Design sensitivity analysis for repeated eigenvalues in structural design

Abstract

Eigenvalue sensitivity can be analytically computed using Fox and Kapoor's formula. However, if the eigenvalues are not distinct, the calculation of eigenvalue sensitivities for the repeated eigenvalues using Fox's formula sometimes does not yield correct answers unless the eigenvectors associated with the repeated eigenvalues are properly defined. It has been found in this paper that for two types of frequently designed structures, although the repeated eigenvalues exist, their sensitivities with respect to specific design variables can be found without forming an auxiliary eigenequation as proposed by earlier researchers

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