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Damped response of an axially excited rotating liquid bridge in zero-gravity

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Summary

The response of a solidly rotating finite liquid bridge due to axial excitation exhibits for frictionless liquid at the resonances singularities. For the experimenter in a spacelabmission the actual resonance amplitude is of quite some importance. For this reason damping, that has to be measured in ground tests, has been introduced into the results of the response.

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Abbreviations

a :

radius of the liquid bridge

h :

length of the liquid bridge

I 0,I 1 :

modified Besselfunctions

J 0,J 1 :

Besselfunctions

r, φ,z :

polar coordinates

t :

time

\(\bar z_0\) :

excitation amplitude

\(\alpha ^2 = 1 - \frac{{4\Omega _0 ^2 }}{{\Omega ^2 }} > 0\) :

elliptic case

\(\beta ^2 = \frac{{4\Omega _0 ^2 }}{{\Omega ^2 }} - 1 > 0\) :

hyperbolic case

\(\gamma _{2n - 1} \equiv \frac{{(2n - 1)\pi a}}{h}\) :

abbreviation

\(\bar \zeta _{2n - 1}\) :

damping factor of liquid

ζ(z, t):

free surface displacement

ε=Ω2 − ω2 :

surface tension

σ:

surface tension

ϱ:

liquid density

Ω0 :

rotational speed of liquid bridge

Ω:

forcing frequency of axial excitation

ω:

natural frequency of liquid bridge

References

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Authors and Affiliations

  1. Institut für Raumfahrttechnik, Universität der Bundeswehr, Werner-Heisenberg-Weg 39, D-8014, Neubiberg, Federal Republic of Germany

    H. F. Bauer

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  1. H. F. Bauer
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Bauer, H.F. Damped response of an axially excited rotating liquid bridge in zero-gravity. Acta Mechanica 79, 295–301 (1989). https://doi.org/10.1007/BF01187268

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  • DOI: https://doi.org/10.1007/BF01187268

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