A remark about the decoupling approximation of damped linear systems

A common approximation in the analysis of non-classically damped systems is to ignore the off-diagonal elements of the modal damping matrix. This procedure is termed the decoupling approximation. Contrary to widely accepted beliefs, it is shown numerically that over a finite range, errors due to the decoupling approximation can continuously increase at any specified rate while the modal damping matrix becomes more and more diagonal.