Vol.3, No 15, 2003 pp.1113-1120
UDC 621+534.12+534.14+534.2
Invited Paper
THE INFLUENCE OF THE NONLINEAR TEMPERATURE FIELD ON THE BEHAVIOR OF THE METALLIC PLATE INDUCED
BY TWO ELECTROMAGNETIC WAVES OBTAINED BY GSP
Vesna Milošević-Mitić, Taško Maneski
Faculty of Mechanical Engineering, University of Belgrade, 27. Marta 80, 11000 Belgrade
e-mail: vmilosevic@alfa.mas.bg.ac.yu, tmaneski@alfa.mas.bg.ac.yu
Abstract.  In the paper the behavior of the elastic metallic plate produced by two harmonic electromagnetic plane waves (one at the upper and the other at the lower surface) is considered. Direction of the propagation of the both waves is normal on the surfaces of the plate (axe x3). As a result of time-changing electromagnetic field conducting currents appear. Distribution of the power of the eddy-current losses across the plate thickness is obtained using complex calculation. It is of exponential type and depends of the plate thickness, wave frequency, electric conductivity, magnetic permeability and magnetic intensity. In further consideration that power is treated as a volume heat source. So, temperature field across the plate thickness is assumed in nonlinear form as ?(x1,x2,t)=?0(x1,x2,t)+?1(x1,x2,t)x3+?2(x1,x2,t)x32 and the system of three coupled differential equations governing temperature field is formed. Equations are solved in analytical form for the stationary state using by integral transform technique (Double Finite Fourier transform). Strain and stress fields are obtained using by FEM for several cases of support position. As the considered structure has symmetry properties, the problem is analyzed using by group supermatrix procedure in the direct stiffness method (GSP), developed by Zlokovic. Performances of GSP are compared with those of the standard finite element analysis (FEM).
Key words: electromagnetic field, temperature, plate, induction, heat, vibration, finite element
UTICAJ NELINEARNOG TEMPERATURNOG POLJA
NA PONAŠANJE METALNE PLOČE
INDUKOVANO POMOĆU DVA ELEKTROMAGNETNA TALASA
DOBIJENO POMOĆU GSP
U radu su prikazani rezultati istraživanja ponašanja elastične metalne ploče proizvedenog pomoću dva harmonijska elektromagnetna ravna talasa (jedan sa donje, a drugi sa gornje površi ploče) . Pravci prostiranja oba talasa su upravni na ravan ploče (osa x3). U rezultatu vremenske promene elektromagnetnog polja javlja se struja. Temperaturno polje je pretpostavljeno u vidu nelinearne funkcije po koordinati u pravcu debljine ploče. Ponašanje sistema je opisano pomoću sistema od tri spregnute jednačine, koje su rešene za stacionarno stanje korišćenjem integralnih transformacija (dvostrukih konačnih Fourier-ovih transformacija). Polje napona i deformacija je dobijeno korišćenjem MKE za neke slučajeve. Razmotrene su strukture koje imaju simetrična svojstva i problem je analiziran korišćenjem grupne supermatrične procedure korišćenjem GSP metode koju je razvio Zloković. Uporedjivani su rezultati dobijeni pomoću GSP kao i MKE analize.