Abstract
Distribution of Joule heating and the corresponding electromagnetic field in the vicinity of the crack in a thermo- and electro-conductive thin-walled shell carrying a non-stationary electrical current is investigated. Specifically, a circular cylindrical shell with one finitely long crack that is perpendicular to the current direction is considered. The crack is free of mechanical loads. The underlying boundary-value problem is addressed via the use of Fourier series expansion and the solution reduces to that of a singular integral equation with Hilbert-type singular kernel. The influence of the presence of crack, and the effect of non-stationarity of the current on the distribution of current and Joule heating in the shell are investigated and pertinent conclusions are drawn. The results are instrumental toward crack detection and active arrest of crack propagation in structures made of electro-conductive materials or aged structure components in aerospace industry.
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