Updating the Damping Matrix Using Frequency Response Data

Abstract

Abstract This paper presents a method for the updating of the damping matrix of a linear dynamic system. For this dynamic study, it is presumed that the characteristic mass and stiffness matrices are perfectly known thanks to the updating of the experimental and calculed frequencies and mode shapes as from a finit element model. Furthermore, it is accepted that damping has only a minor effect on the frequencies and mode shapes of a structure (a hypothesis that has been verified for structures with low damping). It is proposed to adjuste the coefficients of the [D] hysteretic damping matrix as from the superposition of the experimental and analytical Frequency Response Functions (FRF). The frequencies and mode shapes are extracted from the solutions of the caracteristic equation (3) resulting from the classic dynamic equation. An analytical FRF is calculed and then used to establish the sensitivity matrix, translating the influence of the updating parameters on the FRF. To update the [D] matrix, we use a non-linear weighted least squares estimation.