Abstract
We study the transient response of a thermoelastic structure made of two tridimensional 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.
Highlights
We pursue our investigations on thin junctions initiated in [1,2], further developed in [3,4,5,6,7,8,9,10,11], and hereafter consider the situation of a transient multi-physical coupling within the scope of linear thermoelasticity
The interested reader will find good presentations of this theory in classical textbooks such as [13, 14], while Trotter’s fundamental contribution [15] is presented and harnessed in various physical applications in [16]. More recently this theory has been the subject of a revival because of the large number of problems it can address. The power of this method will appear in three ways: first, despite the large number of parameters involved, we are able to carry out a rigorous mathematical study of this transient problem in a unitary manner (Section 2); second, this unitary study reveals a very wide variety of limit models (Section 3); third, we are able to extract new thermomechanical features from our models, such as the appearance of an additional specific heat coefficient for the interface or additional state variables (Section 4)
We study the dynamic response of a linearly thermoelastic structure consisting of two adhering bodies connected by a thin adhesive layer and subjected to a given loading
Summary
We pursue our investigations on thin junctions initiated in [1,2], further developed in [3,4,5,6,7,8,9,10,11], and hereafter consider the situation of a transient multi-physical coupling within the scope of linear thermoelasticity. The interested reader will find good presentations of this theory in classical textbooks such as [13, 14], while Trotter’s fundamental contribution [15] is presented and harnessed in various physical applications in [16] More recently this theory has been the subject of a revival (see [17]) because of the large number of problems it can address. We study the dynamic response of a linearly thermoelastic structure consisting of two adhering bodies connected by a thin adhesive layer and subjected to a given loading. Let ε be a positive number and Ω± := Ω ∩ {±x3 > 0}, the adhesive and the adhering bodies occupy Bε := S ×
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