Ray Method for Rayleigh Waves

Elastic Waves ◽  
2018 ◽  
pp. 247-271
Author(s):  
Vassily M. Babich ◽  
Aleksei P. Kiselev
Keyword(s):  
Rayleigh Waves ◽  
Ray Method

Phase Transformations in Ti-7w/oMo-3w/oMe Alloy

1974 ◽  
Vol 32 ◽  
pp. 514-515
Author(s):  
S. Fujishiro
Keyword(s):  
Electron Microscopy ◽  
Mechanical Properties ◽  
Transmission Electron Microscopy ◽  
Tensile Strength ◽  
Mechanical Processing ◽  
Ray Method ◽  
X Ray ◽  
Transmission Electron ◽  
Water Quench ◽  
Alpha Beta

The mechanical properties of three titanium alloys (Ti-7Mo-3Al, Ti-7Mo- 3Cu and Ti-7Mo-3Ta) were evaluated as function of: 1) Solutionizing in the beta field and aging, 2) Thermal Mechanical Processing in the beta field and aging, 3) Solutionizing in the alpha + beta field and aging. The samples were isothermally aged in the temperature range 300° to 700*C for 4 to 24 hours, followed by a water quench. Transmission electron microscopy and X-ray method were used to identify the phase formed. All three alloys solutionized at 1050°C (beta field) transformed to martensitic alpha (alpha prime) upon being water quenched. Despite this heavily strained alpha prime, which is characterized by microtwins the tensile strength of the as-quenched alloys is relatively low and the elongation is as high as 30%.

Method of first integrals and interface, surface waves

2010 ◽  
Vol 32 (2) ◽  
pp. 107-120
Author(s):  
Pham Chi Vinh ◽  
Trinh Thi Thanh Hue ◽  
Dinh Van Quang ◽  
Nguyen Thi Khanh Linh ◽  
Nguyen Thi Nam
Keyword(s):  
Rayleigh Waves ◽  
Displacement Vector ◽  
Attenuation Factor ◽  
Electrical Potential ◽  
Polarization Vector ◽  
First Integrals ◽  
Dispersion Equations ◽  
Interface Surface ◽  
Electric Induction ◽  
The One

The method of first integrals (MFI) based on the equation of motion for the displacement vector, or  based on the one for the traction vector was introduced  recently in order to find explicit secular equations of Rayleigh waves whose characteristic equations (i.e the equations determining the attenuation factor) are fully quartic or are of higher order (then the classical approach is not applicable). In this paper it is shown that, not only to Rayleigh waves,  the MFI can be applicable also to other waves by running it on the equations for mixed vectors. In particular: (i) By applying the MFI  to the equations for the displacement-traction vector we get the explicit dispersion equations of Stoneley waves in twinned crystals (ii)  Running the MFI on the equations for the traction-electric induction vector and the traction-electrical potential vector provides the explicit dispersion equations of SH-waves in piezoelastic materials. The obtained dispersion equations are identical with the ones previously derived using the method of polarization vector, but the procedure of driving them is more simple.

On a technique for deriving explicit transfer matrices of orthotropic layers

2015 ◽  
Vol 37 (4) ◽  
pp. 303-315 ◽  
Author(s):  
Pham Chi Vinh ◽  
Nguyen Thi Khanh Linh ◽  
Vu Thi Ngoc Anh
Keyword(s):  
Wave Propagation ◽  
Explicit Form ◽  
Half Space ◽  
Transfer Matrix ◽  
Rayleigh Waves ◽  
Secular Equation ◽  
Transfer Matrices ◽  
Orthotropic Layer ◽  
Wave Propagation Problem ◽  
Arbitrary Thickness

This paper presents  a technique by which the transfer matrix in explicit form of an orthotropic layer can be easily obtained. This transfer matrix is applicable for both the wave propagation problem and the reflection/transmission problem. The obtained transfer matrix is then employed to derive the explicit secular equation of Rayleigh waves propagating in an orthotropic half-space coated by an orthotropic layer of arbitrary thickness.

Phase velocity maps of Rayleigh waves in the Ordos block and adjacent regions

2018 ◽  
Vol 31 (5-6) ◽  
pp. 234-241
Author(s):  
Shaoxing Hui ◽  
◽  
Wenhua Yan ◽  
Yifei Xu ◽  
Liping Fan ◽  
...  
Keyword(s):  
Phase Velocity ◽  
Rayleigh Waves ◽  
Ordos Block

Failure and Stress Analysis of Cu TSVs Using GHz-Scanning Acoustic Microscopy and Scanning Infrared Polariscopy

2015 ◽  
Author(s):  
Ingrid De Wolf ◽  
Ahmad Khaled ◽  
Martin Herms ◽  
Matthias Wagner ◽  
Tatjana Djuric ◽  
...  
Keyword(s):  
Failure Analysis ◽  
Stress Analysis ◽  
Rayleigh Waves ◽  
Acoustic Microscopy ◽  
Scanning Acoustic Microscopy ◽  
Through Silicon Vias ◽  
Stress Anisotropy ◽  
Silicon Vias ◽  
Ic Technology ◽  
Detection Of Defects

Abstract This paper discusses the application of two different techniques for failure analysis of Cu through-silicon vias (TSVs), used in 3D stacked-IC technology. The first technique is GHz Scanning Acoustic Microscopy (GHz- SAM), which not only allows detection of defects like voids, cracks and delamination, but also the visualization of Rayleigh waves. GHz-SAM can provide information on voids, delamination and possibly stress near the TSVs. The second is a reflection-based photoelastic technique (SIREX), which is shown to be very sensitive to stress anisotropy in the Si near TSVs and as such also to any defect affecting this stress, such as delamination and large voids.

Rayleigh waves in locally resonant metamaterials

2021 ◽  
Vol 195 ◽  
pp. 106250
Author(s):  
Farhad Zeighami ◽  
Antonio Palermo ◽  
Alessandro Marzani
Keyword(s):  
Rayleigh Waves

Specific Features of Material Recognition by the Multi-Energy X-Ray Method

2019 ◽  
Vol 55 (4) ◽  
pp. 308-321 ◽  
Author(s):  
S. P. Osipov ◽  
E. Yu. Usachev ◽  
S. V. Chakhlov ◽  
S. A. Shchetinkin ◽  
O. S. Osipov
Keyword(s):  
Ray Method ◽  
X Ray ◽  
Material Recognition
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