An inverse eigenvalue method for frequency isolation in spring-mass systems

• Published in: Numerical linear algebra with applications Vol. 9; no. 1; pp. 65 - 79
• Main Authors: Egaña, Juan C., Kuhl, Nelson M., Santos, Luis C.
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 01.01.2002
• Subjects: inverse eigenvalue problem; Jacobi matrix; spring-mass system; δ-Lanczos method
• ISSN: 1070-5325; 1099-1506
• DOI: 10.1002/nla.255

The action of external vibrating forces on mechanical structures can cause severe damages when resonance occurs. The removal of natural frequencies of the structure from resonance bands is therefore of great importance. This problem is called frequency isolation problem and is the subject of this paper. A new inverse eigenvalue method is proposed and applied to spring–mass systems, which have generated much interest in the literature as prototypes of vibrating structures. The novelty of the method lies in using the zeros of the frequency response function at the last mass as control variables in an optimization problem to minimize the impact of redesign. Numerically accurate algorithms for computing the sensitivity with respect to the control variables are presented, which form the basis of an efficient multidimensional search strategy to solve the frequency isolation problem. Copyright © 2001 by John Wiley & Sons, Ltd.