The vibrations and self-heating of a layered metal-polymer rectangular prism kinematically excited by a normally vibrating punch are analyzed numerically. The effect of reinforcement layers on the rate of variation in and the spatial distribution of the temperature field is examined. It is established that thin metallic layers in a polymer matrix change the dissipation mechanism from shear to bulk. The effect of contact stress concentration on the localization of temperature field is studied. It is established that the energy flux through the load application area decreases due to softening of the material. Several reinforcement effects are revealed. It is shown that they are determined by the value of the load parameter. The numerical results are in good agreement with experimental data on self-heating kinetics Keywords: viscoelastic material, vibrations, heating, layered prism Introduction. Research of the vibrations and self-heating of viscoelastic bodies is of theoretical and practical importance for the evaluation of the fatigue strength of polymer and rubber-metal members [2,5,15] and for the development of efficient polymer processes such as ultrasonic welding of plastics and their composites [3].Self-heating models for linear and nonlinear viscoelastic bodies are substantiated in numerous studies [10-12, 17, 21]; their results are systematized in [5,8,9,20]. An analysis of experimental and theoretical studies [13,17,21] shows that the thermomechanical behavior of inelastic bodies under harmonic loading is well described in terms of complex moduli [13,14,16,18]. The major results in this subject area were obtained for homogeneous viscoelastic bodies. The thermomechanical state of bodies with stress concentrators such as cylindrical inclusions and notches was studied in [6,7].Of current importance are viscoelastic laminated composites intended to sustain intensive cyclic loading. The contribution of the distortion and bulk strain energies to the stored and dissipated energies of a disk with polymer layers of different thickness under isothermal cyclic compression was assessed in [18,19]. This paper uses the theory of coupled thermoviscoelasticity [5] to study the vibrations and self-heating of a rectangular prism with polymer and metal layers under normal high-frequency load exerted by a vibrating rectangular punch. The layers are made of polyethylene and copper. The problem posed will be solved numerically, modeling the prism by a piecewise-inhomogeneous body with temperature-dependent properties.

The vibration and vibrational heating of a rectangular prism with copper and polyethylene layers is studied by solving numerically a coupled problem of thermoelasticity. The cases of kinematic and mechanical harmonic shear loads on a section of the prism surface are examined. Local heating regions are revealed. They are due to the stress fields in the neighborhood of the points at which the type of boundary conditions changes. The temperature-time curves have preresonance, resonant, and postresonance sections. The heating process reaches a steady thermal state under kinematic loading and may become avalanche-like (which is typical of thermal instability) under mechanical loading Keywords: viscoelastic material, vibrational heating, layered prism, shear loading Introduction. The vibrational heating of viscoelastic bodies is of theoretical and practical importance for the assessment of the fatigue strength of polymeric, including mechanical-rubber products [3, 5,17] and for the development of efficient polymer processes such as ultrasonic welding [4].Vibrational-heating models for linear and nonlinear viscoelastic and viscoplastic bodies are justified in numerous studies [8,13,15,19,23], their results being systematized and generalized in the monograph [5] and reviews [11,12,22]. An analysis of the experimental and theoretical studies [14,19,23] reveals that the coupled thermomechanical behavior of inelastic bodies under harmonic loading is well described with the help of the concept of complex moduli [14,16,18,20].So far, the major results on the subject have been obtained for homogeneous bodies. Some patterns of vibrational heating of bodies with stress concentrators such as holes, inclusions, or notches were studied in [6,7]. Also, of practical importance are laminated viscoelastic composites used to make products to be subjected to intensive cyclic loading. The relationship between the accumulated and dissipated distortion and dilatation energies for different thicknesses of polymeric layers in a layered disk under isothermal quasistatic compression is analyzed in [20,21].Vibration, vibrational heating, and thermal instability of a layered rectangular metal-polymer prism under normal harmonic loading are addressed in [10].Structural members and technological objects such as layered thin parts may be subject to high-frequency shear loading during ultrasonic welding. Such a loading is specific in that mainly the distortion energy is dissipated. The contribution of the dissipated dilatation energy to the total dissipated mechanical energy is insignificant.By solving a coupled problem of thermoviscoelasticity [5, 18], we will study the vibration and vibrational heating of a rectangular prism consisting of metal and polymeric layers and subjected to high-frequency kinematic and mechanical shear loading. The problem is solved numerically modeling the prism by a piecewise-nonuniform body with temperature-dependent properties.

The thermal instability of a rectangular prism under vibrational heating is studied solving a coupled problem of thermoviscoelasticity and using finite-element modeling. The prism has copper and polyethylene or polymethylmethacrylate layers and undergoes high-frequency mechanical or kinematic compression. It is established that in the case of polyethylene, thermal instability occurs under mechanical loading and does not occur under kinematic loading. In the case of polymethylmethacrylate, thermal instability occurs under both kinds of loading. This is because of the increase in the shear and bulk loss compliances with temperature for each of the polymers. At the transformation temperature, shear dissipation goes over into bulk dissipation, which is predominant in rather thin polymeric layers. Dynamicity influences the critical loads both qualitatively and quantitatively