Sensitivity Analysis of an Axially Vibrating Elastic Rod with Several Lumped Attachments

Abstract

In a recent study, the eigenvalue sensitivities of a combined system consisting of a linear structure with several lumped attachments were analyzed. An efficient approach was developed for the eigenvalue sensitivities with respect to the parameters of the attachments and their locations by using the implicit function theorem. In the study mentioned above, the theory was applied to a Bernoulli–Euler beam with several attachments. Motivated by this study, the methodology established there will be applied, in the present paper, to an axially vibrating rod with several lumped attachments. Hence, the utility of the methodology is justified through a quite different type of vibrational system. The method is shown as an efficient tool that can be taught in related graduate-level courses for the eigenvalue estimation of complex linear systems with several lumped attachments.