Geometrically exact Cosserat rods with Kelvin–Voigt type viscous damping
We present the derivation of a simple viscous damping model of Kelvin–Voigt type for geometrically exact Cosserat rods from three-dimensional continuum theory. Assuming moderate curvature of the rod in its reference configuration, strains remaining small in its deformed configurations, str...
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Copernicus Publications
2013-02-01
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Series: | Mechanical Sciences |
Online Access: | http://www.mech-sci.net/4/79/2013/ms-4-79-2013.pdf |
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doaj-5277827bca0742a497f90bc9f7b05f5a2020-11-24T22:57:36ZengCopernicus PublicationsMechanical Sciences2191-91512191-916X2013-02-0141799610.5194/ms-4-79-2013Geometrically exact Cosserat rods with Kelvin–Voigt type viscous dampingJ. LinnH. LangA. TuganovWe present the derivation of a simple viscous damping model of Kelvin–Voigt type for geometrically exact Cosserat rods from three-dimensional continuum theory. Assuming moderate curvature of the rod in its reference configuration, strains remaining small in its deformed configurations, strain rates that vary slowly compared to internal relaxation processes, and a homogeneous and isotropic material, we obtain explicit formulas for the damping parameters of the model in terms of the well known stiffness parameters of the rod and the retardation time constants defined as the ratios of bulk and shear viscosities to the respective elastic moduli. We briefly discuss the range of validity of the Kelvin–Voigt model and illustrate its behaviour for large bending deformations with a numerical example.http://www.mech-sci.net/4/79/2013/ms-4-79-2013.pdf |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
J. Linn H. Lang A. Tuganov |
spellingShingle |
J. Linn H. Lang A. Tuganov Geometrically exact Cosserat rods with Kelvin–Voigt type viscous damping Mechanical Sciences |
author_facet |
J. Linn H. Lang A. Tuganov |
author_sort |
J. Linn |
title |
Geometrically exact Cosserat rods with Kelvin–Voigt type viscous damping |
title_short |
Geometrically exact Cosserat rods with Kelvin–Voigt type viscous damping |
title_full |
Geometrically exact Cosserat rods with Kelvin–Voigt type viscous damping |
title_fullStr |
Geometrically exact Cosserat rods with Kelvin–Voigt type viscous damping |
title_full_unstemmed |
Geometrically exact Cosserat rods with Kelvin–Voigt type viscous damping |
title_sort |
geometrically exact cosserat rods with kelvin–voigt type viscous damping |
publisher |
Copernicus Publications |
series |
Mechanical Sciences |
issn |
2191-9151 2191-916X |
publishDate |
2013-02-01 |
description |
We present the derivation of a simple viscous damping model of Kelvin–Voigt type for geometrically exact Cosserat rods from three-dimensional continuum theory. Assuming moderate curvature of the rod in its reference configuration, strains remaining small in its deformed configurations, strain rates that vary slowly compared to internal relaxation processes, and a homogeneous and isotropic material, we obtain explicit formulas for the damping parameters of the model in terms of the well known stiffness parameters of the rod and the retardation time constants defined as the ratios of bulk and shear viscosities to the respective elastic moduli. We briefly discuss the range of validity of the Kelvin–Voigt model and illustrate its behaviour for large bending deformations with a numerical example. |
url |
http://www.mech-sci.net/4/79/2013/ms-4-79-2013.pdf |
work_keys_str_mv |
AT jlinn geometricallyexactcosseratrodswithkelvinvoigttypeviscousdamping AT hlang geometricallyexactcosseratrodswithkelvinvoigttypeviscousdamping AT atuganov geometricallyexactcosseratrodswithkelvinvoigttypeviscousdamping |
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1725650101580333056 |