting for both rotational inertia in plate filaments and structural damping of square root type is considered. The panel is taken to be embedded in the boundary of a linear, subsonic potential flow on the positive halfspace in $\mathbb R^3$. Solutions are constructed via a semigroup approach despite the lack of natural dissipativity associated to the generator of the linear dynamics. The flow-plate dynamics are then reduced---via an explicit Neumann-to-Dirichlet (downwash-to-pressure) solver for the flow---to a memory-type dynamical system for the plate. For the non-conservative plate dynamics, a global attractor is explicitly constructed via Lyapunov and quasi-stability methods. Finally, it is shown that via the compactness of the attractor and finiteness of the dissipation integral, that all trajectories converge strongly to the set of stationary states.
