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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 292609, 12 pages
http://dx.doi.org/10.1155/2014/292609
Research Article

A Structured Approach to Solve the Inverse Eigenvalue Problem for a Beam with Added Mass

Department of Mechanical Engineering, University of Ottawa, 161 Louis Pasteur, Ottawa, ON, Canada K1N 6N5

Received 31 October 2013; Revised 17 January 2014; Accepted 24 January 2014; Published 12 March 2014

Academic Editor: Herb Kunze

Copyright © 2014 Farhad Mir Hosseini and Natalie Baddour. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The problem of determining the eigenvalues of a vibrational system having multiple lumped attachments has been investigated extensively. However, most of the research conducted in this field focuses on determining the natural frequencies of the combined system assuming that the characteristics of the combined vibrational system are known (forward problem). A problem of great interest from the point of view of engineering design is the ability to impose certain frequencies on the vibrational system or to avoid certain frequencies by modifying the characteristics of the vibrational system (inverse problem). In this paper, a method to impose two natural frequencies on a dynamical system consisting of an Euler-Bernoulli beam and carrying a single mass attachment is evaluated.