Closure to “Discussion on ‘Vibration Analysis of Non-Classically Damped Linear Systems’ ” (2004, ASME J. Vib. Acoust., 126)

We appreciate S. M. Shahruz for his interest in our paper and for the useful comments on the numerical method for solving the transformed system As pointed out by Shahruz, the numerical method proposed in our paper is an approximate approach. The approximation comes from the assumption that the time-varying matrix $eCtΛ2−C2eCt$ is time-invariant within short time duration $jh<t<j+1h$$j=0,1,2,…,N$ where $h$ is the time step, i.e.,