Matrix techniques for modeling ultrasonic waves in multilayered media
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...Semi-Analytical Finite Element (SAFE) method, also referred as Spectral Finite Element (SFE) method, is a powerful technique that depicts advantages respect to the Finite Element Method and to the methods based on the superposition of bulk waves (SPBW), that include the popular matrix-based methods [1]....
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References
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"Matrix techniques for modeling ultr..." refers background or methods in this paper
...A convenient way of presenting the solutions in vector form is by the Helmholtz method [77], in which longitudinal waves are described by a scalar function and shear waves by a vector function whose direction is normal to both the direction of wave propagation and the direction of particle motion:...
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...for small-displacement dynamic behavior in ultrasonic NDE applications is the Kelvin-Voigt viscoelastic description in which a velocity-dependent damping force is added to the equation of motion for an infinitesimal element of the material [77]....
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"Matrix techniques for modeling ultr..." refers background in this paper
...The development of the equations of motion for an infinite elastic solid has been covered in many texts [ 10 ], [11], [76]....
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...It therefore includes detailed descriptions of both the Transfer Matrix method (Thomson-Haskell) and the Global Matrix method....
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...A small error in his derivation was corrected by Haskell [13]....
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...This is essentially a simple description of the Thomson-Haskell technique....
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...function [13], [14], [40], [46], [51], [61]....
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...The original Thomson-Haskell matrices describe the fields in the layers in terms of plane waves whose amplitudes are constant in all directions....
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