Discussion on “Vibration Analysis of Non-Classically Damped Linear Systems”

In 1, the authors consider n-degree-of-freedom non-classically damped linear systems. They write the system representation in the modal coordinates as for all $t⩾0,$ where the vector of displacements $Xt∈Rn,$ the symmetric and non-negative matrix $C∈Rn×n$ corresponds to the modal damping matrix, and the diagonal matrix has the square of the undamped natural frequencies of the system, $ω12,$$ω22,…,ωn2,$ on its diagonal.