# Solutions of coupled problem of thermomechanics for electroconductive hollow cylinder under non-stationary electromagnetic action

2017;
: pp. 69-77

Received: June 27, 2017
Authors:
1
Lviv Polytechnic National University
2
Lviv Polytechnic National University
3
Lviv Polytechnic National University

A plane axisymmetrical coupled dynamic problem of thermomechanics for an electroconductive hollow cylinder under homogeneous non-stationary electromagnetic action is formulated. To construct its solution, the approximation of the determining functions — the axial component of the magnetic field strength vector, the temperature, and the radial component of the displacement vector with respect to the radial variable — by cubic polynomials is used. As the result, the initial-boundary problem for determining functions is reduced to a Cauchy problem with respect to the time variable for the integral characteristics of these functions. The expressions of integral characteristics are obtained in the form of a convolution of functions describing the uniform solutions and the given limit values of determining functions. As an example, the amplitude-frequency characteristics of the radial stresses in the given cylinder are analyzed numerically, with taking into account the connectivity between the temperature and the displacement fields as well as without such accounting.

1. Batyigin Yu. V., Lavinsky V. I., Himenko L. T. Impulsnyie magnitnyie polya dlya progressivnyih tehnologij [Impulse magnetic fields for advanced technologies].  Harkov, MOST-Tornado Publ., 288 p.  (2003), (in Russian).
2. Tiermoprugost eliectroprovodnykh tiel [Thermoelasticity of conductive bodies]  J. S. Podsrigach, Y. I. Burak, A. R. Hachkevych, L. V. Chernjavska. Kyiv, Naukova dumka. (1977), (in Russian).
3. Silnye i sverhsilnye magnitnyie polia i ikh primenenie [Strong and superstrong magnetic fields and their applications]. Pod red. Herlaha F. Moscow, Mir Publ. (1988), (in Russian).
4. Knopfel G. Sverkhsilnyie impulsnyie magnitnyie polia. Metody generacii i fizicheskie effecty, sviazannyie s sozdaniem impulsnykh polej megaerstednogo diapazona [Superstrong impulse magnetic fields. Methods of generation and physical effects, connected with action of impulse fields of megaersted diapasone]. Moscow, Mir. (1972), (in Russian).
5. Tamm I. E. Osnovy teorii electrichestva [Fundamentals of electricity theory]. Moscow, Nauka. (1976), (in Russian).
6. Moon F. C. Magnetosolid mechanics. New York, Willey. (1984).
7. Gribanov V. F. Sviazannyiie i dinamicheskiie zadachi termouprugosti [Connected and dynamical problems of thermoelasticity]. Moscow, Mashynostroeniie. (1984), (in Russian).
8. Pyriev Yu. O. Poshirennia hvil u pruzhnikh seredovishchakh z urakhuvanniam sviaznosti fiziko-mekhanichnikh poliv [Wave distribution in elastic medium considering connectivity of physico-mechanical fields]. Lviv, Svit. (1988), (in Ukranian).
9. Hachkevych O. R., Musij R. S., Stasiuk H. B. Zviazana zadacha termomekhaniky dlia elektroprovidnoho sharu za odnoridnoij impulsnoij diji [Connected problem of thermomechanics for electroconductive layer  under homogeneous impulse action]. Fiz.-meckh. mekhanika materialiv. 45 (4), 60–66 (2009), (in Ukranian).
10. Musiy R. S. Dynamichni zadachi termomekhaniky electroprovidnykh til kanonichnoji formy [Dynamic problems of thermomechanics for conductive bodies of canonical form]. Lviv, Rastr-7 Publ. (2010), (in Ukranian).
11. Hachkevych O. R., Musij R. S., Tarlakovskyi D. V. Termomekhanika neferomahnitnykh elektroprovidnykh elektromakhnitnykh poliv z moduliatsiieiu amplitudy [The therrmomechanics of nonferromagnetic conductive bodies for the action of the pulse electromagnetic fields with amplitude modulation]. Lviv, SPOLOM. (2011), (in Ukranian).
12. Musij R. S., Shymchak Y. J. The methodology of investigation of resonance phenomena in nonferromagnetic electroconductive solids of canonical form under electromagnetic action with impulse modulating signal. Fizyko-matematychne modeliuvannia ta infopmatsiini tekhnolohuu [Physico-mathematical modelling and informational technologies]. 8, 113–129 (2008), (in Ukranian).
Math. Model. Comput. Vol.4, No.1, pp.69-77 (2017)