Efficient uncoupled stochastic analysis with non-proportional damping

The use of normal modes of vibration in the analysis of structures with nonproportional damping reduces the size of the resulting set of governing equations, but does not decouple them. A common practice consists in decoupling
the equations by disregarding the o -diagonal elements in the modal damping matrix. Recently, an approximation based on an asymptotic expansion of the modal transfer matrix has been proposed in a deterministic framework to partially account for o -diagonal terms, but still with a set of uncoupled equations. This paper aims at extending this method in a stochastic context. First the mathematical background is introduced and the method is illustrated with a simple example. Then its relevance is demonstrated within the context of the structural analysis of a large and realistic structure.