Identification of Damping from Experimental Dynamic Stiffness Matrix: Error Analysis

Some practical issues related to application of the dynamic stiffness matrix (DSM) based damping identification method to real life mechanical systems are studied in this paper. The DSM based direct damping matrix identification method was proposed to identify both the mechanism and spatial distribution of damping as a matrix of general function of frequency. The method obtains the damping matrix from the imaginary part of the DSM, which is computed by inverting the measured frequency response function matrix (FRM). The major issue regarding the feasibility of this method is how the errors in measured frequency response functions (FRF) affect the DSM, because it is known that the DSM is highly sensitive to errors that are present in the FRFs. In this paper, a detailed analytical and computational study is performed, which leads to a sound physical explanation of the high sensitivity of the DSM to measurement errors that was observed in earlier studies. A new and also important conclusion is that the leakage error drastically affects the accuracy of the DSM in addition to other common measurement errors. Based on the findings of this study, recommendations are made for future experimental implementations of the damping identification method.