On the modal diagonalization of viscoelastic mechanical systems

In this paper the modal coupling of linear viscoelastic oscillators is discussed. In particular, it is demonstrated that in presence of space-homogeneous ideal hysteretic damping, namely, viscoelastic materials with loss factor constant as function of frequency, a set of coupled linear oscillators can be always decoupled by a real coordinate transformation. This result can be extended to the case of a not space-homogeneous ideal hysteretic damping if the modes of vibration of the system keep practically real. The proposed approach is applied to a linear Multi-Degree of Freedom system representing the Finite Element Model of an aeronautical structure.