Surface Waves Guided by a Slit in an Elastic Solid

1972 ◽  
Vol 39 (4) ◽  
pp. 1027-1032 ◽  
Author(s):  
L. B. Freund
Keyword(s):  
Surface Waves ◽  
Crack Surface ◽  
Body Wave ◽  
Elastic Solid ◽  
Dispersion Relations ◽  
Finite Width ◽  
Infinite Length ◽  
Open Crack ◽  
Oblique Reflection ◽  
Rate Of Decay

Wave propagation in an isotropic elastic solid containing a slit is studied. The slit is viewed as an open crack of finite width and infinite length. In particular, the propagation of surface waves on the faces of the slit is considered. Making use of a reflection law for the oblique reflection of a Rayleigh wave from the tip of an open half-plane crack, surface waves are superimposed to form guided surface waves in the slit. In order to carry out the construction of dispersion relations, an assumption on the rate of decay of body wave modes localized in the vicinity of the edges of the guide is made, and the range of validity of the assumption is discussed. The dispersion relations are obtained by geometrical construction, and representative dispersion curves are shown.

ELASTODYNAMIC STRESS INTENSITY FACTOR FOR A FINITE CRACK IN ELASTIC SOLID UNDER 3D TRANSIENT LOADING OF MODE I

2013 ◽  
Vol 05 (04) ◽  
pp. 1350044
Author(s):  
XIANHONG MENG ◽  
ZHAOYU BAI ◽  
MING LI
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Integral Transform ◽  
Elastic Solid ◽  
Scattered Wave ◽  
Mode I ◽  
Finite Width ◽  
Infinite Length ◽  
Distance Ratio

In this paper, the three-dimensional dynamic problem for an infinite elastic medium weakened by a crack of infinite length and finite width is analyzed, while the crack surfaces are subjected to mode I transient linear tractions. The integral transform approach is applied to reduce the governing differential equations to a pair of coupled singular integral equations, whose solutions can be obtained with the typical iteration method. The analytical solution of the stress intensity factor when the first wave and the first scattered wave reach the investigated crack tip is obtained. Numerical results are presented for different values of the width-to-longitudinal distance ratio z/l. It is found that the stress intensity factor decreases with the arrival of the first scattered longitudinal wave and increases with the arrival of the first scattered Rayleigh wave and tends to be stable. The static value considering both the first scattered wave and the first wave is about 50% greater than that considering only the first wave, and then the effect of the reflected wave is remarkable and deserves further study.

Three-Dimensional Wave Propagation in a Cracked Elastic Solid

1978 ◽  
Vol 45 (4) ◽  
pp. 807-811 ◽  
Author(s):  
S. Itou
Keyword(s):  
Dynamic Stress ◽  
Dynamic Stress Intensity Factor ◽  
Three Dimensional ◽  
Elastic Solid ◽  
Expansion Method ◽  
The Self ◽  
Finite Width ◽  
Infinite Length ◽  
Dimensional Wave ◽  
Series Expansion Method

The three-dimensional dynamic problem is presented for an infinite elastic medium weakened by a plane crack of infinite length and finite width. On the surfaces of the crack, the self-equilibrated system of a load varies harmonically in time and is distributed arbitrarily on those surfaces. The Fourier transformations are utilized to reduce the problem to a solution of two simultaneous integral equations which can be solved by using the series expansion method. The dynamic stress-intensity factor is computed numerically for some applied loads.

Surface Waves Guided by the Exterior of a Rectangular Elastic Solid

1986 ◽  
Vol 53 (2) ◽  
pp. 379-381 ◽  
Author(s):  
A. K. Gautesen
Keyword(s):  
Surface Waves ◽  
Cross Section ◽  
Cross Sections ◽  
Rectangular Cross Section ◽  
Elastic Solid ◽  
Dispersion Relations ◽  
Ray Theory ◽  
Elastic Bar

We show that surface waves can be guided on the exterior of an isotropic elastic bar with a rectangular cross section. We assume that the dimensionless wavenumber is sufficiently large that elastodynamic ray theory is valid. Dispersion relations are obtained and representative curves for various cross sections are shown.

Guided Surface Waves on an Elastic Half Space

1971 ◽  
Vol 38 (4) ◽  
pp. 899-905 ◽  
Author(s):  
L. B. Freund
Keyword(s):  
Wave Propagation ◽  
Surface Wave ◽  
Surface Waves ◽  
Half Space ◽  
Body Wave ◽  
Three Dimensional ◽  
Elastic Half Space ◽  
Normal Displacement ◽  
Rigid Barrier ◽  
Wave Disturbances

Three-dimensional wave propagation in an elastic half space is considered. The half space is traction free on half its boundary, while the remaining part of the boundary is free of shear traction and is constrained against normal displacement by a smooth, rigid barrier. A time-harmonic surface wave, traveling on the traction free part of the surface, is obliquely incident on the edge of the barrier. The amplitude and the phase of the resulting reflected surface wave are determined by means of Laplace transform methods and the Wiener-Hopf technique. Wave propagation in an elastic half space in contact with two rigid, smooth barriers is then considered. The barriers are arranged so that a strip on the surface of uniform width is traction free, which forms a wave guide for surface waves. Results of the surface wave reflection problem are then used to geometrically construct dispersion relations for the propagation of unattenuated guided surface waves in the guiding structure. The rate of decay of body wave disturbances, localized near the edges of the guide, is discussed.

scholarly journals Asymptotic analysis for dispersion relations and travel times in noise cross-correlations: spherically symmetric case

2018 ◽  
Vol 474 (2218) ◽  
pp. 20180382
Author(s):  
Tianshi Liu ◽  
Haiming Zhang
Keyword(s):  
Asymptotic Analysis ◽  
Surface Waves ◽  
Green's Functions ◽  
Green’S Functions ◽  
Dispersion Relations ◽  
Body Waves ◽  
Spherically Symmetric ◽  
Travel Times ◽  
Cross Correlations ◽  
The Cross

The cross-correlations of ambient noise or earthquake codas are massively used in seismic tomography to measure the dispersion curves of surface waves and the travel times of body waves. Such measurements are based on the assumption that these kinematic parameters in the cross-correlations of noise coincide with those in Green's functions. However, the relation between the cross-correlations of noise and Green's functions deserves to be studied more precisely. In this paper, we use the asymptotic analysis to study the dispersion relations of surface waves and the travel times of body waves, and come to the conclusion that for the spherically symmetric Earth model, when the distribution of noise sources is laterally uniform, the dispersion relations of surface waves and the travel times of SH body-wave phases in noise correlations should be exactly the same as those in Green's functions.

Nonlinear TE surface waves in a ferrite slab bounded by Kerr-type metamaterials

2017 ◽  
Vol 26 (03) ◽  
pp. 1750028 ◽  
Author(s):  
Burhan Zamir ◽  
Rashid Ali
Keyword(s):  
Boundary Conditions ◽  
Surface Waves ◽  
Transverse Electric ◽  
Dispersion Relations ◽  
Double Negative ◽  
Propagation Characteristics ◽  
Special Cases ◽  
Tangential Field ◽  
Effective Wave ◽  
Ferrite Slab

In this paper, nonlinear transverse electric surface waves in a structure consisting of a ferrite slab sandwiched between a Kerr-type double-negative metamaterial (DNG-MTM) have been investigated. In addition to a DNG-MTM, two special cases with nonlinear single-negative metamaterials (SNG-MTMs) have also been discussed. The dispersion relations are obtained by applying the boundary conditions to the tangential field components of each layer. The propagation characteristics are plotted numerically for the effective wave index versus propagation frequency.

scholarly journals Моды волновода с пороговой нелинейностью

2020 ◽  
Vol 46 (16) ◽  
pp. 43
Author(s):  
С.Е. Савотченко
Keyword(s):  
Dielectric Constant ◽  
Optical Properties ◽  
Surface Waves ◽  
Nonlinear Optical ◽  
Layer Structure ◽  
Finite Thickness ◽  
Critical Value ◽  
Field Structure ◽  
Finite Width ◽  
Border Regions

A three-layer structure consisting of a nonlinear optical medium with a stepwise change in the dielectric constant inside which there is a dielectric layer of finite thickness is considered. The surface waves of two types of symmetry with a special field structure can propagate along the layers. Domains of finite width with different optical properties in the border regions in a nonlinear medium are formed. The formation of domains, as well as the existence of surface waves, occurs at interlayer thicknesses not exceeding a certain critical value.

3D elastic full-waveform inversion of surface waves in the presence of irregular topography using an envelope-based misfit function

Geophysics ◽  
2018 ◽  
Vol 83 (1) ◽  
pp. R1-R11 ◽  
Author(s):  
Dmitry Borisov ◽  
Ryan Modrak ◽  
Fuchun Gao ◽  
Jeroen Tromp
Keyword(s):  
Surface Wave ◽  
Objective Function ◽  
Surface Waves ◽  
Large Scale ◽  
Body Wave ◽  
Waveform Inversion ◽  
Full Waveform Inversion ◽  
S Wave ◽  
Near Surface ◽  
Full Waveform

Full-waveform inversion (FWI) is a powerful method for estimating the earth’s material properties. We demonstrate that surface-wave-driven FWI is well-suited to recovering near-surface structures and effective at providing S-wave speed starting models for use in conventional body-wave FWI. Using a synthetic example based on the SEG Advanced Modeling phase II foothills model, we started with an envelope-based objective function to invert for shallow large-scale heterogeneities. Then we used a waveform-difference objective function to obtain a higher-resolution model. To accurately model surface waves in the presence of complex tomography, we used a spectral-element wave-propagation solver. Envelope misfit functions are found to be effective at minimizing cycle-skipping issues in surface-wave inversions, and surface waves themselves are found to be useful for constraining complex near-surface features.

Isoparametric Graded Finite Elements for Nonhomogeneous Isotropic and Orthotropic Materials

2002 ◽  
Vol 69 (4) ◽  
pp. 502-514 ◽  
Author(s):  
Jeong-Ho Kim ◽  
G. H. Paulino
Keyword(s):  
Finite Elements ◽  
Material Property ◽  
Poisson’S Ratio ◽  
Orthotropic Plate ◽  
Poisson's Ratio ◽  
Orthotropic Materials ◽  
Finite Width ◽  
Infinite Length ◽  
Graded Materials ◽  
Isotropic And Orthotropic Materials

Graded finite elements are presented within the framework of a generalized isoparametric formulation. Such elements possess a spatially varying material property field, e.g. Young’s modulus E and Poisson’s ratio ν for isotropic materials; and principal Young’s moduli E11,E22, in-plane shear modulus G12, and Poisson’s ratio ν12 for orthotropic materials. To investigate the influence of material property variation, both exponentially and linearly graded materials are considered and compared. Several boundary value problems involving continuously nonhomogeneous isotropic and orthotropic materials are solved, and the performance of graded elements is compared to that of conventional homogeneous elements with reference to analytical solutions. Such solutions are obtained for an orthotropic plate of infinite length and finite width subjected to various loading conditions. The corresponding solutions for an isotropic plate are obtained from those for the orthotropic plate. In general, graded finite elements provide more accurate local stress than conventional homogeneous elements, however, such may not be the case for four-node quadrilateral (Q4) elements. The framework described here can serve as the basis for further investigations such as thermal and dynamic problems in functionally graded materials.

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