Asymptotic modeling of the transient response of nonlinear Kelvin-Voigt viscoelastic thin plates with Norton or Tresca friction by Trotter theory - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Applications of Mathematics Année : 2023

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

Résumé

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.
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Dates et versions

hal-04239227 , version 1 (12-10-2023)

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Yotsawat Terapabkajornded, Somsak Orankitjaroen, Christian Licht, Thibaut Weller. Asymptotic modeling of the transient response of nonlinear Kelvin-Voigt viscoelastic thin plates with Norton or Tresca friction by Trotter theory. Applications of Mathematics, 2023, pp.1-24. ⟨10.21136/AM.2023.0013-23⟩. ⟨hal-04239227⟩
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