Geometrically exact Cosserat rods with Kelvin–Voigt type viscous damping

Linn, Joachim; Lang, Holger; Tuganov, A.

doi:10.5194/ms-4-79-2013

Cited by 64 publications

(53 citation statements)

References 49 publications

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“…The damping in the nonlinear regime is lower than in the linear regime as is reflected by the damping ratio. The behavior of the isogeometric shell is analogous to the results presented in [LLT13]. We compare the results at the steady state, where the beam also undergoes a sinusoidal deformation similar to the loading but with a phase shift.…”

Section: Beam Released After Initial Loadingsupporting

confidence: 55%

“…The example is taken from the paper on Kelvin-Voigt kinds viscoelasticity for Cosserat rods by Linn et al [LLT13]. In Fig.…”

Section: Beam Released After Initial Loadingmentioning

confidence: 99%

“…Due to its simple application, this model is often extended to introduce viscous damping in nonlinear models, see Linn et. al [LLT13]. We also use it to introduce damping in our nonlinear isogeometric shell model.…”

Section: Viscoelasticitymentioning

confidence: 99%

“…Lastly, the shell theory is extended to include the effects of dissipation in the transient analysis. This is based on the Kelvin-Voigt model for viscoelasticity, following [LLT13].…”

Section: Outline Of the Thesismentioning

confidence: 99%

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Isogeometric shell discretizations for flexible multibody dynamics

et al. 2013

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Section: Beam Released After Initial Loadingsupporting

confidence: 55%

“…The example is taken from the paper on Kelvin-Voigt kinds viscoelasticity for Cosserat rods by Linn et al [LLT13]. In Fig.…”

Section: Beam Released After Initial Loadingmentioning

confidence: 99%

Section: Viscoelasticitymentioning

confidence: 99%

“…Lastly, the shell theory is extended to include the effects of dissipation in the transient analysis. This is based on the Kelvin-Voigt model for viscoelasticity, following [LLT13].…”

Section: Outline Of the Thesismentioning

confidence: 99%

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Isogeometric shell discretizations for flexible multibody dynamics

et al. 2013

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“…where the Young modulus and the shear modulus have been replaced by the shear viscosity constants 3υ and υ, respectively, following the same procedure developed in [27] for a beam-like structure (novel analysis for the shell case is currently in progress). , which are related to the stresses of (7) through the relations: …”

Section: Constitutive Equationsmentioning

confidence: 99%

Structural Dynamics of a Pulsed-Jet Propulsion System for Underwater Soft Robots

Renda

Serchi

Boyer³

et al. 2015

International Journal of Advanced Robotic Systems

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This paper entails the study of the pulsed-jet propulsion inspired by cephalopods in the frame of underwater bioinspired robotics. This propulsion routine involves a sequence of consecutive cycles of inflation and collapse of an elastic bladder, which, in the robotics artefact developed by the authors, is enabled by a cable-driven actuation of a deformable shell composed of rubber-like materials. In the present work an all-comprehensive formulation is derived by resorting to a coupled approach that comprises of a model of the structural dynamics of the cephalopod-like elastic bladder and a model of the pulsed-jet thrust production. The bladder, or mantle, is modelled by means of geometrically exact, axisymmetric, nonlinear shell theory, which yields an accurate estimation of the forces involved in driving the deformation of the structure in water. By coupling these results with those from a standard thrust model, the behaviour of the vehicle propelling itself in water is derived. The constitutive laws of the shell are also exploited as control laws with the scope of replicating the muscle activation routine observed in cephalopods. The model is employed to test various shapes, material properties and actuation routines of the mantle. The results are compared in terms of speed performance in order to identify suitable design guidelines. Altogether, the model is tested in more than 50 configurations, eventually providing useful insight for the development of more advanced vehicles and bringing evidence of its reliability in studying the dynamics of both man-made cephalopodinspired robots and live specimens.Keywords Dynamics, Continuum Robots, Soft Robots, Biologically-Inspired Robots Nomenclature• 0 Variable in the reference configuration.• ⋅ Derivative with respect to time t.• ' Derivative with respect to X .• Converts ℝ 6 in se(3).• Converts ℝ 3 in so(3).• t ∈ ℝ Time. • X ∈ ℝ Reference arc-length parametrization.• ϕ ∈ S 1 Angle of revolution.• (e 1 ,e 2 ,e 3 ) ∈ ℝ 3 × ℝ 3 × ℝ 3 Ambient reference frame.• (e r ,e ϕ ,e 3 ) (X ,ϕ,t • (a,b, − e ϕ ) (X ,ϕ,t) Director orthogonal frame.• g(X ,ϕ,t) ∈ SE (3) Configuration matrix.• ξ(X ,t) ∈ se(3) Local deformation twist vector.• η(X ,t) ∈ se(3) Local velocity twist vector.• ] (X ,t) ∈ se(3) * Wrench vector.• R(X ,ϕ,t) ∈ SO(3) Orientation matrix.• r(X ,ϕ,t) ∈ ℝ 3 Position vector.• g(X ,t) ∈ ℝ 3 Linear strain.• k(X ,t) ∈ ℝ 3 Curvature vector.• v(X ,t) ∈ ℝ 3 Linear velocity.• w(X ,t) ∈ ℝ 3 Angular velocity vector.• c(X ,t) ∈ ℝ 3 Added mass load.• r(X ,t) ∈ ℝ 3 Radius.• z(X ,t) ∈ ℝ Altitude.• θ(X ,t) ∈ S 1 Fibre angle.• λ(X ,t) ∈ ℝ + Tangential strain.• β(X ,t) ∈ ℝ Thickness strain.• μ(X ,t) ∈ ℝ Curvature function.• v a (X ,t) ∈ ℝ Tangential velocity.• v b (X ,t) ∈ ℝ Perpendicular velocity.• w(X ,t) ∈ ℝ Angular velocity function.• N X (X ,t) ∈ ℝ Internal tangential force along a.• H (X ,t) ∈ ℝ Internal thickness force.• M X (X ,t) ∈ ℝ Internal torque along − e ϕ .• N ϕ (X ,t) ∈ ℝ Internal tangential force along − e ϕ .• M ϕ (X ,t) ∈ ℝ Internal torque along a.• f a (...

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Nonlinear finite element analysis of three‐dimensional free and harmonically forced vibrations of stranded conductor cables

Oliveto

Sivaselvan

2014

Earthq Engng Struct Dyn

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The 3D finite deformation beam model originally developed by Simo is appropriately modified to derive a finite element formulation for the static and dynamic analysis of flexible electrical conductors. In contrast to what is currently carried out in the literature, a linear viscoelastic constitutive equation and an additional mass proportional damping mechanism are introduced to account for energy dissipation in a physically consistent way. The model is used for simulation of free and forced vibration tests performed on an actual electrical conductor. Energy balance calculations illustrate the reliability of the computations. The experiments reveal amplitude dependence of both stiffness and damping, pointing out the presence of material nonlinearity in the cable. The development of numerical models that can account for the amplitude dependence of bending stiffness and energy dissipation capacity is subject of current computational and experimental work.

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Geometrically exact Cosserat rods with Kelvin–Voigt type viscous damping

Cited by 64 publications

References 49 publications

Isogeometric shell discretizations for flexible multibody dynamics

Isogeometric shell discretizations for flexible multibody dynamics

Structural Dynamics of a Pulsed-Jet Propulsion System for Underwater Soft Robots

Nonlinear finite element analysis of three‐dimensional free and harmonically forced vibrations of stranded conductor cables

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