Asymptotic analysis of the transient response of a thermoelastic assembly involving a thin layer

Abstract

We study the transient response of a thermoelastic structure made of two three-dimensional bodies connected by a thin adhesive layer. Once more we highlight the powerful flexibility of Trotter’s theory of approximation of semi-groups of operators acting on variable spaces: considering the geometrical and physical characteristics of the thin layer as parameters, we are able to show in a unitary way that this situation leads to a huge variety of limit models the properties of which are detailed. In particular, according to the relative behaviors of the different parameters involved, new features are evidenced such as the apparition of an added specific heat coefficient for the interface or of additional thermomechanical state variables defined not only on the limit geometric interface but on its cartesian product by any interval of real numbers.

Keywords

• Approximation of semi-groups in the sense of Trotter
• Bonding problems
• Linearized thermoelasticity
• Transient problems
• <i>m</i>-Dissipative operators
• Asymptotic mathematical modeling
• Approximation of semi-groups in the sense of Trotter