%0 Journal Article
%T Asymptotic model of linearly visco-elastic Kelvin–Voigt type plates via Trotter theory
%+ Mahidol University [Bangkok]
%+ Centre of Excellence in Mathematics
%+ Mathématiques et Modélisations en Mécanique (M3)
%A Terapabkajornded, Yotsawat
%A Orankitjaroen, Somsak
%A Licht, Christian
%< avec comité de lecture
%@ 1687-1839
%J Advances in Difference Equations
%I Hindawi Publishin Corporation / SpringerOpen
%V 2019
%P 186
%8 2019
%D 2019
%R 10.1186/s13662-019-2104-6
%K Asymptotic model
%K Thin visco-elastic plates
%K Kelvin-Voigt visco-elasticity
%K Trotter theory
%Z MSC: 74B99
%Z Engineering Sciences [physics]/Mechanics [physics.med-ph]/Solid mechanics [physics.class-ph]Journal articles
%X We confirm the study (Licht in C. R., Méc. 341:697-700, 2013) devoted to the quasi-static response for a visco-elastic Kelvin-Voigt plate whose thickness goes to zero. For each thickness parameter, the quasi-static response is given by a system of partial differential equations with initial and boundary conditions. Reformulating scaled systems into a family of evolution equations in Hilbert spaces of possible states with finite energy, we use Trotter theory of convergence of semi-groups of linear operators to identify the asymptotic behavior of the system. The asymptotic model we obtain and the genuine one have the same structure except an occurrence of a new state variable. Eliminating the new state variable from our asymptotic model leads to the asymptotic model in (Licht in C. R., Méc. 341:697-700, 2013) which involves an integro-differential system.
%G English
%2 https://hal.science/hal-02318639/document
%2 https://hal.science/hal-02318639/file/Art_Licht_al_Advances_difference_equations_2019.pdf
%L hal-02318639
%U https://hal.science/hal-02318639
%~ CNRS
%~ LMGC
%~ MIPS
%~ UNIV-MONTPELLIER
%~ UM-2015-2021