Structural modification analysis using Rayleigh quotient iteration

This paper highlights the application to structural dynamics of the sensitivity analysis methods developed by numerical analysts and presents a historical development of first- and higher-order eigenvalue and eigenvector sensitivities. Different formulae for an eigenvalue sensitivity are presented and it is shown that all of these are implicitly the same. A condition number is presented to give the limited bound of application for the first-order eigenvalue and eigenvector sensitivities. An alternative structural modification method based on Rayleigh Quotient Iteration is presented. A lumped spring-mass system with 7 degrees-of-freedom (7DoF) is used to show the applicability of the Rayleigh quotient iteration method.