Vol.3, No 12, 2002 pp. 405-416
UDC 539.3:539:537.61.8
TEMPERATURE, STRAIN AND STRESS FIELDS
PRODUCED BY IMPULSIV ELECTROMAGNETIC RADIATION IN THE THIN METALLIC PLATE
Vesna Milošević-Mitić
Faculty of Mechanical Engineering, University of Belgrade, 27. marta 80, Yugoslavia
Phone: +(381) 11 3370-379, e-mail: mvesna@alfa.mas.bg.ac.yu
In the paper the case of transversal vibrations of the thin elastic metallic plate produced by impulsive electromagnetic radiation at the upper surface is considered. As each electromagnetic wave can be represented as a sum of simple plane waves, an analytical solution is given for only one plane wave. It is assumed that all field quantities of the wave vary with time as exp(j?t) and are represented in the complex form. As a result of time-changing electromagnetic field conducting currents are appearing. Using complex calculation we arrive to the distribution of the power of the eddy-current losses in the plate. That power can be treated as a volume heat source. Impulsive radiation can be represented mathematically as the sum of Heaviside functions. Using integral transform technique we can solve differential equations governing temperature field, transverse vibrations and stress field. In the case when the skin depth is small compared to the plate thickness, the problem can be treated as a thermal shock problem. The power which electromagnetic wave gives to the plate can be calculated by Pointing's vector. If we want to solve some geometrically complicated problem, we have to discuss Snellius laws. Using Fresnel coefficients of reflection and transmission the power of the interrupted wave can be found as a function of an interrupted angle. The calculation (for example, for radar and air space structures) can be performed using FEM.
Key words:  electromagnetic field, temperature, plate, induction, heat, vibration, finite element.
POLJA TEMPERATURE, NAPONA I DEFORMACIJE TANKE METALNE PLOČE IZAZVANA IMPULSNIM ELEKTOMAGNETSKIM TALASOM
U radu su razmatrane poprečne vibracije tanke elastične metalne ploče izazvane delovanjem impulsnog elektromagnetskog talasa (na gornjoj površini ploče). Kako svaki elektromagnetski talas može da se prikaže kao zbir prostih ravanskih talasa, analitičko rešenje je dato samo za jedan ravanski talas. To podrazumeva da se sve karakteristike polja menjaju po eksponencijalnom zakonu exp(j?t), pa se prikazuju u kompleksnom obliku. Kao proizvod vremenski promenljivog elektromagnetskog polja pojavljuju se kondukcione struje. Primenom kompleksnog računa dolazimo do raspodele snage toplotnih gubitaka u ploči, koja se može tretirati kao zapreminski izvor toplote. Impulsni talas može se matematički prikazati preko sume Hevisajdovih funkcija. Primenom tehnike integralnih transformacija možemo rešiti diferencijalne jednačine koje opisuju polje temperature, napona i pomeranja. U slučaju kada je dubina prodiranja mala u poređenju sa debljinom ploče problem može da se tretira kao termički udar. Energija koju elektromagnetski talas predaje ploči može da se odredi pomoću Pointingovog vektora. Ako želimo da rešimo geometrijski komplikovaniji problem moramo da razmotrimo i Snelijusove zakone prelamanja. Primenom Frenelovih koeficijenata refleksije i transmisije snaga upadnog talasa može se odrediti na osnovu upadnog ugla. Račun (na primer za radare i aero strukture) može se izvesti primenom metode konačnih elemenata.