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

Abstract

In 1, the authors consider n-degree-of-freedom non-classically damped linear systems. They write the system representation in the modal coordinates as Display FormulaẌ(t)+2CẊ(t)+Λ2X(t)=0, X(0)=X0, Ẋ(0)=Ẋ0for all t≥0, where the vector of displacements X(t)∊Rn, the symmetric and non-negative matrix C∊Rn×n corresponds to the modal damping matrix, and the diagonal matrix Display FormulaΛ2=diag[ω12,ω22,[[ellipsis]],ωn2]∊Rn×nhas the square of the undamped natural frequencies of the system, ω12,ω22,[[ellipsis]],ωn2, on its diagonal.