The vibrations and self-heating of a viscoelastic prism with a cylindrical inclusion under harmonic loading are studied through numerical simulation. The effects of the stiffness of the inclusion and the mechanical and kinematic types of loading on kinetics, spatial temperature distribution, and thermal instability parameters are examined Keywords: viscoelastic material, vibrations heating, rectangular prism, cylindrical inclusion Introduction. Intensive vibrations of viscoelastic bodies are generally accompanied by vibrational heating, which is because of the conversion of mechanical energy into heat. Heating can noticeably reduce the performance and life of structural members such as rubber shock absorbers, solid-propellant engines [11,26], etc. Also, vibrational heating is a crucial factor for some high-intensity processes such as ultrasonic plastic welding [7][8][9]. The stationary vibrations and vibrational heating of linear viscoelastic bodies were studied and associated models were validated in [20][21][22]. The results obtained there were generalized in [2,11,[16][17][18][19]25]. The cited publications employed the concept of complex moduli, which was convincingly substantiated, both experimentally and theoretically, during the early development of the theory of linear thermoviscoelasticity in [1, 12, 14, 15, etc.].One of the special features of vibrational heating is the effect of thermal instability. It manifests itself as abrupt increase in temperature and leads to thermal fatigue failure of structural members [6,14,15,26]. Relevant results are reviewed in [3,4,16,18,19,23].Fracture usually sets in near stress concentrators. It is these areas that become sources of vibrational heating. Such processes in bodies with cylindrical inclusions under compressive and shear loading of kinematic type were studied in [8,9]. Vibrational heating in laminated prisms acted upon by a vibrating punch was addressed in [13,16].Intensive high-frequency loading of a rectangular prism with an inclusion produces a number of specific effects. The major effect is concentration of stress, dissipation rate, and temperature. It was established that the level of vibrational heating is strongly dependent on the type of loading and the stiffness of the inclusion.The present paper studies the kinetics of vibrational heating and thermal instability of a rectangular prism with an inclusion under harmonic compressive loading of mechanical type. We will compare the mechanical and kinematic types of excitation and examine the cases of rigid and soft inclusion.

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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.