A method for damping matrix identification using frequency response data

Accurate modeling of damping in structures is of great importance for vibration response analysis and control. This paper addresses the issue of identification of damping matrix of a structure by posing it as a finite element damping matrix updating problem. Many of the current updating approaches, dealing with updating of damping matrix, perform simultaneous updating of mass, stiffness and damping matrices. However, such a strategy is faced with numerical problems in practical implementation, since the magnitude of stiffness and mass matrix elements is generally much more than that of the damping matrix elements causing difficulties in accurate identification of the damping matrix. Some other approaches divide the process of updating of the mass and stiffness matrix and the damping matrix into two stages, but their application is restricted to structures with low levels of damping. This paper addresses these issues by developing an updating formulation that seeks to separate updating of the damping matrix from that of updating of the stiffness and the mass matrix. The proposed damping matrix updating method utilizes the concept of normal frequency response functions (FRFs) available in the literature. The method is formulated so as to reduce the difference between the complex FRFs, which can be measured in practice, and the normal FRFs, whose estimates can be obtained from the measured complex FRFs. The effectiveness of the proposed method is demonstrated through a numerical study on a simple but representative beam structure. The issue of coordinate incompleteness and robustness of the method under presence of noise is investigated. It is found that the proposed method is effective in the accurate identification of the damping matrix in cases of complete, incomplete and noisy data and is not limited by the level of damping in the structure. (C) 2012 Elsevier Ltd. All rights reserved.