论文标题
关于腔内充满可压缩液的腔的钟摆的运动
On the Motion of a Pendulum with a Cavity Filled with a Compressible Fluid
论文作者
论文摘要
我们研究了耦合系统的运动，$ \ mathscr s $，由物理摆，$ \ mathscr b $构成，内部空腔完全充满了粘性，可压缩的液体，$ \ Mathscr f $。流体的存在可能会对$ \ Mathscr b $的运动有强烈影响。实际上，我们证明，在适当的假设下，液体充当阻尼器，即，$ \ mathscr s $最终必须达到休息状态。这样的状态的特征是$ \ mathscr f $的合适时间无关的密度分布以及$ \ Mathscr s $的质量中心的相应平衡位置。这些结果在弱解决方案的非常一般的类别中得到了证明，除了具有有限能量外，不需要对初始数据进行任何限制。我们通过一些数值测试来补充我们的发现。后一个节目，除其他外，有趣的属性``大型压缩性都有利于阻尼效果，因为它大大减少了$ \ mathscr s $需要休息的时间。
We study the motion of the coupled system, $\mathscr S$, constituted by a physical pendulum, $\mathscr B$, with an interior cavity entirely filled with a viscous, compressible fluid, $\mathscr F$. The presence of the fluid may strongly affect on the motion of $\mathscr B$. In fact, we prove that, under appropriate assumptions, the fluid acts as a damper, namely, $\mathscr S$ must eventually reach a rest-state. Such a state is characterized by a suitable time-independent density distribution of $\mathscr F$ and a corresponding equilibrium position of the center of mass of $\mathscr S$. These results are proved in the very general class of weak solutions and do not require any restriction on the initial data, other than having a finite energy. We complement our findings with some numerical tests. The latter show, among other things, the interesting property that ``large" compressibility favors the damping effect, since it drastically reduces the time that $\mathscr S$ takes to go to rest.
