Variation in the Geometric Interpretation of the Eigenvalue Problem of a Structure Due to Damage

This paper studies the behavior of the geometric interpretation of the eigenvalue problem. An arbitrary two degree of freedom structure is modeled as a two mass, two spring system. The damage in the system is represented as a reduction in stiffness and the structure is assumed to be a natural conservative system. The geometric interpretation of the system is an ellipse which is examined under various damage conditions occurring on the structure. It is shown that this representation is a convex set and that damage produces a new set which is the convex hull of the existing condition. These results are graphed for several damage scenarios of the system.