Quantification of non-viscous damping in discrete linear systems

The damping forces in a multiple-degree-of-freedom engineering dynamic system may not be accurately described by the familiar ‘viscous damping model’. The purpose of this paper is to develop indices to quantify the extent of any departures from this model, in other words the amount of ‘non-viscosity’ of damping in discrete linear systems. Four indices are proposed. Two of these indices are based on the non-viscous damping matrix of the system. A third index is based on the residue matrices of the system transfer functions and the fourth is based on the (measured) complex modes of the system. The performance of the proposed indices is examined by considering numerical examples.