The Modal Expansion For Calculating The Coefficients Of The Puiseux Series Of Defective Eigenpairs In The Generalized Eigenvalue Problem

Sensitivity analysis of eigenvalue problem plays an important role not only in theoretical aspect, but also in vibration control, structural damage detection, model updating, structural optimization and many other applicationsThe paper mainly studies the modal expansion method for calculating the coefficients of the Puiseux series of defective eigenpairs in the generalized eigenvalue problem. Firstly, the governing equations for the coefficients of the Puiseux series of eigenpairs are derived by substituting the Puiseux series of eigenpairs into the generalized eigenvalue problem and comparing the both sides of the resulted equations. Then, based on the Weierstrass canonical form for the generalized eigenvalue problem, we express the coefficients of the Puiseux series of eigenvectors as the linear combination of all eigenvectors and generalized eigenvectors of the generalized eigenvalue problem and give the formulation for the first-to third-order coefficients of the eigenvalues and the first-to second-order coefficients of the eigenvectors. Finally, the numerical examples show the validity of the proposed method.