Diffractions of Elastic Waves and Stress Concentration Near a Cylindrical Nano-Inclusion Incorporating Surface Effect

2009 ◽  
Vol 131 (6) ◽  
Author(s):  
Y. Ru ◽  
G. F. Wang ◽  
T. J. Wang
Keyword(s):  
Stress Concentration ◽  
Elastic Waves ◽  
Surface Effect ◽  
Potential Method ◽  
P Wave ◽  
Compressional Waves ◽  
Displacement Potential ◽  
Elastic Fields ◽  
P And Sv Waves ◽  
Incident Waves

The diffractions of plane compressional waves (P-wave) and shear waves (SV-wave) by a cylindrical nano-inclusion are investigated in this paper. To account for the surface/interface effect at nanoscale, the surface/interface elasticity theory is adopted in the analysis. Using the displacement potential method, we obtain the solutions for the elastic fields induced by incident P- and SV-waves near a cylindrical nano-inclusion. The results show that surface/interface has a significant effect on the diffractions of elastic waves as the radius of the inclusion shrinks to nanoscale. For incident waves with different frequencies, the effects of interfacial properties on the dynamic stress concentration around the nano-inclusion are discussed in detail.

scholarly journals Surface Effect on Diffractions of Elastic Waves and Stress Concentration near a Cluster of Cylindrical Nanoholes Arranged as Quadrate Shape

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Ru Yan
Keyword(s):  
Stress Concentration ◽  
Multiple Scattering ◽  
Elastic Waves ◽  
Surface Effect ◽  
Surface Elasticity ◽  
Expansion Method ◽  
Potential Method ◽  
P Wave ◽  
Displacement Potential ◽  
P And Sv Waves

We consider the multiple scattering of elastic waves (P-wave and SV-wave) by a cluster of nanosized cylindrical holes arranged as quadrate shape. When the radius of the holes shrinks to nanometers, the surface elasticity theory is adopted in analysis. Using the displacement potential method and wave functions expansion method, we obtain that the multiple scattering fields induced by incident P- and SV-waves around the holes are derived. The dynamic stress concentration around the holes is calculated to illustrate the effect of surface effects on the multiple scattering of P- and SV-waves.

scholarly journals Study on the Single Scattering of Elastic Waves by a Cylindrical Fiber with a Partially Imperfect Bonding Using the Collocation Point Method

2018 ◽  
Vol 2018 ◽  
pp. 1-14
Author(s):  
Jun Zhang ◽  
Longhai Zeng ◽  
Chuanlin Hu ◽  
Wensheng Yan
Keyword(s):  
Elastic Waves ◽  
Collocation Point ◽  
Single Scattering ◽  
Imperfect Interface ◽  
P Wave ◽  
Imperfect Bonding ◽  
Imperfect Interfaces ◽  
Cylindrical Fiber ◽  
P And Sv Waves ◽  
Wave Incidence

The single scattering of P- and SV-waves by a cylindrical fiber with a partially imperfect bonding to the surrounding matrix is investigated, which benefits the characterization of the behavior of elastic waves in composite materials. The imperfect interface is modelled by the spring model. To solve the corresponding single scattering problem, a collocation point (CP) method is introduced. Based on this method, influence of various aspects of the imperfect interface on the scattering of P- and SV-waves is studied. Results indicate that (i) the total scattering cross section (SCS) is almost symmetric about the axis α=π/2 with respect to the location (α) of the imperfect interface, (ii) imperfect interfaces located at α=0 and α=π highly reduce the total SCS under a P-wave incidence and imperfect interfaces located at α=π/2 reduce the total SCS most significantly under SV-incidence, and (iii) under a P-wave incidence the SCS has a high sensitivity to the bonding level of imperfect interfaces when α is small, while it becomes more sensitive to the bonding level when α is larger under SV-wave incidence.

scholarly journals Vertical to Horizontal Spectral Ratio (VHSR) Response of Seismic Wave Propagation in a Homogeneous Elastic – Poroelastic Medium Using The Spectral Finite Element Method

2021 ◽  
Vol 11 (1) ◽  
pp. 95
Author(s):  
Sudarmaji Saroji ◽  
Budi Eka Nurcahya ◽  
Nivan Ramadhan Sugiantoro
Keyword(s):  
Finite Element Method ◽  
Elastic Medium ◽  
Seismic Waves ◽  
Low Frequency ◽  
Seismic Wave Propagation ◽  
P Wave ◽  
Poroelastic Medium ◽  
Compressional Waves ◽  
Spectral Finite Element Method ◽  
Spectral Finite Element

<p>Numerical modeling of 2D seismic wave propagation using spectral finite element method to estimate the response of seismic waves passing through the poroelastic medium from a hydrocarbon reservoir has been carried out. A hybrid simple model of the elastic - poroelastic - elastic with a mesoscopic scale element size of about 50cm was created. Seismic waves which was in the form of the ricker function are generated on the first elastic medium, propagated into the poroelastic medium and then transmitted to the second elastic medium. Pororoelastic medium is bearing hydrocarbon fluid in the form of gas, oil or water. Vertical and horizontal component of velocity seismograms are recorded on all mediums. Seismograms which are recorded in the poroelastic and second elastic medium show the existence of slow P compressional waves following fast P compressional waves that do not appear on the seismogram of the first elastic medium. The slow P wave is generated when the fast P wave enters the interface of the elastic - poroelastic boundary, propagated in the poroelastic medium and is transmited to the second elastic medium. The curves of Vertical to horizontal spectrum ratio (VHSR) which are observed from seismograms recorded in the poroelastic and the second elastic medium show that the peak of VHSR values at low frequency correlated with the fluid of poroelastic reservoir. The highest VHSR value at the low frequency which is recorded on the seismogram is above the 2.5 Hz frequency for reservoirs containing gas and oil in the second elastic medium, while for the medium containing water is the highest VHSR value is below the 2.5 Hz frequency.</p>

Polar radiation patterns of P and SV waves in a multi-layered medium

1973 ◽  
Vol 63 (2) ◽  
pp. 529-547
Author(s):  
Tien-Chang Lee ◽  
Ta-Liang Teng
Keyword(s):  
Displacement Field ◽  
Layered Medium ◽  
Focal Depth ◽  
Focal Mechanisms ◽  
P Wave ◽  
Wave Radiation ◽  
Radiation Patterns ◽  
Double Couple ◽  
Spatial Coordinates ◽  
P And Sv Waves

abstract The displacement field in a multi-layered medium due to incident plane P or SV waves is formulated in terms of Haskell's layer matrices. Based on the reciprocity theorem, the far-field polar radiation patterns of single force, double force, single couple, double couple, and dilatation in a multi-layered medium can be obtained from the displacement field and its first derivatives with respect to the spatial coordinates. Numerical results for models of one layer overlying a half-space indicate that (1) the radiation patterns are sensitive to the variation of focal depth, (2) the layering has a more pronounced effect on SV-wave radiation patterns than on P-wave radiation patterns, (3) the radiation patterns become simpler as the wavelength increases, (4) polarity may reverse abruptly somewhere beyond the critical angle in SV-wave radiation patterns, (5) radiation may be discontinuous across interfaces for some assumed focal mechanisms applied slightly above and below the interfaces, and (6) no clearcut distinction among the various radiation patterns can be used to single out one type of the assumed focal mechanisms from the rest.

A computer program for the application of Zoeppritz's amplitude equations and Knott's energy equations

1976 ◽  
Vol 66 (6) ◽  
pp. 1881-1885 ◽  
Author(s):  
G. B. Young ◽  
L. W. Braile
Keyword(s):  
Computer Program ◽  
Elastic Waves ◽  
Displacement Amplitude ◽  
Plane Interface ◽  
Angle Of Incidence ◽  
Amplitude Equations ◽  
Elastic Solids ◽  
Displacement Potential ◽  
Energy Equations ◽  
Sample Case

abstract A computer program is presented which calculates Zoeppritz's displacement amplitude coefficients, displacement potential coefficients, and Knott's energy coefficients for plane harmonic elastic waves of P or SV type incident on a plane interface between two isotropic, homogeneous elastic solids. A discussion of these three basic types of coefficients is included. Results of applying the program to a sample case are presented in the form of a graph of the energy coefficients computed for all possible wave types and over a range of angle of incidence of 0° to 90°.

scholarly journals Effect of Adjacent Hole on the Blast-Induced Stress Concentration in Rock Blasting

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Yuezong Yang ◽  
Zhushan Shao ◽  
Junfeng Mi ◽  
Xiaofeng Xiong
Keyword(s):  
Stress Concentration ◽  
Stress Wave ◽  
Surface Effect ◽  
Material Model ◽  
Major Effect ◽  
Hole Diameter ◽  
Rock Blasting ◽  
Induced Stress ◽  
Hole Wall ◽  
Hole Effect

To investigate the effect of an adjacent hole on the blast-induced stress concentration in rock blasting, a rock blasting model with an adjacent hole is explored through theoretical analysis and numerical simulation. The commercial software LS-DYNA is utilized to simulate adjacent hole effect in rock blasting, in which the Johnson–Holmquist concrete material model is used to simulate rock and the high-explosive-burn-explosive and the equation of state of JWL are used to simulate explosive. Influences of the key parameters of adjacent hole effect in rock blasting, pitch of holes, adjacent hole diameter, and uncoupled medium in a blasting hole are extensively explored. According to the simulation results, when the explosion stress wave spreads to the adjacent hole wall, the tangential stress on the adjacent hole wall induced by the explosion stress wave is always greater than the radial stress. Adjacent hole diameter has a major effect on stress concentration, but with the adjacent hole diameter increasing, the stress concentration phenomenon weakens and the free surface effect of the adjacent hole plays a more important role.

STANDING‐WAVE PHENOMENA IN SHORT‐PERIOD SEISMIC NOISE

Geophysics ◽  
1965 ◽  
Vol 30 (6) ◽  
pp. 1179-1186 ◽  
Author(s):  
Indra N. Gupta
Keyword(s):  
Steady State ◽  
Standing Wave ◽  
Seismic Noise ◽  
P Wave ◽  
Stratified Medium ◽  
Alternative Theory ◽  
Compressional Waves ◽  
Short Period ◽  
Wave Phenomena ◽  
Phase Spectra

Short‐period vertical seismometers are used in deep holes at several sites to obtain the change with depth in amplitude and phase spectra of short‐period seismic noise. Although the observed spectra can be explained by an arbitrary combination of several Rayleigh modes, an alternative theory is suggested here. An attempt is made to explain both amplitude and phase spectra of observed microseisms of period less than 6 sec in terms of standing‐wave phenomena caused by steady‐state plane harmonic compressional waves propagating vertically through a horizontally stratified medium. At most sites, the observed data indicate satisfactory agreement with the expected results. A considerable fraction of the short‐period noise may, therefore, be regarded as P‐wave noise propagating vertically from below.

scholarly journals Simulation of the effect of stress-induced anisotropy on borehole compressional wave propagation

Geophysics ◽  
2014 ◽  
Vol 79 (4) ◽  
pp. D205-D216 ◽  
Author(s):  
Xinding Fang ◽  
Michael C. Fehler ◽  
Arthur Cheng
Keyword(s):  
Wave Propagation ◽  
Stress Concentration ◽  
Elastic Properties ◽  
Wave Velocity ◽  
Wave Amplitude ◽  
P Wave ◽  
Azimuthal Variation ◽  
P Wave Velocity ◽  
Velocity Region

Formation elastic properties near a borehole may be altered from their original state due to the stress concentration around the borehole. This can lead to an incorrect estimation of formation elastic properties measured from sonic logs. Previous work has focused on estimating the elastic properties of the formation surrounding a borehole under anisotropic stress loading. We studied the effect of borehole stress concentration on sonic logging in a moderately consolidated Berea sandstone using a two-step approach. First, we used an iterative approach, which combines a rock-physics model and a finite-element method, to calculate the stress-dependent elastic properties of the rock around a borehole subjected to an anisotropic stress loading. Second, we used the anisotropic elastic model obtained from the first step and a finite-difference method to simulate the acoustic response of the borehole. Although we neglected the effects of rock failure and stress-induced crack opening, our modeling results provided important insights into the characteristics of borehole P-wave propagation when anisotropic in situ stresses are present. Our simulation results were consistent with the published laboratory measurements, which indicate that azimuthal variation of the P-wave velocity around a borehole subjected to uniaxial loading is not a simple cosine function. However, on field scale, the azimuthal variation in P-wave velocity might not be apparent at conventional logging frequencies. We found that the low-velocity region along the wellbore acts as an acoustic focusing zone that substantially enhances the P-wave amplitude, whereas the high-velocity region caused by the stress concentration near the borehole results in a significantly reduced P-wave amplitude. This results in strong azimuthal variation of P-wave amplitude, which may be used to infer the in situ stress state.

Effects of Surface Elasticity on Scattering of P Waves by an Elastic Half-Plane with a Nanosized Semi-Cylindrical Inclusion

2013 ◽  
Vol 303-306 ◽  
pp. 2661-2666
Author(s):  
Zhi Ying Ou ◽  
Cheng Liu ◽  
Xiao Wei Liu
Keyword(s):  
Surface Energy ◽  
Half Plane ◽  
Surface Effect ◽  
Surface Elasticity ◽  
Expansion Method ◽  
Cylindrical Inclusion ◽  
P Waves ◽  
Wave Function Expansion Method ◽  
Plane P Waves ◽  
Incident Waves

The scattering of plane P waves by a nanosized semi-cylindrical inclusion embedded in an elastic half-plan has been studied in this paper. To account for the surface effect at nanoscale, the surface elasticity is also adopted. When the boundary condition at the straight edge of the half-plane is traction free, the analytical solutions of stress fields of the half plan with semi-cylindrical inclusion are expressed by employing a wave function expansion method. The results show that surface energy has a significant effect on the scattering of plane P waves as the radius of the semi-cylindrical inclusion shrinks to nanoscale. For incident waves with different frequencies, radius of semi-cylindrical inclusion, the effects of surface energy on the dynamic stress concentration near the semi-cylindrical inclusion are discussed in detail.

Complex Analysis of Plane Problem of Two-Dimensional Quasicrystals

2012 ◽  
Vol 236-237 ◽  
pp. 52-54
Author(s):  
Lin Yang ◽  
Qin He ◽  
Shu Yong Zhou ◽  
Wu Li
Keyword(s):  
Stress Concentration ◽  
Plane Problem ◽  
Complex Potential ◽  
Fracture Behavior ◽  
Complex Analysis ◽  
Potential Method ◽  
Two Dimensional ◽  
Complex Potential Method ◽  
Important Significance

The fracture behavior of materials and structures are always caused by stress concentration near the defects in materials. This article describes the complex potential method for solving plane problems of quasicrystalline materials with defects. In order to prove effectiveness and success of the method, an example is given, and the results have very important significance in studying two-dimensional quasicrystals.

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