Approximate Decoupling of the Equations of Motion of Large Flexible Structures

One common method in solving a normalized linear system (representing a large flexible structure), with small off-diagonal damping elements is to replace the normalized damping matrix by a selected diagonal matrix. The extent of approximation introduced by this method of decoupling the system is evaluated, and tight error bounds are derived. Moreover, it is shown that, if the normalized damping matrix is diagonally dominant, then among all diagonal matrices, the one that minimizes the error bound is simply the diagonal matrix obtained by neglecting the off-diagonal elements of the normalized damping matrix.