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.
Volume Subject Area:17th Biennial Conference on Mechanical Vibration and Noise
Keywords:damage, convex set, eigenvalue problem, vibrations
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