Near-field effects in Green's function retrieval from cross-correlation of elastic fields: Experimental study with application to elastography

2013 ◽  
Vol 133 (5) ◽  
pp. 2755-2766 ◽  
Author(s):  
N. Benech ◽  
J. Brum ◽  
S. Catheline ◽  
T. Gallot ◽  
C. Negreira
Keyword(s):  
Experimental Study ◽  
Green’S Function ◽  
Green's Function ◽  
Cross Correlation ◽  
Near Field ◽  
Elastic Fields ◽  
Field Effects

Experimental study of the convergence of two‐point cross‐correlation toward the Green's Function

2008 ◽  
Vol 123 (5) ◽  
pp. 3842-3842
Author(s):  
Pierre Gouedard ◽  
Philippe Roux ◽  
Michel Campillo ◽  
Arie Verdel ◽  
Xander Campman
Keyword(s):  
Experimental Study ◽  
Green’S Function ◽  
Green's Function ◽  
Cross Correlation

The breakdown of the linearized theory and the role of quadrupole sources in transonic rotor acoustics

1991 ◽  
Vol 226 ◽  
pp. 591-624 ◽  
Author(s):  
H. Ardavan
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Impulsive Noise ◽  
Near Field ◽  
Point Of View ◽  
Rotating Frame ◽  
Homogeneous Wave ◽  
Linearized Theory ◽  
Near Field Sound ◽  
Rotor Acoustics

The retarded Green's function for the linearized version of the equation of the mixed type governing the potential flow around a rotating helicopter blade or a propeller (with no forward motion) is derived and is shown to constitute the unifying feature of the various existing approaches to rotor acoustics. This Green's function is then used to pinpoint the singularity predicted by the linearized theory of rotor acoustics which signals its experimentally confirmed breakdown in the transonic regime: the gradient of the near-field sound amplitude, associated with a linear flow which is steady in the blade-fixed rotating frame, diverges on the sonic cylinder at the dividing boundary between the subsonic and supersonic regions of the flow. Prom the point of view of the equivalent Cauchy problem for the homogeneous wave equation, this singularity is caused by the imposition of entirely non-characteristic initial data on a space—time hypersurface which, at its points of intersection with the sonic cylinder, is locally characteristic. It also emerges from the analysis presented that the acoustic discontinuities detected in the far zone are generated by the quadrupole source term in the Ffowcs Williams-Hawkings equation and that the impulsive noise resulting from these discontinuities would be removed if the flow in the transonic region were to be rendered unsteady (as viewed from the blade-fixed rotating frame).

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.

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