The Reconstruction of a Specially Structured Jacobi Matrix with an Application to Damage Detection in Rods

摘要

A finite-element discretization of the differential equation for the axial vibration of a rod with varying cross-section leads to a specially structured n x n matrix pencil. The reconstruction of this pencil from its spectrum can be achieved by the reconstruction of a unique Jacobi matrix using half of its spectrum and half of the spectrum of its principal submatrix of order (n - 1). The technique is used in an optimization problem formulated for damage detection in rods defined in terms of changes in the effective cross-sectional area.