Local Sensitivity Analysis in Structural Dynamics Using Structural Dynamic Modification

It is well known that the eigenvalues and eigenvectors of a structural system with closely spaced modes are highly sensitive to small perturbations of mass and stiffness. In this work, the eigenvalue problem derived from the structural dynamic modification theory is used to determine the sensitivities of the eigenvalues and eigenvectors of systems with repeated or closely spaced eigenvalues. The accuracy of the proposed technique is studied by numerical simulations carried out on undamped structural models with repeated and closely spaced modes, which are perturbed with stiffness and mass changes defined by the matrices ΔK and ΔM, respectively. The solution provided by the structural dynamic modification theory is compared with the results obtained with the first-order sensitivity equations.