On the modal diagonalization of viscoelastic mechanical systems

•FEM equations of a viscoelastic media obtained by first principles of mechanics.•Causality of the considered viscoelastic model has been discussed.•Modal diagonalization of the viscoelastic space-discretized system is considered.•Spectral properties of viscoelastic systems with hysteretic damping a...

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Bibliographic Details
Published in:Mechanical systems and signal processing 2017-11, Vol.96, p.159-175
Main Authors: Mastroddi, F., Eugeni, M., Erba, F.
Format: Article
Language:English
Subjects:
Aeronautics
Coordinate transformations
Damping
Finite element analysis
Finite element method
Finite Element Modelling
Hysteresis
Hysteretic damping
Mechanical systems
Modal analysis
Oscillators
Vibration
Vibration mode
Viscoelastic materials
Viscoelasticity
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Summary:•FEM equations of a viscoelastic media obtained by first principles of mechanics.•Causality of the considered viscoelastic model has been discussed.•Modal diagonalization of the viscoelastic space-discretized system is considered.•Spectral properties of viscoelastic systems with hysteretic damping are analyzed.•Not-space-homogenous hysteretic damping may be equivalent to a non-homogeneous one. 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.
ISSN:0888-3270
1096-1216
DOI:10.1016/j.ymssp.2017.04.009