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04.03.2020 | Original Paper | Ausgabe 5/2020

Acta Mechanica 5/2020

A rotating elastic cylinder moving on an elliptic orbit

Zeitschrift:
Acta Mechanica > Ausgabe 5/2020
Autor:
Kazumi Watanabe
Wichtige Hinweise
Dedicated to Professor Hans Irschik, Johannes Kepler University of Linz, for his happy retirement.

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Abstract

The deformation of a rotating elastic cylinder moving on an elliptic orbit is discussed analytically. Firstly, one solution method is developed for a coupled displacement equation, which includes the centrifugal force and the 2D-Coriolis effects fully. Secondly, the obtained general solution is applied to a rotating cylinder moving on an elliptic orbit. For a rotating hollow cylinder, the non-circular deformation of its outer surface and the centrifugal/centripetal force produced by the motion on the elliptic orbit are discussed. It is shown that the non-circular deformation is more affected by the rotational velocity of the cylinder than by the angular velocity on the elliptic orbit. For a solid cylinder, the movement/displacement of the cylinder center is discussed, and some interesting and beautiful motion trajectory patterns are found. Due to the low-frequency nature in the practical applications, the low-frequency approximation is also carried out for all quantities, and it is confirmed that their approximate formulas are valid in the practical frequency range.

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