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.
