QUANTIFICATION OF THE EXTENT OF NONPROPORTIONAL VISCOUS DAMPING IN DISCRETE VIBRATORY-SYSTEMS

The primary objective of this paper is to present several numerical indices developed to determine quantitatively the extent of non-proportional damping present within a discrete vibratory system. A total of five distinct indices are considered. Two of these are based on the complex modes of a generally damped system, and three are based on the configuration of the system damping matrix after transformation into real normal coordinates. Application of the indices is illustrated through a four degree of freedom system example problem. As part of this exercise, an effort is made to relate the magnitudes of the indices to the frequency response errors induced by two proportional damping approximations often found in the literature.