Applications of Mathematics, Vol. 69, No. 1, pp. 25-48, 2024
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
Received January 13, 2023. Published online July 21, 2023.
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.
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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Affiliations: Yotsawat Terapabkajornded, Department of Mathematics, Faculty of Science, Mahidol University, 272 Rama VI Road, Thung Phayathai, Ratchathewi, Bangkok 10400, Thailand, e-mail: ongyosawat@gmail.com; Somsak Orankitjaroen, Department of Mathematics, Faculty of Science, Mahidol University, 272 Rama VI Road, Thung Phayathai, Ratchathewi, Bangkok 10400, Thailand; Centre of Excellence in Mathematics, MHESI, 272 Rama VI Road, Faculty of Science, Mahidol University, Bangkok 10400, Thailand, e-mail: somsak.ora@mahidol.ac.th; Christian Licht, Department of Mathematics, Faculty of Science, Mahidol University, 272 Rama VI Road, Thung Phayathai, Ratchathewi, Bangkok 10400, Thailand; Centre of Excellence in Mathematics, MHESI, 272 Rama VI Road, Faculty of Science, Mahidol University, Bangkok 10400, Thailand; LMGC - UMR 5508, Université de Montpellier, cc048, 163 rue Auguste Broussonnet, 34090 Montpellier, France, e-mail: christian.licht@umontpellier.fr; Thibaut Weller (corresponding author), LMGC - UMR 5508, Université de Montpellier, cc048, 163 rue Auguste Broussonnet, 34090 Montpellier, France, e-mail: thibaut.weller@umontpellier.fr
