Near-surface waves in a system consisting of a covering layer and a half-space with imperfect interface under two-axial initial stresses

2016 ◽  
Vol 23 (1) ◽  
pp. 55-68 ◽  
Author(s):  
Surkay D Akbarov ◽  
Masoud Negin
Keyword(s):  
Half Space ◽  
Three Dimensional ◽  
Wave Dispersion ◽  
Imperfect Interface ◽  
Initial Stresses ◽  
Imperfect Contact ◽  
Near Surface ◽  
Covering Layer ◽  
Third Order Elastic Constants ◽  
Shear Spring

The influence of shear-spring + normal-spring type imperfect interface conditions on the dispersion of the generalized Rayleigh waves in a system consisting of a covering layer and a half-space with two-axial homogeneous initial stresses is investigated. The three-dimensional linearized theory of elastic waves in initially stressed bodies is employed and the plane-strain state is considered. The elasticity relations of the materials of the constituents are described through the Murnaghan potential and the influence of the third order elastic constants which enter the expression of this potential is taken into consideration. The corresponding dispersion equation is derived and an algorithm is developed for numerical solution to this equation. Numerical results on the action of the parameters, which enter the formulation of the imperfect contact conditions, on the wave dispersion curves are presented and discussed. The results of these investigations can be successfully used for estimation of the degree of the bonded defects between the covering layer and the half-space.

Transient and Time-Harmonic Infinite Elements for Near-Surface Computations of Three-Dimensional Structures Submerged in a Half-Space

1995 ◽  
Author(s):  
Loukas F. Kallivokas ◽  
Jacobo Bielak
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Half Space ◽  
Three Dimensional ◽  
Scattering Problems ◽  
Near Surface ◽  
Infinite Element ◽  
Infinite Elements ◽  
Time Harmonic ◽  
Element Method

Abstract This paper is concerned with the numerical solution by the finite element method of transient and time-harmonic three-dimensional acoustic scattering problems in infinite and semi-infinite domains. Its main objective is to illustrate how a local second-order surface-only infinite element — either transient or time-harmonic — developed recently for the three-dimensional wave equation in a full-space can be applied readily to scattering problems with penetrable objects near a planar free surface. Taking a problem in structural acoustics as a prototype, the combined infinite element-finite element method is used here to determine the total and scattered pressure patterns generated when a traveling plane wave impinges upon a structure of general geometry submerged in an acoustic fluid in half-space. One key feature of this methodology is that the ordinary differential equations that result from the spatial discretization maintain the symmetry and sparsity associated with problems defined only over interior domains; the resulting equations can then be solved by standard step-by-step time integration techniques. Thus, the combination of low bandwidth matrices with the ease of use of the infinite elements places the method in an ideal position to meet the large computational demands typically associated with large-scale underwater acoustics problems.

Three-Dimensional Analysis of Surface Cracks in an Elastic Half-Space

1996 ◽  
Vol 63 (2) ◽  
pp. 287-294 ◽  
Author(s):  
Quanxin Guo ◽  
Jian-Juei Wang ◽  
R. J. Clifton
Keyword(s):  
Integral Equation ◽  
Numerical Method ◽  
Half Space ◽  
Crack Opening ◽  
Three Dimensional ◽  
Elastic Half Space ◽  
Surface Cracks ◽  
Opening Displacement ◽  
Near Surface ◽  
Total Potential

A numerical method is presented for analyzing arbitrary planar cracks in a half-space. The method is based on the fundamental solution for a dislocation loop in a half-space, which is derived from the Mindlin solution (Mindlin, Physics, Vol. 7, 1936) for a point force in a half-space. By appropriate replacement of the Burgers vectors of the dislocation by the differential crack-opening displacement, a singular integral equation is obtained in terms of the gradient of the crack opening. A numerical method is developed by covering the crack with triangular elements and by minimizing the total potential energy. The singularity of the kernel, when the integral equation is expressed in terms of the gradient of the crack opening, is sufficiently weak that all integrals exist in the regular sense and no special numerical procedures are required to evaluate the contributions to the stiffness matrix. The integrals over the source elements are converted into line integrals along the perimeter of the element and evaluated analytically. Numerical results are presented and compared with known results for both surface breaking cracks and near surface cracks.

On Transient Three-Dimensional Absorbing Boundary Conditions for the Modeling of Acoustic Scattering from Near-Surface Obstacles

1997 ◽  
Vol 05 (01) ◽  
pp. 117-136 ◽  
Author(s):  
Loukas F. Kallivokas ◽  
Aggelos Tsikas ◽  
Jacobo Bielak
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Half Space ◽  
Three Dimensional ◽  
Acoustic Scattering ◽  
Absorbing Boundary Conditions ◽  
Scattering Problems ◽  
Absorbing Boundary ◽  
Near Surface ◽  
Stiffness Matrices

We have recently developed absorbing boundary conditions for the three-dimensional scalar wave equation in full-space. Their applicability has been extended to half-space scattering problems where the scatterer is located near a pressure-free surface. A variational scheme was also proposed for coupling the structural acoustics equations with the absorbing boundary conditions. It was shown that the application of a Galerkin method on the variational form results in an attractive finite element scheme that, in a natural way, gives rise to a surface-only absorbing boundary element on the truncation boundary. The element — the finite element embodiment of a second-order absorbing boundary condition — is completely characterized by a pair of symmetric, frequency-independent damping and stiffness matrices, and is equally applicable to the transient and harmonic steady-state regimes. Previously, we had applied the methodology to problems involving scatterers of arbitrary geometry. In this paper, we validate our approach by comparing numerical results for rigid spherical scatterers submerged in a half-space, against a recently developed analytic solution.

Thermomechanical Coupling of a Hyper-viscoelastic Truck Tire and a Pavement Layer and its Impact on Three-dimensional Contact Stresses

2021 ◽  
pp. 036119812110171
Author(s):  
Angeli Jayme ◽  
Imad L. Al-Qadi
Keyword(s):  
Contact Stress ◽  
Contact Area ◽  
Three Dimensional ◽  
Interaction Model ◽  
Rolling Resistance ◽  
Contact Stresses ◽  
Thermomechanical Coupling ◽  
Temperature Profiles ◽  
Near Surface ◽  
Truck Tire

A thermomechanical coupling between a hyper-viscoelastic tire and a representative pavement layer was conducted to assess the effect of various temperature profiles on the mechanical behavior of a rolling truck tire. The two deformable bodies, namely the tire and pavement layer, were subjected to steady-state-uniform and non-uniform temperature profiles to identify the significance of considering temperature as a variable in contact-stress prediction. A myriad of ambient, internal air, and pavement-surface conditions were simulated, along with combinations of applied tire load, tire-inflation pressure, and traveling speed. Analogous to winter, the low temperature profiles induced a smaller tire-pavement contact area that resulted in stress localization. On the other hand, under high temperature conditions during the summer, higher tire deformation resulted in lower contact-stress magnitudes owing to an increase in the tire-pavement contact area. In both conditions, vertical and longitudinal contact stresses are impacted, while transverse contact stresses are relatively less affected. This behavior, however, may change under a non-free-rolling condition, such as braking, accelerating, and cornering. By incorporating temperature into the tire-pavement interaction model, changes in the magnitude and distribution of the three-dimensional contact stresses were manifested. This would have a direct implication on the rolling resistance and near-surface behavior of flexible pavements.

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.

Third Order Elastic Constants and Rayleigh Wave Dispersion of Shot Peened Aero-Engine Materials

2013 ◽  
Vol 768-769 ◽  
pp. 201-208 ◽  
Author(s):  
Marek Rjelka ◽  
Martin Barth ◽  
Sven Reinert ◽  
Bernd Koehler ◽  
Joachim Bamberg ◽  
...  
Keyword(s):  
Residual Stress ◽  
Rayleigh Wave ◽  
Elastic Constants ◽  
Cold Work ◽  
High Strength ◽  
Wave Dispersion ◽  
Third Order ◽  
Third Order Elastic Constants ◽  
Aero Engine ◽  
Rayleigh Wave Dispersion

Aero-engine components exposed to high mechanical stresses are made of high-strength alloys and additionally, they are surface treated by shot peening. This process introduces compressive residual stress into the material making it less sensitive to stress corrosion cracking and fatigue and therefore benefits the components performance and lifetime. Moreover cold work is induced in an amount depending on the peening parameters. To approximate the remaining lifetime, a quantitative, non-destructive method for stress assessment is required. It was shown that surface treatment of such alloys can be characterized by broadband Rayleigh wave dispersion measurements. However, the relative contributions of residual stress and cold work, respectively, remained an open point. This paper presents the determination of third order elastic constants (TOEC) for IN718 and Ti6246, providing, together with a model for the inversion of dispersion data, a quantitative access to the acoustoelastic effect. Finally, some measurements of differently treated samples are given.

DISPERSION IN SEISMIC SURFACE WAVES

Geophysics ◽  
1951 ◽  
Vol 16 (1) ◽  
pp. 63-80 ◽  
Author(s):  
Milton B. Dobrin
Keyword(s):  
Surface Waves ◽  
Water Waves ◽  
Seismic Refraction ◽  
Wave Theory ◽  
Wave Dispersion ◽  
Surface Zone ◽  
Surface Wave Dispersion ◽  
Near Surface ◽  
Arrival Times ◽  
Ground Roll

A non‐mathematical summary is presented of the published theories and observations on dispersion, i.e., variation of velocity with frequency, in surface waves from earthquakes and in waterborne waves from shallow‐water explosions. Two further instances are cited in which dispersion theory has been used in analyzing seismic data. In the seismic refraction survey of Bikini Atoll, information on the first 400 feet of sediments below the lagoon bottom could not be obtained from ground wave first arrival times because shot‐detector distances were too great. Dispersion in the water waves, however, gave data on speed variations in the bottom sediments which made possible inferences on the recent geological history of the atoll. Recent systematic observations on ground roll from explosions in shot holes have shown dispersion in the surface waves which is similar in many ways to that observed in Rayleigh waves from distant earthquakes. Classical wave theory attributes Rayleigh wave dispersion to the modification of the waves by a surface layer. In the case of earthquakes, this layer is the earth’s crust. In the case of waves from shot‐holes, it is the low‐speed weathered zone. A comparison of observed ground roll dispersion with theory shows qualitative agreement, but it brings out discrepancies attributable to the fact that neither the theory for liquids nor for conventional solids applies exactly to unconsolidated near‐surface rocks. Additional experimental and theoretical study of this type of surface wave dispersion may provide useful information on the properties of the surface zone and add to our knowledge of the mechanism by which ground roll is generated in seismic shooting.

Three-Dimensional Green’s Functions in Anisotropic Elastic Bimaterials With Imperfect Interfaces

2003 ◽  
Vol 70 (2) ◽  
pp. 180-190 ◽  
Author(s):  
E. Pan
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
Three Dimensional ◽  
Imperfect Interface ◽  
Boundary Integral ◽  
Stress Fields ◽  
Superposition Method ◽  
Interface Conditions ◽  
Complementary Part ◽  
Anisotropic Elastic

In this paper, three-dimensional Green’s functions in anisotropic elastic bimaterials with imperfect interface conditions are derived based on the extended Stroh formalism and the Mindlin’s superposition method. Four different interface models are considered: perfect-bond, smooth-bond, dislocation-like, and force-like. While the first one is for a perfect interface, other three models are for imperfect ones. By introducing certain modified eigenmatrices, it is shown that the bimaterial Green’s functions for the three imperfect interface conditions have mathematically similar concise expressions as those for the perfect-bond interface. That is, the physical-domain bimaterial Green’s functions can be obtained as a sum of a homogeneous full-space Green’s function in an explicit form and a complementary part in terms of simple line-integrals over [0,π] suitable for standard numerical integration. Furthermore, the corresponding two-dimensional bimaterial Green’s functions have been also derived analytically for the three imperfect interface conditions. Based on the bimaterial Green’s functions, the effects of different interface conditions on the displacement and stress fields are discussed. It is shown that only the complementary part of the solution contributes to the difference of the displacement and stress fields due to different interface conditions. Numerical examples are given for the Green’s functions in the bimaterials made of two anisotropic half-spaces. It is observed that different interface conditions can produce substantially different results for some Green’s stress components in the vicinity of the interface, which should be of great interest to the design of interface. Finally, we remark that these bimaterial Green’s functions can be implemented into the boundary integral formulation for the analysis of layered structures where imperfect bond may exist.

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