Coupling Vibration of Tapered Rod

Abstract

In rod's free vibration, its easy to obtain normal modes. However, if there is rigid body displacement, the problem will be much more complex. To solve these kinds of problems, single flexible body dynamics is needed. As the first part of the paper, considering rods rigid body displacement, the free vibration of tapered rod is discussed. By solving partial differential equation of rods free vibration, normal frequencies of tapered rod are obtained. As the second part of the paper, coupling vibration is discussed, in which process quasi-variational principle as the most important tool is used. Finally, first-order frequency of coupled vibration of rod is represented.