Thermoviscoelastic model of a layer between two bodies and conditions of their conjugation
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THERMOVISCOELASTIC MODEL OF A LAYER BETWEEN TWO BODIES AND CONDITIONS OF THEIR CONJUGATION I. S. Skorodyns’kyi
UDC 539.37
On the basis of the Kelvin–Voigt-type thermomechanical theory of viscoelasticity, by the method of averaging over the thickness, we develop a thermoviscoelastic model of thin intermediate layer and establish generalized Winkler-type thermomechanical conjugation conditions for solid bodies in the dynamical mode for the case of imperfect thermal contact. It is shown that these conditions can be regarded as a generalization of the classical model. Relations convenient for practical applications are deduced. Various classical conditions of thermomechanical contact and their generalizations are obtained as a result of the limiting transition performed under additional assumptions concerning the moduli of elasticity of the intermediate layer.
Glue joints, sealing gaskets, thin heat insulators, and vibration dampers are used more and more extensively in contemporary machines and structures. As a result, the mechanical and thermal contact between solid bodies is often realized through thin intermediate (adhesive) layers and inclusions with their own physicomechanical properties and characteristics [1–11]. Thus, it is necessary to develop complex models of contact interaction of the bodies taking into account intermediate (adhesive) layers and capable of describing the interface defects and contact phenomena, such as sliding, nonthrough cracks in the region of contact, intercontact gaps [12], etc. In this case, it is reasonable to exclude the intermediate layers from consideration due to their small thickness as compared with the sizes of the conjugated bodies. In [6, 8], the conditions of imperfect thermal contact were obtained within the framework of the classical theory of heat conduction. These conditions take into account the contact thermal conductivity (thermal resistance), reduced heat capacity of the intermediate layer, and heat conduction in the tangential direction. Later [7], this approach was generalized by taking into account thermal inertia, and the mechanical conjugation conditions (through a thin isotropic elastic inclusion in the unbounded continuous medium) were deduced [5]. Further, the conditions of interface contact through a thin elastic anisotropic layer and the corresponding relations for layered structures were obtained by the variational method in [4]. For interlayers inhomogeneous over the thickness whose temperature and displacements vary across the thickness according to the cubic law, this approach was developed in [2, 3]. An important role in the investigation of contact problems is played by the Winkler-type bases and coatings. These models of elastic interlayers in the normal and tangential directions are used, in particular, in [1, 9]. Moreover, in [1], one can find the solutions of some contact problems for thin viscoelastic coatings with nonlinear aging obtained by using the nonlinear Winkler-type models. Recently, a one-dimensional Maxwell-type model of thin visco
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