亚音速流场中固支von Karman板的颤振消除
Eliminating flutter for clamped von Karman plates immersed in subsonic flows
摘要：
本文研究了无粘势流中非旋转冯卡门板的长时间行为。该模型出现在气动弹性和模型之间的相互作用薄，非线性面板和气流，它是沉浸[6，21，23]。[16，18]中的最新结果表明，动力学的板分量（在存在物理板非线性的情况下）收敛到有限维的全局紧吸引集;这些结果是在没有任何类型的机械阻尼的情况下获得的。在这里，我们表明，通过将机械阻尼的全流板系统，完整的轨迹-板和流-强烈收敛到（一组）稳态。弱收敛的结果需要“最小”的内部阻尼，和强收敛的动态显示足够大的阻尼。我们要求存在一个“好的”能量平衡方程，它只有在亚音速流动时才可用。我们的证明是基于第一次显示的正则解，这反过来又需要传播的初始正则性的无限地平线上的收敛性。然后，我们利用两个板轨迹的差异的指数衰减，以表明全流板轨迹是均匀的时间阿达玛连续。这允许我们将平滑初始数据的收敛性质传递到有限能量类型的初始数据。物理上，我们的研究结果意味着颤振（非静态端行为）不会发生在亚音速动力学。虽然这样的结果是已知的旋转（紧凑/规则）板块动力学[14]（和其中的参考文献），本文提出的结果是第一个这样的结果获得的非正规化-最物理相关的-模型。
英文摘要：
We address the long-time behavior of a non-rotational von Karman plate in an inviscid potential flow. The model arises in aeroelasticity and models the interaction between a thin, nonlinear panel and a flow of gas in which it is immersed [6, 21, 23]. Recent results in [16, 18] show that the plate component of the dynamics (in the presence of a physical plate nonlinearity) converge to a global compact attracting set of finite dimension; these results were obtained in the absence of mechanical damping of any type. Here we show that, by incorporating mechanical damping the full flow-plate system, full trajectories---both plate and flow---converge strongly to (the set of) stationary states. Weak convergence results require "minimal" interior damping, and strong convergence of the dynamics are shown with sufficiently large damping. We require the existence of a "good" energy balance equation, which is only available when the flows are subsonic. Our proof is based on first showing the convergence properties for regular solutions, which in turn requires propagation of initial regularity on the infinite horizon. Then, we utilize the exponential decay of the difference of two plate trajectories to show that full flow-plate trajectories are uniform-in-time Hadamard continuous. This allows us to pass convergence properties of smooth initial data to finite energy type initial data. Physically, our results imply that flutter (a non-static end behavior) does not occur in subsonic dynamics. While such results were known for rotational (compact/regular) plate dynamics [14] (and references therein), the result presented herein is the first such result obtained for non-regularized---the most physically relevant---models.
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