### Abstract

This paper considers the damped transverse vibration of flexural structures. Viscous damping models available to date suffer from the deficiency that predicted modal damping is strongly frequency-dependent, a situation not often encountered in experiments with built-up structures. Strain-based viscous damping, which corresponds to the case of stiffness-proportional damping, yields modal damping that increases linearly with frequency. Motion-based viscous damping, which corresponds to the case of mass-proportional damping, yields modal damping that decreases linearly with frequency. The proposed model introduces a viscous "geometric" damping term in which a resisting shear force is proportional to the time rate of change of the slope. In a discretized (finite element) context, the resulting damping matrix resembles the geometric stiffness matrix used to account for the effects of membrane loads on lateral stiffness. For an illustrative example of a simply-supported beam, this model yields constant modal damping that is independent of frequency. For some boundary conditions, the corresponding mode shapes are real. These conclusions are verified through additional finite element analysis. Such a viscous damping model should prove useful to researchers and engineers who need a time-domain damping model that exhibits realistic frequency-independent damping.

Original language | English (US) |
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Title of host publication | 51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference |

State | Published - 2010 |

Event | 51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference - Orlando, FL, United States Duration: Apr 12 2010 → Apr 15 2010 |

### Other

Other | 51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference |
---|---|

Country | United States |

City | Orlando, FL |

Period | 4/12/10 → 4/15/10 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Civil and Structural Engineering
- Mechanics of Materials
- Building and Construction
- Architecture

### Cite this

*51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference*[2010-3111]

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*51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference.*, 2010-3111, 51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Orlando, FL, United States, 4/12/10.

**Frequency-independent modal damping for flexural structures via a viscous "Geometric" damping model.** / Lesieutre, George A.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Frequency-independent modal damping for flexural structures via a viscous "Geometric" damping model

AU - Lesieutre, George A.

PY - 2010

Y1 - 2010

N2 - This paper considers the damped transverse vibration of flexural structures. Viscous damping models available to date suffer from the deficiency that predicted modal damping is strongly frequency-dependent, a situation not often encountered in experiments with built-up structures. Strain-based viscous damping, which corresponds to the case of stiffness-proportional damping, yields modal damping that increases linearly with frequency. Motion-based viscous damping, which corresponds to the case of mass-proportional damping, yields modal damping that decreases linearly with frequency. The proposed model introduces a viscous "geometric" damping term in which a resisting shear force is proportional to the time rate of change of the slope. In a discretized (finite element) context, the resulting damping matrix resembles the geometric stiffness matrix used to account for the effects of membrane loads on lateral stiffness. For an illustrative example of a simply-supported beam, this model yields constant modal damping that is independent of frequency. For some boundary conditions, the corresponding mode shapes are real. These conclusions are verified through additional finite element analysis. Such a viscous damping model should prove useful to researchers and engineers who need a time-domain damping model that exhibits realistic frequency-independent damping.

AB - This paper considers the damped transverse vibration of flexural structures. Viscous damping models available to date suffer from the deficiency that predicted modal damping is strongly frequency-dependent, a situation not often encountered in experiments with built-up structures. Strain-based viscous damping, which corresponds to the case of stiffness-proportional damping, yields modal damping that increases linearly with frequency. Motion-based viscous damping, which corresponds to the case of mass-proportional damping, yields modal damping that decreases linearly with frequency. The proposed model introduces a viscous "geometric" damping term in which a resisting shear force is proportional to the time rate of change of the slope. In a discretized (finite element) context, the resulting damping matrix resembles the geometric stiffness matrix used to account for the effects of membrane loads on lateral stiffness. For an illustrative example of a simply-supported beam, this model yields constant modal damping that is independent of frequency. For some boundary conditions, the corresponding mode shapes are real. These conclusions are verified through additional finite element analysis. Such a viscous damping model should prove useful to researchers and engineers who need a time-domain damping model that exhibits realistic frequency-independent damping.

UR - http://www.scopus.com/inward/record.url?scp=84855638752&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84855638752&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84855638752

SN - 9781600867422

BT - 51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference

ER -