Uticaj nelinearnog temperaturnog polja na ponašanje metalne ploče indukovano pomoću dva elektromagnetna talasa dobijeno pomoću GSP
The influence of the nonlinear temperature field on the behavior of the metallic plate induced by two electromagnetic waves obtained by GSP
Апстракт
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. Upoređivani su rezultati dobijeni pomoću GSP kao i MKE analize.
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 è(x1,x2,t)= ô0(x1,x2,t) ô1(x1,x2,t)x3+ ô2(x1,x2,t)x3 2 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 integ...ral 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).
Кључне речи:
vibration / temperature / plate / induction / heat / finite element / electromagnetic fieldИзвор:
Facta universitatis - series: Mechanics, Automatic Control and Robotics, 2003, 3, 15, 1113-1120Издавач:
- Univerzitet u Nišu, Niš
Институција/група
Inovacioni centarTY - JOUR AU - Milošević-Mitić, Vesna AU - Maneski, Taško PY - 2003 UR - https://machinery.mas.bg.ac.rs/handle/123456789/376 AB - 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. Upoređivani su rezultati dobijeni pomoću GSP kao i MKE analize. AB - 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 è(x1,x2,t)= ô0(x1,x2,t) ô1(x1,x2,t)x3+ ô2(x1,x2,t)x3 2 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). PB - Univerzitet u Nišu, Niš T2 - Facta universitatis - series: Mechanics, Automatic Control and Robotics T1 - Uticaj nelinearnog temperaturnog polja na ponašanje metalne ploče indukovano pomoću dva elektromagnetna talasa dobijeno pomoću GSP T1 - The influence of the nonlinear temperature field on the behavior of the metallic plate induced by two electromagnetic waves obtained by GSP EP - 1120 IS - 15 SP - 1113 VL - 3 UR - https://hdl.handle.net/21.15107/rcub_machinery_376 ER -
@article{ author = "Milošević-Mitić, Vesna and Maneski, Taško", year = "2003", abstract = "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. Upoređivani su rezultati dobijeni pomoću GSP kao i MKE analize., 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 è(x1,x2,t)= ô0(x1,x2,t) ô1(x1,x2,t)x3+ ô2(x1,x2,t)x3 2 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).", publisher = "Univerzitet u Nišu, Niš", journal = "Facta universitatis - series: Mechanics, Automatic Control and Robotics", title = "Uticaj nelinearnog temperaturnog polja na ponašanje metalne ploče indukovano pomoću dva elektromagnetna talasa dobijeno pomoću GSP, The influence of the nonlinear temperature field on the behavior of the metallic plate induced by two electromagnetic waves obtained by GSP", pages = "1120-1113", number = "15", volume = "3", url = "https://hdl.handle.net/21.15107/rcub_machinery_376" }
Milošević-Mitić, V.,& Maneski, T.. (2003). Uticaj nelinearnog temperaturnog polja na ponašanje metalne ploče indukovano pomoću dva elektromagnetna talasa dobijeno pomoću GSP. in Facta universitatis - series: Mechanics, Automatic Control and Robotics Univerzitet u Nišu, Niš., 3(15), 1113-1120. https://hdl.handle.net/21.15107/rcub_machinery_376
Milošević-Mitić V, Maneski T. Uticaj nelinearnog temperaturnog polja na ponašanje metalne ploče indukovano pomoću dva elektromagnetna talasa dobijeno pomoću GSP. in Facta universitatis - series: Mechanics, Automatic Control and Robotics. 2003;3(15):1113-1120. https://hdl.handle.net/21.15107/rcub_machinery_376 .
Milošević-Mitić, Vesna, Maneski, Taško, "Uticaj nelinearnog temperaturnog polja na ponašanje metalne ploče indukovano pomoću dva elektromagnetna talasa dobijeno pomoću GSP" in Facta universitatis - series: Mechanics, Automatic Control and Robotics, 3, no. 15 (2003):1113-1120, https://hdl.handle.net/21.15107/rcub_machinery_376 .