Sensitivity analysis of a system with two closely spaced modes using structural dynamic modification

Abstract

The first-order sensitivity equations based upon a Taylor expansion are not accurate in systems with closely space modes. Moreover, a good correlation can exist in terms of mass and stiffness between two models with closely spaced modes, but low values of modal assurance criteria (MAC) can be obtained because mode shapes rotate in the subspace spanned by the closely spaced mode shapes. In this work, the sensitivity of the eigenvalues and eigenvectors of a system with two closely spaced modes is studied, solving analytically the corresponding un-damped eigenvalue problem derived from the structural dynamic modification theory. Three different perturbation cases have been considered: stiffness change ΔK, mass change ΔM, and simultaneous mass and stiffness changes. The accuracy of the equations presented in this paper has been validated by simulations in a 4 DOF system with the first two modes closely spaced. The predictions provided by the analytical equations (local eigenvalue problem) are compared with the results obtained solving the full eigenvalue problem.