Quantification of non-proportionality of damping in discrete vibratory systems

Quantification of the non-proportionality of damping is very important in m odal testing, model correlation, and model modifications. Three new indices measuring the damping non-proportionality are proposed in this study. The proposed indices are based on the complex modes of a generally damped syste m. The mathematical development is built on a common assumption that the mo dal matrix can be represented by a product of a real matrix and complex mat rix. The complex matrix represents modal coupling due to the non-proportion ality. The relation between the complex matrix and the modal damping matrix is derived and used as a base for the proposed indices. The first index me asures the correlation between the real and the imaginary parts of a comple x mode. The second index measures the magnitude of the imaginary parts of a complex mode that is scaled in a way that maximizes its real parts. The th ird index quantifies the degree of modal coupling using the magnitude of th e imaginary part of the entire scaled modal matrix. The applicability of th e proposed indices is demonstrated by numerical simulations. The performanc e of the proposed indices is compared with three existing indices. The exam ple also tests the robustness of the proposed indices, when the complex mod es are corrupted by a measurement noise. (C) 2000 Elsevier Science Ltd. All rights reserved.