Evaluation of damping non-proportionality using identified modal information

Abstract This paper focuses on quantification of damping non-proportionality present in a discrete vibratory system. The study assumes that the information available is a set of identified system eigenvalues and eigenvectors and that the system parameters such as mass, stiffness, and damping matrices are unknown a priori . This set of modal parameters may be incomplete. The investigation is concentrated on how two existing analytical indices can be utilised when the modal damping matrix is not available. The quantification procedure starts with extraction of normal modes using a known algorithm. It is shown that two matrices, by-products of the normal model extraction, can be used to study damping non-proportionality. The first matrix is a scaled modal damping matrix. The paper shows that the indices developed from the scaled modal damping matrix preserves the properties of the indices based on the analytical modal damping matrix. The second matrix is a complex matrix which 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, three 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 described in literature.