## Abstract

Morphological Indicators are dimensionless numbers that represent a property of a structure (e.g.

volume, stiffness) and depend only on a small number of variables. These indicators include

optimization at the stage of conceptual design. The most important indicators are the Indicator of

Volume, related to the strength of the structure, and the Indicator of Displacement, related to the

stiffness of the structure. These indicators, in their most simple appearance, are function only of the

geometrical slenderness of the structure, under the assumption that the structure is not subjected to

second order effects and that shear effects are not predominant.

The Indicator of Volume allows choosing the structural typology with a minimum of volume of

material. When using the Indicator of Volume at the stage of conceptual design, important areas of

slenderness appear to bring about problems of resonance. This is particularly the case for structures

which:

- have predominant co-vibrating loads

- have large spans

- are using a material with a small stiffness/strength ratio

Two methods to avoid resonance and their influence on the Indicator of Volume exist and are

investigated for statically determined beams.

Resonance can be reduced by placing a tuned mass damper in the anti-node of the mode. This tuned

mass damper, if well adjusted, vibrates in anti-phase with the structure and subdues thus resonance

peak. Optimally designed tuned mass dampers can be characterized by one single parameter which is

the ratio of its mass to the vibrating mass of the structure. However, for practical reasons, it is limited.

Resonance can also be avoided by a reduction of the stress level of the structure. This comes at the cost

of volume of material.

Both methods penalize the Indicator of Volume. These penalizations allow choosing a structural

typology that is the most economic in terms of used volume of material, considering dynamic effects

and damping solutions.

volume, stiffness) and depend only on a small number of variables. These indicators include

optimization at the stage of conceptual design. The most important indicators are the Indicator of

Volume, related to the strength of the structure, and the Indicator of Displacement, related to the

stiffness of the structure. These indicators, in their most simple appearance, are function only of the

geometrical slenderness of the structure, under the assumption that the structure is not subjected to

second order effects and that shear effects are not predominant.

The Indicator of Volume allows choosing the structural typology with a minimum of volume of

material. When using the Indicator of Volume at the stage of conceptual design, important areas of

slenderness appear to bring about problems of resonance. This is particularly the case for structures

which:

- have predominant co-vibrating loads

- have large spans

- are using a material with a small stiffness/strength ratio

Two methods to avoid resonance and their influence on the Indicator of Volume exist and are

investigated for statically determined beams.

Resonance can be reduced by placing a tuned mass damper in the anti-node of the mode. This tuned

mass damper, if well adjusted, vibrates in anti-phase with the structure and subdues thus resonance

peak. Optimally designed tuned mass dampers can be characterized by one single parameter which is

the ratio of its mass to the vibrating mass of the structure. However, for practical reasons, it is limited.

Resonance can also be avoided by a reduction of the stress level of the structure. This comes at the cost

of volume of material.

Both methods penalize the Indicator of Volume. These penalizations allow choosing a structural

typology that is the most economic in terms of used volume of material, considering dynamic effects

and damping solutions.

Original language | English |
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Title of host publication | IASS Symposium 2006 |

Editors | Kawaguchi Mamoru |

Publisher | International Association Shells and Space Structures |

Publication status | Published - 2006 |

Event | Finds and Results from the Swedish Cyprus Expedition: A Gender Perspective at the Medelhavsmuseet - Stockholm, Sweden Duration: 21 Sep 2009 → 25 Sep 2009 |

### Publication series

Name | IASS Symposium 2006 |
---|

### Conference

Conference | Finds and Results from the Swedish Cyprus Expedition: A Gender Perspective at the Medelhavsmuseet |
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Country/Territory | Sweden |

City | Stockholm |

Period | 21/09/09 → 25/09/09 |

### Bibliographical note

Kawaguchi Mamoru## Keywords

- Structural vibrations
- Tuned mass damping
- Beams