Sensitivity of EigenValues and Vectors for Variations of Parameters of Finite Element Models of Construction

A problem of determination of first- and second-order functions of sensitivity of eigenvalues and eigenvectors on the basis of modern software packages for finite element simulation is considered. Based on the generalized problem on eigenvalues some dependences for finding the eigenvalue sensitivity functions are obtained which are simple from the calculation point of view. For finding the eigenvector sensitivity functions the vector decomposition along the orthogonal basis is used which allow one to avoid solving the system of higher-order algebraic equations. The influence of close frequencies on the convergence of calculation procedures is analyzed. Results are illustrated by an example.