Geodesic
Asymptotic modeling of the transient response of nonlinear Kelvin-Voigt viscoelastic thin plates with Norton or Tresca friction by Trotter theory
Applications of Mathematics, Tome 69 (2024) no. 1, pp. 25-48

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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.
DOI : 10.21136/AM.2023.0013-23
Classification : 74-10
Keywords: thin viscoelastic plate; Norton or Tresca friction; transient problem; multivalued operator; nonlinear semigroup of operators; Trotter's theory of convergence of semi-groups 
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     title = {Asymptotic modeling of the transient response of nonlinear {Kelvin-Voigt} viscoelastic thin plates with {Norton} or {Tresca} friction by {Trotter} theory},
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Terapabkajornded, Yotsawat; Orankitjaroen, Somsak; Licht, Christian; Weller, Thibaut. Asymptotic modeling of the transient response of nonlinear Kelvin-Voigt viscoelastic thin plates with Norton or Tresca friction by Trotter theory. Applications of Mathematics, Tome 69 (2024) no. 1, pp. 25-48. doi: 10.21136/AM.2023.0013-23

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