Asymptotic modeling of the transient response of nonlinear Kelvin-Voigt viscoelastic thin plates with Norton or Tresca friction by Trotter theory

Yotsawat Terapabkajornded; Somsak Orankitjaroen; Christian Licht; Thibaut Weller

Applications of Mathematics (2024)

  • Issue: 1, page 25-48
  • ISSN: 0862-7940

Abstract

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We study the dynamic response of a thin viscoelastic plate made of a nonlinear Kelvin-Voigt material in bilateral contact with a rigid body along a part of its lateral boundary with Norton or Tresca friction. We opt for a direct use of the Trotter theory of convergence of semi-groups of operators acting on variable spaces. Depending on the various relative behaviors of the physical and geometrical data of the problem, the asymptotic analysis of its unique solution leads to different limit models whose properties are detailed. We highlight the appearance of an additional state variable that allows us to write these limit systems of equations in the same form as the genuine problem.

How to cite

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Terapabkajornded, Yotsawat, et al. "Asymptotic modeling of the transient response of nonlinear Kelvin-Voigt viscoelastic thin plates with Norton or Tresca friction by Trotter theory." Applications of Mathematics (2024): 25-48. <http://eudml.org/doc/299207>.

@article{Terapabkajornded2024,
abstract = {We study the dynamic response of a thin viscoelastic plate made of a nonlinear Kelvin-Voigt material in bilateral contact with a rigid body along a part of its lateral boundary with Norton or Tresca friction. We opt for a direct use of the Trotter theory of convergence of semi-groups of operators acting on variable spaces. Depending on the various relative behaviors of the physical and geometrical data of the problem, the asymptotic analysis of its unique solution leads to different limit models whose properties are detailed. We highlight the appearance of an additional state variable that allows us to write these limit systems of equations in the same form as the genuine problem.},
author = {Terapabkajornded, Yotsawat, Orankitjaroen, Somsak, Licht, Christian, Weller, Thibaut},
journal = {Applications of Mathematics},
keywords = {thin viscoelastic plate; Norton or Tresca friction; transient problem; multivalued operator; nonlinear semigroup of operators; Trotter's theory of convergence of semi-groups},
language = {eng},
number = {1},
pages = {25-48},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Asymptotic modeling of the transient response of nonlinear Kelvin-Voigt viscoelastic thin plates with Norton or Tresca friction by Trotter theory},
url = {http://eudml.org/doc/299207},
year = {2024},
}

TY - JOUR
AU - Terapabkajornded, Yotsawat
AU - Orankitjaroen, Somsak
AU - Licht, Christian
AU - Weller, Thibaut
TI - Asymptotic modeling of the transient response of nonlinear Kelvin-Voigt viscoelastic thin plates with Norton or Tresca friction by Trotter theory
JO - Applications of Mathematics
PY - 2024
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
IS - 1
SP - 25
EP - 48
AB - We study the dynamic response of a thin viscoelastic plate made of a nonlinear Kelvin-Voigt material in bilateral contact with a rigid body along a part of its lateral boundary with Norton or Tresca friction. We opt for a direct use of the Trotter theory of convergence of semi-groups of operators acting on variable spaces. Depending on the various relative behaviors of the physical and geometrical data of the problem, the asymptotic analysis of its unique solution leads to different limit models whose properties are detailed. We highlight the appearance of an additional state variable that allows us to write these limit systems of equations in the same form as the genuine problem.
LA - eng
KW - thin viscoelastic plate; Norton or Tresca friction; transient problem; multivalued operator; nonlinear semigroup of operators; Trotter's theory of convergence of semi-groups
UR - http://eudml.org/doc/299207
ER -

References

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