Abstract
We give a brief survey of recent research on the problems of mathematical modeling of the thermomechanical behavior of deformable bodies with different electrical conductivity, magnetizability, and polarizability subject to a quasisteady electromagnetic field in the radio and infrared frequency ranges.
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Literature Cited
G. Belyaewa, V. Ya. Boichuk, and A. R. Gachkevich, “Rational regimes for induction heating of cylindrical articles for graphitation,”J. Sov. Math.,65, No. 5, 1832–1836 (1993).
A. G. Blokh, Yu. A. Zhuravlev, and L. N. Ryzhkov,Radiative Heat Transfer: A Handbook [in Russian], Energoatomizdat, Moscow (1991).
Ya. I. Burak, M. V. Antonishin, A. R. Gachkevich, V. I. Kolomiets, and M. T. Solodyak, “Mathematical modeling of the thermoelastic processes in ferromagnetic plates caused by magnetostatic waves,”Modelir. Mekh.,2(19), No. 5, 26–33 (1988).
Ya. I. Burak, A. R. Gachkevich, and M. T. Solodyak, “Thermoelasticity of electrically conducting magnetically hard bodies in external steady electromagnetic fields,”Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 5, 26–29 (1988).
Ya. I. Burak, A. R. Gachkevich, and R. F. Terletskii, “Thermomechanics of bodies of low electrical conductivity in external quasisteady electromagnetic fields,”Dokl. Adad. Nauk Ukr. SSR, Ser. A, No. 6, 39–43 (1989).
Ya. I. Burak, A. R. Gachkevich, and R. F. Terletskii, “Thermomechanics of bodies of low electrical conductivity subject to electromagnetic radiation in the infrared frequency range,”Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 7, 39–41 (1990).
A. R. Gachkevich, “Mathematical modeling of the thermomechanical behavior of electrically conducting bodies in external quasisteady electromagnetic fields,”Izv. Akad. Nauk Armen. Mekh.,44, No. 6, 17–27 (1991).
A. R. Gachkevich, “Mechanics of electrically conducting bodies during thermal processing using quasisteady electromagnetic fields,” in:Proceedings of the Seventh All-Union Congress on Theoretical and Applied Mechanics [in Russian], Govemment Printing Office, Moscow (1991), p. 98.
A. R. Gachkevich, “Determination and optimization of the thermally stressed state of electrically conducting bodies in external quasistationary electromagnetic fields,”J. Sov. Math.,67, No. 2, 2930–2934 (1993).
A. R. Gachkevich,Thermomechanics of Electrically Conducting Bodies Subject to Quasisteady Electromagnetic Fields [in Russian], Naukova Dumka, Kiev (1992).
A. R. Gachkevich, “Thermoelasticity of electrically conducting bodies subject to electromagnetic radiation in the infrared frequency range,” Preprint, Ukrainian Academy of Sciences Institute for Applied Problems of Mechanics and Mathematics, No. 10-93, L'vov (1993).
A. R. Gachkevich and V. Ya. Boichuk, “Thermomechanical behavior of nonmetallic electrical conductors during high-temperature treatment,”J. Math. Sci.,86, No. 2, 2585–2589 (1997).
A. R. Gachkevich and N. G. Gachkevich, “Optimal heating of piecewise-homogeneous shells of revolution by the environment, the inner heat sources being available,”Sov. Appl. Mech.,31, No. 11, 911–916 (1995).
A. R. Gachkevich, V. O. Drabyk, B. S. Malkiel', and R. F. Terletskii, “The thermally stressed state of the glass shell of a kinescope under heating by electromagnetic radiation,”J. Sov. Math.,65, No. 5, 1837–1840 (1993).
A. R. Gachkevich and R. S. Musii, “On the determination of the temperature and mechanical fields in electrically conducting plates subject to an external electromagnetic field,”Mat. Met. Fiz.-Mekh. Polya, No. 20, 49–54 (1984).
A. R. Gachkevich and R. S. Musii, “The thermomechanics of electrically conducting bodies subject to nonsteady electromagnetic fields,” Preprint, Ukrainian Academy of Sciences Institute for Applied Problems of Mechanics and Mathematics, No. 3-93, L'vov (1993).
A. R. Gachkevich and M. T. Solodyak, “A study of the deformation process of electrically conducting ferromagnetic bodies in harmonic external electromagnetic fields,”J. Sov. Math.,64, No. 3, 908–913 (1993).
A. R. Gachkevich and M. T. Solodyak, “Thermomechanical behavior of a layer under the influence of a harmonic electromagnetic field,”Sov. Appl. Mech.,25, No. 12, 1251–1258 (1989).
A. R. Gachkevich and R. F. Terletskii, “The thermomechanical behavior of layered systems subject to electromagnetic radiation,” in:Proceedings of the International Scientific Conference on “Engineering-Physics Problems of Aeronautical and Space Technology” [in Russian], Egor'evsk (1995), Pt. 1, 2, pp. 114–115.
A. R. Gachkevich and B. I. Chornyi, “Temperature fields and strasses in an electrically conducting plate under surface heating by a ring-shaped conductor,”J. Sov. Math.,67, No. 5, 3301–3305 (1993).
A. R. Gachkevich and M. G. Hachkevych, “Optimization of regimes for heating by the surrounding medium of piecewise-homogeneous shells of revolution in the presence of heat sources,” in:Boundary-Value Problems of Thermomechanics [in Ukrainian], Ukrainian Academy of Sciences, Kiev (1996), Pt. 1, pp. 98–102.
A. R. Gachkevich, O. M. Dzyubachyk and M. T. Solodyak, “The temperature fields and loads in magnetically soft bodies under transverse induction heating,”Visn. L'viv. Univ. Ser. Mekh.Mat. Pit. Dif. Ribn. Mat. Mod., No. 45, 36–44 (1996).
A. R. Gachkevich, Z. Kaspers'kyi, M. T. Solodyak, and R. F. Terlets'kyi, “Mathematical modeling and optimization of the physico-mechanical processes in electrically conducting bodies due to a quasisteady electromagnetic field,”J. Math. Sci.,88, No. 3, 380–385 (1998).
A. R. Gachkevich, Z. Kaspers'kyi, M. Solodyak, and R. Terlets'kyi, “Resonance phenomena in thermoelastic electrically conducting solid bodies caused by an external quasisteady electromagnetic field,” in:Boundary-Value Problems of Thermomechanics [in Ukrainian], Ukrainian Academy of Sciences Institute of Mathematics, Kiev (1996), Pt. 1, pp. 102–108.
O. Hachkevych, Z. Kaspers'kyi and R. Terlets'kyi, “Mathematical modeling of the mechanical behavior of piecewise-homogeneous electrically conducting solid bodies in an external quasisteady field,” in:Proceedings of the Third International Symposium of Ukrainian Mechanical Engineers [in Ukrainian], L'vov Polytechnic (1997), p. 2421.
O. Hachkevych, T. Kurnyts'kyi, and R. Terlets'kyi, “Thermomechanical behavior of elastic systems subject to electromagnetic radiation in the infrared range,” in:Proceedings of the Second International Symposium of Ukrainian Mechanical Engineers [in Ukrainian], L'vov Polytechnic (1995), p. 46.
O. R. Hachkevych and R. S. Musii, “The thermostressed state of an electrically conducting bar in a homogeneous quasisteady electromagnetic field,”Visn. Derzh. Univ. “L'viv Politekh.” No. 281, 7–11 (1994).
O. R. Hachkevych, M. T. Solodyak, and O. M. Dzyubachyk, “Determination of the hysteresis heat in ferrites under induction heating,”Visn. L'viv Univ. Ser. Mekh-Mat. Zad. Met. Prikl. Mat., No. 44, 97–102 (1996).
O. R. Hachkevych, R. F. Terlets'kyi, and Yu. R. Sosnovyi, “Some problems of vacuum technology of manufacture of black-and-white and color kinescopes,”Vopr. Atom. Nauki Tekh. Ser. Yadr.-Fiz. Issled. (Teor. Eksp.), No. 1(27), 47–50 (1994).
O. R. Gachkevich and B. I. Chornij, “On the determination of the parameters that describe a quasistatic electromagnetic field in an electrically conducting shell,”J. Math. Sci.,81, No. 6, 3058–3062 (1993).
R. Siegel and G. Howell,Radiative Heat Transfer [Russian translation], Mir, Moscow (1975).
G. Knopfel',Superstrong Pulsed Magnetic Fields [Russian translation], Mir, Moscow (1972).
A. D. Kovalenko,Selected Works [in Russian], Naukova Dumka, Kiev (1976).
B. A. Kudryavtsev and B. Z. Parton, “Magnetothermoelasticity,”Itogi Nauki Tekh., Ser. Mekh. Deform. Tver. Tela,4, 3–59, VINITI, Moscow (1981).
T. L. Kurnyts'kyi, “Determination of the temperature of crystal dielectrics using Monte-Carlo methods in modeling the process of heat transfer by a photon flux,” Preprint, Ukrainian Academy of Sciences Institute for Applied Problems of Mechanics and Mathematics, No. 1-96, L'viv (1996).
L. D. Landau and E. M. Lifshits,Electrodynamics of Solid Media [in Russian], Fizmatgiz, Moscow (1959).
S. Malkiel', A. R. Gachkevich, Yu. R. Sosnovyi, and R. F. Terletskii, “Temperature fields and stresses in a system of plane-parallel layers under heating by electromagnetic radiation,”J. Sov. Math.,63, No. 1, 23–27.
R. S. Musii, “The dynamic problem of electromagnetothermoelasticity for a long hollow cylinder subject to electromagnetic video pulses on its surfaces,”Teroet. Elektrotekh., No. 53, 94–102 (1996).
V. Z. Parton, B. A. Kudryavtsev, Ya. I. Burak, and A. R. Gachkevich, and V. F. Kondrat, “Thermoelasticity of electrically conducting nonferromagnetic bodies subject to external electromagnetic fields,” in: V. Z. Parton and B. A. Kudryavtsev, eds.,Elecromagnetoelasticity of Piezoelectric and Electrically Conducting Bodies [in Russian], Nauka, Moscow (1988), pp. 352–418.
Ya. S. Podstrigach, Ya. I. Burak, A. R. Gachkevich, and L. V. Chernyavskaya,Thermoelasticity of Electrically Conducting Bodies [in Russian], Naukova Dumka, Kiev (1977).
Yu. R. Sosnovyi, O. R. Hachkevych, M. H. Hachkevych, and R. F. Terlets'kyi, “Optimization of regimes of thermal processing of electrovacuum devices applying electromagnetic radiation,”Tr. Ukr. Vakuum. Obshch.,1, 317–320 (1995).
N. E. Tamm,Fundamentals of the Theory of Electricity [in Russian], Nauka, Moscow (1976).
R. F. Terletskii, “A study of thermoelastic behavior of a cylinder of low electrical conductivity in a uniform steady external electromagnetic field,”J. Math. Sci.,86, No. 2, 2590–2595 (1993).
R. F. Terletskii, “Mathematical simulation of thermomechanical processes in bodies of low electrical conductivity in an external quasistationary electromagnetic field,”J. Sov. Math.,67, No. 5, 3292–3295.
W. Bojczuk, “Model obliczeniowy stanu termosprezystego przewodnikow elektrycznych w zewnetraznym polu elektromagnetycznym,”Ziszyty naukovwe Wyzsaej Szkoly Inzynierskeij w Opulu. Budownictwo, Z. 37, 85–98 (1994).
Ya. Yo. Burak, A. R. Gachkevich, and M. T. Solodiak, “On thermomechanical processes study in electroconductive ferromagnetic solids in steady electromagnetic fields,” in:Mechanical Models of New Electromagnetic Materials: Proceedings of the UITAM Symposium in Stockholm, Elsevier, Amsterdam (1990), pp. 329–335.
A. Gaczkiewicz and Z. Kasperski, “Nieliniowy uklad rownan rozniczkowych czastkowych opisujacych stan sprezysty w termicznie czulych cialach stalych,”Zeszyty naukowe Politechniki Opolskiej, No. 230, Matematyka, Z. 14, 5–10 (1997).
A. Gaczkiewicz, Z. Kasperski and B. Czornyj, “Asymptotyczna metoda rozwiazywania zagadnien termomechaniki powlok przewodzacych przy powierzchniowym nagrzewaniu indukcyjnym,”Zeszyty maukowe Politechniki Opolskiej, No. 230, Matematyka, Z. 14, 21–29 (1997).
A. Gaczkiewicz, Z. Kasperski and R. Terlecki, “Zasady modelowania matematycznego w termomechanice cial przewodzacych przy oddzialywaniu quasi-ustalonego pola elektromagnetycznego,”Zeszty naukowe Politechniki Opolskeij, No. 230, Matematyka, Z. 14, 11–20 (1997).
A. Gachkevich, Z. Kasperski, R. Terletski, and M. Solodiak, “Mathematical modeling of resonance phenomena in electroconductive solids subjected to external quasisteady electromagnetic fields,”Zeszyty naukowe Politechniki Rzeszowskiej, No. 151, Mechanika, Z. 48. Problemy dynamiki kontrukcji,2, 47–52 (1996).
A. Gachkevich, M. Solodyak, and O. Dziubachyk, “The thermoelasticity of ferromagnetic solids by deep induction heating,” in:Proceedings of the Sixth International Conference on Mathematical Methods in Electromagnetic Theory, L'viv (1996), pp. 219–222.
A. R. Gachkevich, M. T. Solodiak, and R. E. Zamora, “Mathematical modeling of mechanical and thermal properties of ferromagnetic films in devices operating on magnetostatic waves,” inThe material research modeling: Abstr. of reports of Int. conf. “Factor '90”, L'vov (1990), pp. 73–75.
A. R. Gachkevich and R. F. Terletsky, “Heating and deformation of low-electroconductive solids under the heat treatment for use of electromagnetic radiation,” in:Heat and mass transfer in technological processes: Abstr. Of reports of Int. Conf., Latvian Science Relations Center, Jurmala (1991), pp. 225–226.
R. K. T. Hsieh, ed.,Mechanical Modeling of New Electromagnetic Materials.Proceedings of the IUTAM Symposium on the Mechanical Modeling of New Electromagnetic Materials, Stockholm, 2–6 April 1990, Elsevier, Amsterdam (1990).
F. C. Moon, “Problems in magneto-solid-mechanics,”Mechanics Today,4, 307–390 (1978).
R. Musij, “Thermostressed state of bimetallic plate under radiopulse action on its surfaces,” in:Methods and Techniques of Signal Processing in Physical Measurements. Proceedings of the Third International Seminar of Metrologists, L'vov (1995), pp. 141–148.
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Translated fromMatematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 41, No. 1, 1998, pp. 97–107.
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Hachkevych, O.R. Mathematical models of thermomechanics of magnetizable and polarizable electrically conducting bodies subject to quasisteady electromagnetic radiation. J Math Sci 97, 3846–3853 (1999). https://doi.org/10.1007/BF02364924
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DOI: https://doi.org/10.1007/BF02364924