Abstract
A variational formulation is set up for the damped forced vibration of a straight, non-uniform rod in longitudinal or torsional vibration. Correction terms to take account of Poisson contraction and lateral shear are included for longitudinal vibration and allowance is made for energy dissipation in the material. It is assumed that the rod is driven by a sinusoidal force at one end and that a load with complex impedance Z is applied at the other. The rod is assumed to be circular in section and to be made up of a number of linearly tapered elements. Discontinuities are allowed at the joints between elements. A computer programme is described which is based on the finite element method and which uses cubic approximations to the displacements in the elements. The programme computes the displacements and stress distribution in the rod. As an example of its usefulness the programme is used to compute the impedance of a number of thin, undamped, linearly tapered rods with different loads.
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