Surface/sub-surface crack-scattered nonlinear rayleigh waves: A full analytical solution based on elastodynamic reciprocity theorem

Ultrasonics ◽  
2022 ◽  
Vol 118 ◽  
pp. 106578
Author(s):  
Lei Xu ◽  
Kai Wang ◽  
Yiyin Su ◽  
Yi He ◽  
Jianwei Yang ◽  
...  
Keyword(s):  
Analytical Solution ◽  
Surface Crack ◽  
Rayleigh Waves ◽  
Reciprocity Theorem

Use of reciprocity theorem for obtaining Rayleigh wave radiation patterns

1966 ◽  
Vol 56 (4) ◽  
pp. 925-936 ◽  
Author(s):  
I. N. Gupta
Keyword(s):  
Rayleigh Wave ◽  
Rayleigh Waves ◽  
Three Dimensional ◽  
Reciprocity Theorem ◽  
Point Sources ◽  
Dimensional Case ◽  
Wave Radiation ◽  
Radiation Patterns ◽  
Homogeneous Half Space ◽  
Double Couple

abstract The reciprocity theorem is used to obtain Rayleigh wave radiation patterns from sources on the surface of or within an elastic semi-infinite medium. Nine elementary line sources first considered are: horizontal and vertical forces, horizontal and vertical double forces without moment, horizontal and vertical single couples, center of dilatation (two dimensional case), center of rotation, and double couple without moment. The results are extended to the three dimensional case of similar point sources in a homogeneous half space. Haskell's results for the radiation patterns of Rayleigh waves from a fault of arbitrary dip and direction of motion are reproduced in a much simpler manner. Numerical results on the effect of the depth of these sources on the Rayleigh wave amplitudes are shown for a solid having Poisson's ratio of 0.25.

scholarly journals An Approach to Size Sub-Wavelength Surface Crack Measurements Using Rayleigh Waves Based on Laser Ultrasounds

Sensors ◽  
2020 ◽  
Vol 20 (18) ◽  
pp. 5077
Author(s):  
Haiyang Li ◽  
Qianghua Pan ◽  
Xiaotong Zhang ◽  
Zhiwu An
Keyword(s):  
Theoretical Analysis ◽  
Rayleigh Wave ◽  
Surface Crack ◽  
Rayleigh Waves ◽  
Critical Frequency ◽  
Experimental Results ◽  
Notch Depth ◽  
Frequency Method ◽  
Threshold Phenomenon ◽  
Sub Wavelength

In this paper, the interaction of a broadband Rayleigh wave generated by a laser and an artificial rectangular notch is analyzed theoretically and experimentally. For the theoretical analysis, a Gaussian function is adopted to analyze the modulation of notch depth on the frequency spectrum via reflection and transmission coefficients. By the finite element method, the Rayleigh wave generated by pulsed laser beam irradiation and its scattering waves at cracks are calculated. A curve with a slope close to 4 fitted by crack depth and critical wavelength of the threshold phenomenon is obtained by the wavelet transform and Parseval’s theorem according to simulated and experimental results. Based on this relationship, the critical frequency at which the threshold phenomenon happens due to energy transformation of transmission/reflection Rayleigh waves is adopted to determine the size of sub-wavelength surface crack. The experimental results of artificial notch depth estimation on aluminum alloy specimens consistent with theoretical analysis validates the usefulness of the critical frequency method based on a broadband Rayleigh wave generated by laser ultrasonic.

scholarly journals Investigation of Beam Features of Unidirectional Rayleigh Waves Electromagnetic Acoustic Transducers (EMATs) by a Wholly Analytical Solution

2020 ◽  
Author(s):  
Yuedong Xie ◽  
Wuliang Yin ◽  
Lijun Xu
Keyword(s):  
Analytical Solution ◽  
Analytical Model ◽  
Lorentz Force ◽  
Rayleigh Waves ◽  
Force Distribution ◽  
Design And Optimization ◽  
Electromagnetic Acoustic Transducers ◽  
Displacement Distribution ◽  
Acoustic Transducers ◽  
Beam Directivity

Electromagnetic acoustic transducers (EMATs) are widely used in industries due to its non-contact nature. This paper investigates the beam features of unidirectional Rayleigh waves EMATs, especially the effect of the wire length on beam directivity. A wholly analytical model is developed to calculate the Lorentz force distribution and ultrasound displacement distribution. The modelling results indicate that, compared to the coil consists of shorter wires, the coil consists of longer wires results in a narrower bandwidth of main lobe of unidirectional Rayleigh waves, which means the ultrasound are more concentrated. This study can be used for unidirectional Rayleigh waves EMATs design and optimization.

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