Forced Oscillations of a Spring-Mounted Body by a Viscous Liquid: Rotational Case
We study the periodic motions of the coupled system $\mathscr S$, consisting of an incompressible Navier-Stokes fluid interacting with a structure formed by a rigid body subject to {\em undamped} elastic restoring forces and torque around its rotation axis. The motion of $\mathscr S$ is driven by th...
Saved in:
| Main Authors | , , |
|---|---|
| Format | Journal Article |
| Language | English |
| Published |
10.04.2025
|
| Subjects | |
| Online Access | Get full text |
| DOI | 10.48550/arxiv.2504.07716 |
Cover
| Summary: | We study the periodic motions of the coupled system $\mathscr S$, consisting
of an incompressible Navier-Stokes fluid interacting with a structure formed by
a rigid body subject to {\em undamped} elastic restoring forces and torque
around its rotation axis. The motion of $\mathscr S$ is driven by the uniform
flow of the liquid, far away from the body, characterized by a time-periodic
velocity field, $\mathbf{V}$, of frequency $f$. We show that the corresponding
set of governing equations always possesses a time-periodic weak solution of
the same frequency $f$, whatever $f>0$, the magnitude of $\mathbf{V}$ and the
values of physical parameters. Moreover, we show that the amplitude of linear
and rotational displacement is always pointwise in time uniformly bounded by
one and the same constant depending on the data, regardless of whether $f$ is
or is not close to a natural frequency of the structure. Thus, our result rules
out the occurrence of resonant phenomena. |
|---|---|
| DOI: | 10.48550/arxiv.2504.07716 |