A simple Cosserat model is used to explore the coupled planar flexural and axial vibrations of a slender rod clamped at one end with a heavy attached mass free to move at the other. By assuming that the inertia of the rod is small compared to that of the attached mass it is shown how the equations of motion reduce to a dynamical system. The effects of gravity on the rod can be incorporated within this framework and the linearised stability of the system is discussed in terms of solutions to the Mathieu-Hill equation.

HOME