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arXiv · 2210.16950

On the Motion of a Pendulum with a Cavity Filled with a Compressible Fluid

Giovanni Paolo Galdi·Václav Mácha·Šárka Nečasová·Bangwei She
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Abstract

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.

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Giovanni Paolo Galdi, Václav Mácha, Šárka Nečasová, Bangwei She. 2022-10-30. On the Motion of a Pendulum with a Cavity Filled with a Compressible Fluid. https://arxiv.org/abs/2210.16950

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