On Axial Vibrations of a Whirling Bar

Abstract

Axial vibrations of whirling bars are studied by using undeformed or Lagrangian coordinates. In general, whirling lowers the natural frequencies of the bars. In the static case, an interesting and previously unreported result is obtained as a special case of the dynamic problem. When the angular velocity of the bar approaches certain critical values, “static resonances” or instabilities occur, and the axial displacements everywhere in the bar tend to become unboundedly large. These resonances are explained physically. The same problem is also solved by using deformed or Eulerian coordinates, and it is shown that the static resonances are concealed in such an analysis.