Geometrically exact Cosserat rods with Kelvin-Voigt type viscous damping

Linn J, Lang H, Tuganov A (2013)

Publication Language: English

Publication Type: Journal article

Publication year: 2013

Journal

Mechanical Sciences Copernicus Publications

Publisher: Copernicus Publications

Book Volume: 4

Pages Range: 79-96

DOI: 10.5194/ms-4-79-2013

Open Access Link: http://www.mech-sci.net/4/79/2013/

Abstract

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.

Authors with CRIS profile

Holger Lang Institute of Applied Dynamics

Additional Organisation(s)

Institute of Applied Dynamics

Related research project(s)

Complex frequency response for linear viscoelastic beams of Kelvin-Voigt type Jan. 1, 2011 - June 30, 2021

Involved external institutions

Fraunhofer-Institut für Techno- und Wirtschaftsmathematik (ITWM) / Fraunhofer Institute for Industrial Mathematics DE Germany (DE)

How to cite

APA:

Linn, J., Lang, H., & Tuganov, A. (2013). Geometrically exact Cosserat rods with Kelvin-Voigt type viscous damping. Mechanical Sciences, 4, 79-96. https://doi.org/10.5194/ms-4-79-2013

MLA:

Linn, Joachim, Holger Lang, and Andrey Tuganov. "Geometrically exact Cosserat rods with Kelvin-Voigt type viscous damping." Mechanical Sciences 4 (2013): 79-96.

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