The self-excited vibrations of an axially retracting cantilever beam using the Galerkin method with fitted polynomial basis functions.

In the present study, the self-excited vibrations of an axially retracting beam under gravity is investigated. A GFB method is presented to discretize the system energy functions, in which the orthogonality relationships between the basis functions are needless. In this way, the motion equations can be derived in a much simpler way of matrix. The presented method and the derived motion equations are validated by comparing the computed results with which from previous literature. Based on the computed dynamic responses, the effect of gravity on beam dynamic behavior is investigated. An interesting phenomenon of self-excited vibration is observed as the beam retracts with a certain axial speed. Finally, the effects of retracting speed, structural damping and static tip deflection on self-excited vibration are investigated. [ABSTRACT FROM AUTHOR]