Kelvin–Voigt versus Bürgers internal damping in modeling of axially moving viscoelastic web

Marynowski, Krzysztof; Kapitaniak, Tomasz

doi:10.1016/s0020-7462(01)00142-1

Cited by 128 publications

(76 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The deformation of an elastic material depends only on the applied forces; it has no explicit time dependence. Paper, however, is a more compli- Marynowski and Kapitaniak (2002) and Lee and Oh (2005), but using the partial time derivative in the viscoelastic constitutive relations.…”

Section: Introductionmentioning

confidence: 99%

Mechanics of Moving Materials

Баничук¹,

Jeronen²,

Neittaanmäki³

et al. 2014

Solid Mechanics and Its Applications

View full text Add to dashboard Cite

PrefaceMechanics of moving materials is currently attracting considerable attention.Interest in research in the eld has grown in connection with the rapid development of process industry and precision machinery, especially in the eld of paper making.Specialized areas of investigation include dynamics and mechanical stability of travelling elastic materials, failure and reliability analysis, including modern fracture mechanics, and runnability optimization problems taking into account factors of uncertainty and incomplete data.Problems of mechanics of moving materials have not only practical but also theoretical importance. The investigation into new types of mathematical problems is interesting in itself. It is noteworthy that there are some nonconservative stability problems, and runnability optimization problems under fracture and stability constraints with uncertainties in positioning and sizes of initial defects (cracks), for which there are no systematic techniques of investigation. The most appropriate approach to tackle the complex problem varies depending on the case.This monograph is devoted to the exposition of new ways of formulating and solving problems of mechanics of moving materials. We present some research results concerning dynamics of travelling elastic strings, membranes, panels and plates. We study mechanical stability of axially moving elastic panels, accounting for the interaction between the structural element and its environment, such as axial potential ow. Most of the attention in this book is devoted to out-of-plane dynamics and stability analysis for isotropic and orthotropic travelling elastic and viscoelastic materials, with and without uid-structure interaction, using analytical and numerical approaches. Also such topics as fracture and fatigue are discussed in the context of moving materials. The last part of the book deals with some runnability optimization problems with physical constraints arising from the stability and fatigue analyses including uncertainties in the parameters. The approach taken in this monograph is to proceed analytically as far as is reasonable, and only then nish the investigation numerically.In this book, we oer a systematic and careful development of many aspects of mechanics of travelling materials, particularly for panels and plates.Some of the presented results are new, and some have appeared only in specialized journals or in conference proceedings. Some aspects of the theory presented here, such as the semi-analytical treatment of the uidstructure interaction problem of a travelling panel, studies of spectral problems with free boundary singularities, and optimization of problem parameters under crack growth and instability constraints have not been considered before to any extent.Important new results relate to optimization of runnability with a longevity constraint. Damage accumulation is modelled using the theory of fatigue crack growth, with the travelling material element subjected to cyclic load-3 ing. Uncertainties must be accounted for, beca...

show abstract

Section: Introductionmentioning

confidence: 99%

Mechanics of Moving Materials

Баничук¹,

Jeronen²,

Neittaanmäki³

et al. 2014

Solid Mechanics and Its Applications

View full text Add to dashboard Cite

show abstract

“…However, (Mochensturm & Guo, 2005) convincingly argued that the Kelvin model generalized to axially moving materials should contain the material time derivative to account for the added "steady state" dissipation of an axially moving viscoelastic string. Actually the material time derivative was also used in other works on axially moving viscoelastic beams (Marynowski, 2002(Marynowski, , 2004(Marynowski, , 2006, (Marynowski & Kapitaniak, 2002, , , , ) and . Here a coordinate transform will be proposed to develop the governing equations, which can introduce naturally the material time derivative in the viscoelastic constitutive relations.…”

Section: Governing Equations 21 Coupled Vibrationmentioning

confidence: 99%

“…The Galerkin discretization is not only the priority of discretization-perturbations reviewed in Subsection 3.2, but also feasible approach to numerical solutions. Using the 3 order Galerkin discretization of governing equation (in the type of equation (18)) for transverse motion of axially moving viscoelastic beams excited by the changing tension, (Marynowski, 2002) and (Marynowski & Kapitaniak, 2002) numerically investigated the effects of different viscoelastic models, such as the Kelvin model, the Maxwell model, and the standard linear solid model, on the dynamic response and found that different viscoelastic models yield very close numerical results for small damping. The Galerkin procedure has been mainly use to calculate long time nonlinear dynamical behaviors, which will be addressed in Subsection 5.1.…”

Section: Galerkin Proceduresmentioning

confidence: 99%

Nonlinear Vibrations of Axially Moving Beams

Chen¹

2010

Nonlinear Dynamics

View full text Add to dashboard Cite

“…They found out that both models gave accurate results with small damping coefficients, but with a large damping coefficient, the Burgers model was more accurate [44]. In 2007, they compared the models with the Zener model studying the dynamic behaviour of an axially moving viscoelastic beam [45].…”

Section: Introductionmentioning

confidence: 99%

The origin of in-plane stresses in axially moving orthotropic continua

Kurki

Jeronen

Saksa

et al. 2016

International Journal of Solids and Structures

View full text Add to dashboard Cite

Highlights• In-plane motion of an axially travelling orthotropic sheet was modelled• Velocity difference between supports generates strain due to mass conservation• In a travelling viscoelastic material the axial strain varies along the length• Small deformations of free edges due to the Poisson effect affect the velocity• Inertial effects lead to additional cross-directional contraction AbstractIn this paper, we address the problem of the origin of in-plane stresses in continuous, two-dimensional high-speed webs. In the case of thin, slender webs, a typical modeling approach is the application of a stationary in-plane model, without considering the effects of the in-plane velocity field. However, for high-speed webs this approach is insufficient, because it neglects the coupling between the total material velocity and the deformation experienced by the material. By using a mixed Lagrange-Euler approach in model derivation, the solid continuum problem can be transformed into a solid continuum flow problem. Mass conservation in the flow problem, and the behaviour of free edges in the two-dimensional case, are both seen to influence the velocity field. We concentrate on solutions of a steady-state type, and study briefly the coupled nature of material viscoelasticity and transport velocity in one dimension. Analytical solutions of the one-dimensional equation are presented with both elastic and viscoelastic material models. The two-dimensional elastic problem is solved numerically using a nonlinear finite element procedure. An important new fundamental feature of the model is the coupling of the driving velocity field to the deformation of the material, while accounting for small deformations of the free edges. The results indicate that inertial effects produce an additional contribution to elastic contraction in unsupported, free webs.

show abstract

Kelvin–Voigt versus Bürgers internal damping in modeling of axially moving viscoelastic web

Cited by 128 publications

References 18 publications

Mechanics of Moving Materials

Mechanics of Moving Materials

Nonlinear Vibrations of Axially Moving Beams

The origin of in-plane stresses in axially moving orthotropic continua

Contact Info

Product

Resources

About