Complex modes and frequencies in damped structural vibrations

It is demonstrated that a state space formulation of the equation of motion of damped structural elements like cables and beams leads to a symmetric eigenvalue problem if the stiffness and damping operators are self-adjoint, and that this is typically the case in the absence of gyroscopic forces. Th...

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Bibliographic Details
Published in:Journal of sound and vibration 2004-03, Vol.270 (4), p.981-996
Main Author: Krenk, Steen
Format: Article
Language:English
Subjects:
Exact sciences and technology
Fundamental areas of phenomenology (including applications)
Physics
Solid mechanics
Structural and continuum mechanics
Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...)
Vibrations and mechanical waves
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Summary:It is demonstrated that a state space formulation of the equation of motion of damped structural elements like cables and beams leads to a symmetric eigenvalue problem if the stiffness and damping operators are self-adjoint, and that this is typically the case in the absence of gyroscopic forces. The corresponding theory of complex modal analysis of continuous systems is developed and illustrated in relation to optimal damping and impulse response of cables and beams with discrete viscous dampers.
ISSN:0022-460X
1095-8568
DOI:10.1016/S0022-460X(03)00768-5