Closeness of the Solutions of Approximately Decoupled Damped Linear Systems to Their Exact Solutions

The simplest technique of decoupling the normalized equations of motion of a linear nonclassically damped second-order system is to neglect the off-diagonal elements of the normalized damping matrix. In this paper, the error introduced in the system response due to this decoupling technique is studied. Conditions are derived under which the solution of an approximately decoupled system is "close" to the exact solution of the system.