A physical and mathematical model for determining the thermostressed state of an electroconductive solid ball under the action of an amplitude modulated radioimpulse is proposed. The centrally symmetric problem of thermomechanics for the considered ball is formulated. The azimuthal component of the magnetic field strength vector, temperature, and the radial component of the displacement vector were chosen as the determining functions. To construct solutions of the formulated components of the initial-boundary value problems of electrodynamics, heat conductivity, and thermoelasticity, a polynomial approximation of the determining functions over the radial variable is used. As a result, the initial-boundary value problems on the determining functions are reduced to the corresponding Cauchy problems on the integral characteristics of these functions over the radial variable. General solutions of Cauchy problems under homogeneous nonstationary electromagnetic action are obtained. Based on these solutions, the change in time of Joule heat, ponderomotor force, temperature and stresses in the ball under the action of amplitude-modulated radioimpulse depending on its amplitude-frequency characteristics and duration is numerically analyzed.
- Podstrigach Ya. S., Burak Ya. I., Gachkevich A. R., Chernyavskaya L. V. Thermoelasticity of electrically conductive bodies. Kiev, Naukova Dumka (1977), (in Russian).
- Gachkevich A. R. Thermomechanics of electrically conductive bodies under the influence of quasi-established electromagnetic fields. Kiev, Naukova Dumka (1992), (in Russian).
- Hachkevych O. R., Drobenko B. D., Vankevych P. I., Yakovlev M. Y. Optimization of the High-Temperature Induction Treatment Modes for Nonlinear Electroconductive Bodies. Strength of Materials. 49 (3), 429–435 (2017).
- Zhuravchak L. M., Kruk O. S. Consideration of the nonlinear behavior of environmental material and a three-dimensional internal heat sources in mathematical modeling of heat conduction. Mathematical Modeling and Computing. 2 (1), 107–113 (2015).
- Hachkevych O., Musij R. Mathematical modeling in thermomechanics of electroconductive bodies under the action of the pulsed electromagnetic fields with modulation of amplitude. Mathematical Modeling and Computing. 6 (1), 30–36 (2019).
- Hachkevych O. R., Musij R. S., Tarlakovskyi D. V. The thermomechanics of nonferromagnetic conductive bodies for the actions of pulsed electromagnetic fields with amplitude modulation. Lviv, SPOLOM (2011), (in Ukranian).
- Musii R. S., Nakonechnyy A. Y. Mathematical model for temperature estimation forecasting of electrically conductive plate elements under action of pulsed electromagnetic radiation of radio-frequency range. Mathematical Modeling and Computing. 8 (1), 35–42 (2021).
- Musii R., Melnyk N., Dmytruk V., Bilyk O., Kushka B., Shayner H. Modeling and calculation of the temperature-force regime of functioning of an electrical conductive spherical sensor under the action of an amplitude-modulated radio pulse. 2019 IEEE 15th International Conference on the Experience of Designing and Application of CAD Systems (CADSM). 1–4 (2019).
- Musii R., Melnyk N., Drohomyretska K., Dmytruk V., Marikutza U., Nakonechny R. Modeling and calculation of the temperature-force regime of functioning of an electrically conductive cylindrical sensor under the pulsed electromagnetic action in the mode of the damped sinusoid. 2019 IEEE XVth International Conference on the Perspective Technologies and Methods in MEMS Design (MEMSTECH). 101–104 (2019).
- Musii R. S., Melnyk N. B., Dmytruk V. A., Zhydyk U. V. Technological forecast of bearing capacity and properties of contact connection of bimetallic hollow actionspheres under electromagnetic pulses. Mathematical Modeling and Computing. 7 (1), 79–87 (2020).
- Musii R. S., Melnyk N. B., Drohomyretska K. T., Zakaulova J. V. Thermomechanical behavior of an electrically conductive cylindrical implant under the action of external unstable electromagnetic fields. Mathematical Modeling and Computing. 8 (2), 184–191 (2021).
- Gribanov V. F. Panichkin N. G. Connected and dynamic problems of thermoelasticity. Moscow, Mashinostroenie (1984), (in Russian).
- Podstrigach Ya. S., Kolyano Yu. M. Generalized thermomechanics. Кiev, Naukova dumka (1976), (in Russian).
- Musij R. S. Dynamic problem of thermomechanics for conductive bodies of canonical form. Lviv, Rastr-7 (2010), (in Ukranian).
- Batygin Yu. V., Lavinsky V. I., Himenko L. T. Impulse magnetic fields for advanced technologies. Harkov, MOST-Tornado (2003), (in Russian).
- Gonorovsky I. S. Radio engineering circuits and signals. Moscow, Radio and communication (1986), (in Russian).