Modal Expansion Method for Eigensensitivity Calculations of Cyclically Symmetric Bladed Disks

Abstract

A diverse set of technical fields such as design optimization, structural system identification, and probabilistic modeling require accurate and efficient calculation of modal sensitivities to structural parameters for bladed disks (blisks). However, obtaining sensitivities by traditional finite difference schemes of full blisk finite element models fails to meet the efficiency requirement. An approach is presented here that meets both the accuracy and efficiency requirements for calculating modal sensitivities by formulating a modal expansion method for blisk models. This approach accommodates repeated eigenvalues common to blisks, where traditional approaches result in singular equations when solving for sensitivities. Results illustrate the efficiency and efficacy of the approach for a simple academic model and an industrial model. It is also shown that repeated eigenvalues and eigenvectors also have repeated derivatives.