On the quantification of damping model uncertainty

The characterization of uncertainty in the damping forces in a vibrating structure is of significant interest in structural dynamics. The most common approach is to use a viscous damping matrix with uncertain coefficients. The viscous damping is not the only damping model within the scope of linear analysis. Any model which makes the energy dissipation functional non-negative is a possible candidate for a valid damping model. There are many functional forms which can be used as damping models. In this paper, two approaches are proposed to quantify such ‘model-form uncertainty’ associated with the use of the viscous damping model (not only the model parameters). The first approach is based on an ensemble of equivalent damping functions and the second approach is based on the random matrix theory. The results obtained from the two methods are compared using numerical examples. It was observed that the random matrix theory can be used to quantify damping model uncertainty in some cases.