Efficient uncoupled stochastic analysis with non-proportional damping

The use of normal modes of vibration in the analysis of structures with non-proportional 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 off-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 off-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.