### Abstract

An increasing number of flexible structures such as cable-stayed bridges, pedestrian
bridges and high-rise buildings are fitted with local dampers to mitigate vibration problems.
In principle the effect of local dampers can be analyzed by use of complex modes, e.g. in
conjunction with an averaging technique for local linearization of the damper characteristics.
However, the complex mode shapes and frequencies depend on the magnitude of the damper
and therefore are less suitable for design of the damper system. An efficient alternative consists
in the use of a two-component representation of the damped modes of the structure. The idea is
to represent the damped mode as a linear combination of the modes that occur in two distinctly
different situations representing extreme conditions: the mode shape of the structure without the
damper(s), and the mode shape of the structure, when the damper is locking the local relative
motion of the structure. Both of these situations are undamped, and therefore both sets of mode
shapes and modal frequencies can be obtained by a classic real-valued eigenvalue analysis,
available in most commercial structural analysis programs. The two components form a twodimensional
subspace, and a two-dimensional set of equations of motion can be formulated
explicitly by use of the two sets of undamped modal data, when combined with the properties
of the damper(s). The effect of the damper(s) can be characterized by a simple approximation,
where the root locus of the complex frequency - containing the resulting modal damping via the
imaginary part - is given by an explicit formula. For very flexible structures, e.g. cables, only
moderate damping is involved, and the explicit approximation is very accurate. However, even
for stiffer structures the explicit form gives a quite good estimate for use in design calculations.
The efficiency of the damper configuration depends on damper placement as well as damper
properties. Thus a stiffness component in the damper characteristic leads to a decrease in
damping efficiency. The method is illustrated by some simple examples, also demonstrating the
effect of damper characteristics on optimal tuning and on the amount of damping obtained in
the structure.

Original language | English |
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Title of host publication | Compdyn 2007 : Computational Methods in Structural Dynamics and Earthquake Engineering |

Editors | M. Papadrakakis, D.C. Charmpis, N.D. Lagaros, Y. Tsompanakis |

Volume | CD-ROM |

Publisher | Civil Engineering Software |

Publication date | 2007 |

Publication status | Published - 2007 |

Event | Computational Methods in Structural Dynamics and Earthquake Engineering - Rethymno, Greece Duration: 13 Jun 2007 → 16 Jun 2007 http://194.42.10.251/compdyn2007/index.html |

### Conference

Conference | Computational Methods in Structural Dynamics and Earthquake Engineering |
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Country | Greece |

City | Rethymno |

Period | 13/06/2007 → 16/06/2007 |

Internet address |

## Cite this

Høgsberg, J. R., & Krenk, S. (2007). System Reduction and Damping of Flexible Structures. In M. Papadrakakis, D. C. Charmpis, N. D. Lagaros, & Y. Tsompanakis (Eds.),

*Compdyn 2007: Computational Methods in Structural Dynamics and Earthquake Engineering*(Vol. CD-ROM). Civil Engineering Software.