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Abstract This paper investigates the propagation of longitudinal waves in some possible models of compressible Kelvin-Voigt viscoelastic solids. With respect to the elastic part two extensions of the classical neo-Hookean material model are proposed: the A-model, which incorporates a logarithmic volumetric function, and the B-model, based on the deviatoric invariants and a power-law volumetric function. For both models, we assume the same dissipative part given by the classical Navier–Stokes constitutive equation. These models are analyzed for their ability to describe a recovery phenomenon, ensuring conditions for monotonicity, boundedness, and uniqueness of solutions. The propagation of longitudinal traveling waves is proved. We show that the equation governing such motions is indeed a special case of the viscous p-system and a weakly nonlinear analysis demonstrates the emergence of Burgers’ equations.
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A NEW GOVERNING EQUATION FOR WEB TENSION BY EMPLOYING A NEO-HOOKEAN MATERIAL MODEL
In this work, we derive a governing equation for web tension in a span by employing a Neo-Hookean material model that is applicable for transport of web materials under both small and large strains. This governing equation may be employed to study the evolution of tension within a span as well as propagation of tension variations from span to span as the web is transported in the machine. First, we find the stretch in a web span and relate it to web tension via a Neo-Hookean material model; the Neo-Hookean model is linear for small strain and nonlinear otherwise. Second, we conduct a dimensional analysis by defining several key coefficients that aid in grouping the machine and web material parameters separately in order to obtain a compact system of governing equations; this representation may be utilized to efficiently study the impact of web and roller properties on transport behavior.
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- Award ID(s):
- 1635636
- PAR ID:
- 10110994
- Date Published:
- Journal Name:
- Proceedings of the Fifteenth International Conference on Web Handling
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
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