POLE ASSIGNMENT FOR THE VIBRATING ROD

Relocating some poles of an axially vibrating rod by feedback leads to a certain integrodifferential eigenvalue problem. An explicit solutio n to the problem of determining the force needed to assign part of the spectrum while leaving the remaining spectrum unchanged is presented, and the conditions under which this solution is unique are determined . The results are then used to determine a certain self-adjoint contro l, analogous to symmetric rank-one update in finite-dimensional system s, which solves the partial pole assignment problem with a control whi ch satisfies the reciprocity law relating displacement and force. The results obtained may be used in practical engineering applications of reducing the forced vibration response of harmonically excited systems .