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Abstract
The present thesis consists of an extended summary and four papers
concerning damping of structures and algorithmic damping in
numerical analysis.
The first part of the thesis deals with the efficiency and the
tuning of external collocated dampers acting on flexible
structures. The dynamics, and thereby the damping, of flexible
structures are generally described in terms of the dominant
vibration modes. A system reduction technique, where the damped
vibration mode is constructed as a linear combination of the
undamped mode shape and the mode shape obtained by locking the
damper, is applied. This twocomponent representation leads to a
simple solution for the modal damping representing the natural
frequency and the associated damping ratio. It appears from
numerical examples that this system reduction technique provides
very accurate results.
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Analytical expressions for the optimal tuning and the maximum
attainable damping are found by maximizing the expression for the
damping ratio. The theory is formulated for linear damper models,
but may also be applied for nonlinear dampers in terms of
equivalent linear parameters for stiffness and damping,
respectively. The format of the expressions obtained by the
present system reduction technique is similar to that for damping
of cables.
The characteristics of dampers are governed by the relation
between the damping component (energy dissipation) and the
stiffness component (restoring force). This relation is
conveniently described by the representative angle of the damper
force in phaseplane. It is demonstrated how efficiency of the
damper increases with the phase angle, and in particular how phase
lead, where the damper force acts ahead of velocity, implies large
damping. However, phase lead is equivalent to negative stiffness,
and therefore only realizable by means of active control. The
present thesis demonstrates how stiffness affects both the
performance and the tuning of the damper.
The final part of the thesis considers algorithmic damping in
connection with Newmark time integration. The damping
characteristics of the Newmark method are improved by introducing
a negative damping component, governed by a first order linear
filter. This additional force component is designed so that it
compensates for the undesirable damping introduced by the Newmark
method in the lowfrequency range, while it provides adjustable
highfrequency damping. The filter method gives a general
synthesis for the various alphamodifications of the Newmark
method and an improved weighting of the external load.
Original language  English 

Place of Publication  Kgs. Lyngby 

Publisher  Technical University of Denmark 
Number of pages  124 
ISBN (Print)  8789502590 
Publication status  Published  May 2006 
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Projects
 1 Finished

Modelling of Dampers and Damping in structures
Høgsberg, J. B., Brennan, M. J., Preumont, A., Nielsen, S. R. K. & Krenk, S.
01/09/2002 → 22/05/2006
Project: PhD