Three-dimensional eddy current problems using the T-Ω method and fredholm integral equations

1983 ◽  
Vol 19 (2) ◽  
pp. 120-125 ◽  
Author(s):  
K. Davey ◽  
W. Barnes
Keyword(s):  
Integral Equations ◽  
Eddy Current ◽  
Three Dimensional ◽  
Fredholm Integral Equations

Dynamic Analysis of a Piezoelectric Material with an Impermeable Penny-Shaped Crack under Pure Torsional Wave

2007 ◽  
Vol 345-346 ◽  
pp. 433-436
Author(s):  
Zeng Tao Chen
Keyword(s):  
Integral Equations ◽  
Three Dimensional ◽  
Integral Transforms ◽  
Hankel Transform ◽  
Fredholm Integral Equations ◽  
Dual Integral Equations ◽  
Transient Wave ◽  
Total Displacement ◽  
Penny Shaped Crack ◽  
Shaped Crack

A torsional transient wave was assumed acting at infinity on the piezoelectric body with an embedded penny-shaped crack. Appropriate governing equations and boundary conditions have been built within the three-dimensional electroelasticity. The total displacement field was simply considered as the combination of two parts, one related to incident waves inducing an oscillating motion, and another with the scattered waves. An electric impermeable crack was assumed to simplify the mathematical analysis. The problem was formulated in terms of integral transforms techniques. Hankel transform were applied to obtain the dual integral equations, which were then expressed to Fredholm integral equations of the second kind.

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