Mathematical modeling in thermomechanics of electroconductive bodies under the action of the pulsed electromagnetic fields with modulation of amplitude

2019;
: pp. 30-36
https://doi.org/10.23939/mmc2019.01.030
Received: May 02, 2019
Accepted: June 01, 2019
1
Pidstryhach Institute for Applied Problems of Mechanics and Mathematics National Academy of Sciences of Ukraine
2
Lviv Polytechnic National University

A mathematical model of description and a method for determining the thermostressed state of non-ferromagnetic electroconductive bodies under the influence of external unsteady electromagnetic fields of pulsed type are proposed.  Such fields have the character of a regime with amplitude modulation under the action of pulse modulated signal and are widely used in technologies of magnetic pulsed processing electroconductive materials.  This model is the development of well-known models for quasi-steady and pulsed electromagnetic fields.  As an example, the results of investigation of the thermomechanical behavior of solid and hollow cylinders under the influence of electromagnetic pulse are given.

  1. Batygin Yu., Lavinsky V., Khimenko L. T.  Pulsed Magnetic Fields for Advanced Technologies.  Kharkov, BRIDGE Tornado (2003), (in Russian).
  2. Shneerson G. A., Dolotenko M. I., Krivosheev S. I.  Strong and Superstrong Pulsed Magnetic Fields Generation.  De Gruyter (2010).
  3. Asai S.  Electromagnetic Processing of Materials.  Springer, Netherlands (2012).
  4. Parkinson A. H., Mullhall B. E.  The generation of high magnetic fields.  New York, Plenum Press (1967).
  5. Miura N., Herlach F.  Pulsed and ultrastrong magnetic fields.  In: Herlach F. (eds) Strong and Ultrastrong Magnetic Fields and Their Applications. Top. Appl. Phys. Vol. 57. Springer, Berlin, Heidelberg (1985).
  6. Herlach F.  Pulsed Magnets.  Rep. Prog. Phys. 62 (6), 859--920 (1999).
  7. Montgomery D. B.  Solenoid Magnet Design.  Wiley-Interscience (1969).
  8. Knoepfel H.  Pulsed High Magnetic Fields.  North-Holland Publ. (1970).
  9. Moon F. C.  Problems in magneto-solid-mechanics.  Mech. Today. 4, 307--390 (1978).
  10. Moon F. C.  Mechanics of Superconducting Structures.  New York, ASME, AMD vol. 41 (1980).
  11. Moon F. C., Chattopadhyay S.  Magnetically Induced Stress Waves in a Conduction Solid -- Theory and Experiment.  J. Appl. Mech. 41 (3), 641--646 (1974).
  12. Hachkevych O. R., Musii R. S.  Temperature fields and stress state of an electrically conductive layer under the magnetic shock on its surfaces.  In: Physicomechanical fields in deformable media.  Kiev, Naukova Dumka, 28--33 (1978), (in Russian).
  13. Hachkevych O. R., Musii R. S.  Temperature fields and thermoelastic state of electrically conductive plates under the magnetic shock.  Math. Meth. Phys. Mech. Fields. 7, 115--118 (1978), (in Russian).
  14. Ambartsumian S. A., Bagdasarian G. E., Belubekian M. V.  On the magnetoelasticity of thin shells and plates: PMM Vol. 37, N°1, 1973, pp. 114–130.  J. Appl. Math. Mech. 37 (1), 102--118 (1973).
  15. Podstrigach Ya. S., Burak Ya. Y., Hachkevych O. R., Chernyavskaya L. V.  Thermoelasticity of electrically conductive bodies.  Kiev, Naukova Dumka (1977), (in Russian).
  16. Maugin G. A.  Continuum Mechanics of Electromagnetic Solids.  North-Holland (1988).
  17. Burak Ya. Y., Gachkevich A. R., Musii R. S.  Thermoelasticity of conductive solids under the conditions of pulsed electromagnetic fields.  Matematychni Metody ta Fizyko-Mekhanichni Polya. 49 (1), 75--84 (2006), (in Ukrainian).
  18. Gachkevich A. R., Musii R. S., Tarlakovsky D. V.  Thermomechanics of Non-ferromagnetic Conductive Solids under the Action of Pulsed Electromagnetic Fields with Amplitude Modulation.  Lviv, SPOLOM (2011), (in Ukrainian).
  19. Musii R. S.  Thermal Stressed State of Conducting Cylinders Subjected to the Electromagnetic Action in the Mode with Pulsed Modulating Signals.  Materials Science. 50 (4),  496--506 (2015).
  20. Boley B. A., Weiner J. H.  Theory of Thermal Stresses.  New York, Wiley (1960).
  21. Kovalenko A. D.  Thermoelasticity: Basic Theory and Applications.  Wolters-Noordhoff Publ. (1970).
  22. Nowacki W.  Dynamic Problems of Thermoelasticity.  Springer (1975).
  23. Hetnarski R. B., Eslami M. R.  Thermal Stresses -- Advanced Theory and Applications.  Springer Netherlands (2009).
Math. Model. Comput. Vol.6, No.1, pp.30-36 (2019)