Here is a method for converting modal damping to a damping coefficient matrix for all modes. It is based on a pseudo inversion of the modal damping matrix.
The resulting coefficient matrix will be fully populated. The damping terms will not necessary corresponding to physical dashpots, but the modal damping will be fully represented. This is useful for the case where a direct solution method will be used, such as the Newmark-beta method.
Here is a Matlab script: c_matrix.zip
– Tom Irvine