Complex eigenvalue analyses of Love and Rayleigh waves

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.

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On a technique for deriving explicit transfer matrices of orthotropic layers

Vietnam Journal of Mechanics ◽

10.15625/0866-7136/37/4/6534 ◽

2015 ◽

Vol 37 (4) ◽

pp. 303-315 ◽

Cited By ~ 1

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.

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A Finite Element Approach to the Transient Dynamics of Rolling Tires with Emphasis on Rolling Noise Simulation4

Tire Science and Technology ◽

10.2346/1.2768975 ◽

2007 ◽

Vol 35 (3) ◽

pp. 165-182 ◽

Cited By ~ 12

Author(s):

Maik Brinkmeier ◽

Udo Nackenhorst ◽

Heiner Volk

Keyword(s):

Finite Element ◽

Traffic Noise ◽

Complex Eigenvalue ◽

Arbitrary Lagrangian Eulerian ◽

Finite Element Approach ◽

Road Systems ◽

Element Approach ◽

Road Surface Roughness ◽

Complex Eigenvalue Analysis ◽

Rolling Noise

Abstract The sound radiating from rolling tires is the most important source of traffic noise in urban regions. In this contribution a detailed finite element approach for the dynamics of tire/road systems is presented with emphasis on rolling noise prediction. The analysis is split into sequential steps, namely, the nonlinear analysis of the stationary rolling problem within an arbitrary Lagrangian Eulerian framework, and a subsequent analysis of the transient dynamic response due to the excitation caused by road surface roughness. Here, a modal superposition approach is employed using complex eigenvalue analysis. Finally, the sound radiation analysis of the rolling tire/road system is performed.

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

Earthquake Science ◽

10.29382/eqs-2018-0234-3 ◽

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

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

ISTFA 2015: Conference Proceedings from the 41st International Symposium for Testing and Failure Analysis ◽

10.31399/asm.cp.istfa2015p0124 ◽

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.

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