Constructing the shape of a rod from eigenvalues
Yitshak M. Ram, Sylvan Elhay · Communications in Numerical Methods in Engineering · 1998
The discretization of the differential equation governing the axial vibration of a rod with varying cross-section leads to a specially structured matrix pencil. This paper deals with the reconstruction of this pencil from its spectrum. An iterative algorithm for this problem and an analytic characterization of complementary solutions are given. The method is demonstrated on some examples. © 1998 John Wiley & Sons, Ltd.