Asymptotic expansion of slightly coupled modal dynamic transfer functions

In case of non-diagonal modal damping, normal modes of vibration do not decouple
modal equations. The usual way to handle such a non-diagonal modal damping matrix
is to neglect its off-diagonal elements. In this paper, we propose an approximatemethod
based on an asymptotic expansion of the transfer function. It is intermediate between
the classical decoupling approximation and the formal solution requiring a full matrix
inversion. Indeed, on the one hand, it allows to partially account for modal coupling and,
on the other hand, still allows the modal equations to be solved independently from
each other. We first provide the mathematical background necessary to canvass the
proposed method, then consider a benchmark against which the benefits of the method
are measured.