Evaluation of damping non-proportionality using identified modal information

This paper focuses on quantification of damping non-proportionality present in a discrete vibratory system. The study assumes that the information ava ilable is a set of identified system eigenvalues and eigenvectors and that the system parameters such as mass, stiffness, and damping matrices are unk nown a priori. This set of modal parameters may be incomplete. The investig ation is concentrated on how two existing analytical indices can be utilise d when the modal damping matrix is not available. The quantification proced ure starts with extraction of normal modes using a known algorithm. It is s hown that two matrices, by-products of the normal model extraction, can be used to study damping non-proportionality. The first matrix is a scaled mod al damping matrix. The paper shows that the indices developed from the scal ed modal damping matrix preserves the properties of the indices based on th e analytical modal damping matrix. The second matrix is a complex matrix wh ich is obtained by expanding complex modes into the subspace of real modes. The off-diagonal elements of the complex matrix indicate coupling between modes due to damping non-proportionality. Based on this characteristic, thr ee new indices are proposed. Numerical examples are presented to illustrate the use of the new indices and to compare them with the indices that are d escribed in literature. (C) 2001 Academic Press.