Green's function formulation of laplace's equation for electromagnetic crack detection

1999 ◽  
Vol 23 (5-6) ◽  
pp. 420-429 ◽  
Author(s):  
T. A. Cruse ◽  
A. P. Ewing ◽  
J. P. Wikswo
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Crack Detection ◽  
Laplace’S Equation ◽  
Laplace's Equation ◽  
Function Formulation

On Green’s function for Laplace’s equation in a rigid tube

2021 ◽  
Vol 80 (1) ◽  
pp. 87-98
Author(s):  
P. Martin
Keyword(s):  
Point Source ◽  
Green’S Function ◽  
Potential Theory ◽  
Green's Function ◽  
Classical Problem ◽  
Extensive Literature ◽  
Laplace’S Equation ◽  
Laplace's Equation ◽  
Rigid Tube

A classical problem from potential theory (a point source inside a long rigid tube) is revisited. It has an extensive literature but its resolution is not straightforward: standard approaches lead to divergent integrals or require the discarding of infinite constants. We show that the problem can be solved rigorously using classical methods.

A Green’s Function Formulation of Anticracks and Their Interaction With Load-Induced Singularities

1989 ◽  
Vol 56 (3) ◽  
pp. 550-555 ◽  
Author(s):  
John Dundurs ◽  
Xanthippi Markenscoff
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Edge Dislocation ◽  
Weight Functions ◽  
Bimaterial Interface ◽  
Elastic Fields ◽  
Function Formulation ◽  
Concentrated Forces ◽  
Concentrated Couple ◽  
Working Out

This paper provides a Green’s function formulation of anticracks (rigid lamellar inclusions of negligible thickness that are bonded to the surrounding elastic material). Apart from systematizing several previously known solutions, the article gives the pertinent fields for concentrated forces, dislocations, and a concentrated couple applied on the line of the anticrack. There is a reason for working out these results: In contrast to concentrated forces, a concentrated couple approaching the tip of an anticrack makes the elastic fields explode. Finite limits can be achieved, however, by appropriately diminishing the magnitude of the couple, which then leads to fields that are intimately connected with the weight functions for the anticrack. An edge dislocation going to the tip of an anticrack puts a net force on the lamellar inclusion, which is shown to be related to a previously known feature of dislocations near a bimaterial interface.

scholarly journals The effect of an enclosed air cavity on a rectangular drum

1983 ◽  
Vol 24 (3) ◽  
pp. 343-349 ◽  
Author(s):  
H. P. W. Gottlieb
Keyword(s):  
Green’S Function ◽  
Frequency Shift ◽  
Green's Function ◽  
Natural Vibration ◽  
Frequency Equation ◽  
Vibration Frequencies ◽  
Air Cavity ◽  
First Order ◽  
Degenerate Mode ◽  
Function Formulation

AbstractThe effect of an enclosed air cavity on the natural vibration frequencies of a rectangular membrane is investigated. The modes specified by an even integer are not affected. For the odd-odd modes, the frequency equation is found via a Green's function formulation and is solved to first order in a parameter representing the effect of the cavity of the rectangular drum. The frequencies are raised, with the fundamental being most affected. In the case of degeneracies, each degenerate mode contributes to the frequency shift, but the degeneracy itself is not broken to first order.

Sign in / Sign up

Export Citation Format

Share Document