Reflection and transmission of obliquely incident Rayleigh waves by a surface‐breaking crack

1984 ◽  
Vol 75 (2) ◽  
pp. 313-319 ◽  
Author(s):  
Y. C. Angel ◽  
J. D. Achenbach
Keyword(s):  
Rayleigh Waves ◽  
Reflection And Transmission ◽  
Obliquely Incident ◽  
Surface Breaking Crack

Reflection and transmission of obliquely incident Rayleigh waves at a vertical discontinuity between two welded quarter-spaces

1979 ◽  
Vol 69 (5) ◽  
pp. 1409-1423
Author(s):  
Thomas C. Chen ◽  
Leonard E. Alsop
Keyword(s):  
Free Surface ◽  
Phase Velocity ◽  
Rayleigh Waves ◽  
Velocity Ratio ◽  
Normal Incidence ◽  
Angle Of Incidence ◽  
Reflection And Transmission ◽  
Obliquely Incident ◽  
Vertical Boundary ◽  
Diffraction Effects

abstract We use an approximate method to study the reflection and transmission of obliquely incident Rayleigh waves on a vertical boundary between two welded quarter-spaces. For two media with a phase velocity ratio of 1.16 our calculation shows that the transmitted energy follows a reciprocity relation and decreases from near 100 per cent at normal incidence to 50 per cent at about 40°. The reflected energy is less than 1 per cent for angles of reflection less than 40°. When the Rayleigh wave impinges upon the less rigid medium, the reflected energy decreases as the angle of incidence increases; whereas for incidence at the more rigid medium, the reflected energy decreases at first, and then it increases as the angle of incidence increases. Since boundary conditions on the free surface are not taken into account by our method, diffraction effects are ignored. The effect of neglecting the free surface requirement is difficult to quantify, but we believe that it is small since the calcualted and experimental results agree well at normal incidence.

The acoustic signature for a surface-breaking crack produced by a point focus microscope

1992 ◽  
Vol 438 (1902) ◽  
pp. 47-65 ◽  
Keyword(s):  
Free Surface ◽  
Rayleigh Wave ◽  
Reflection And Transmission Coefficients ◽  
Reflection And Transmission ◽  
Acoustic Microscope ◽  
Transmission Coefficients ◽  
Acoustic Signature ◽  
Surface Breaking Crack ◽  
Line Focus ◽  
Fourier Integrals

The acoustic signature of a crack, breaking the surface of an otherwise homogeneous, isotropic elastic material, produced by a point focus scanning acoustic microscope is constructed theoretically. This work is patterned after a similar calculation carried out for the line focus microscope. The incident axisymmetric focused beam is constructed as a Fourier integral that produces a specified profile in the focal plane. The wavefields scattered from the specimen are also represented as Fourier integrals. Because the lens of the acoustic microscope is characterized by a large Fresnel number and an F number of order one, the Fourier integrals can be asymptotically approximated to obtain explicit expressions for the incident wavefield and for the wavefield scattered from a defect-free surface. The latter wavefield contains the leaky Rayleigh wave that is incident to the surface-breaking crack. The surface­-breaking crack is characterized by assigning it reflection and transmission coefficients. The wavefield scattered from the crack is estimated by tracing the leaky Rayleigh rays reflected and transmitted by the crack. The net wavefield scattered from the surface is then constructed by adding this crack scattered wavefield to that calculated for a defect-free surface. Lastly, the acoustic signature is calculated by using the appropriate incident and scattered wavefields in an electromechanical reciprocity identity that links the voltage measured at the microscope’s transducer to the scattered acoustic wavefields at the surface of the specimen. Expressions for acoustic signatures made using the line focus and point focus microscopes are compared. Moreover, from the expression for the acoustic signature, the Rayleigh wave reflection and transmission coefficients can be partly extracted.

Scattering of surface waves obliquely incident on a fixed half immersed circular cylinder

1984 ◽  
Vol 96 (2) ◽  
pp. 359-369 ◽  
Author(s):  
B. N. Mandal ◽  
S. K. Goswami
Keyword(s):  
Integral Equation ◽  
Surface Water ◽  
Circular Cylinder ◽  
Water Waves ◽  
Wave Number ◽  
Angle Of Incidence ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Obliquely Incident ◽  
Surface Water Waves

AbstractThe problem of scattering of surface water waves obliquely incident on a fixed half immersed circular cylinder is solved approximately by reducing it to the solution of an integral equation and also by the method of multipoles. For different values of the angle of incidence and the wave number the reflection and transmission coefficients obtained by both methods are evaluated numerically and represented graphically to compare the results obtained by the respective methods.

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