Zeitschriftenartikel: „Semi-infinite elastic media“

1

Alshits, V. I., A. N. Darinskii und A. L. Shuvalov. „Elastic waves in infinite and semi-infinite anisotropic media“. Physica Scripta T44 (01.01.1992): 85–93. http://dx.doi.org/10.1088/0031-8949/1992/t44/014.

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2

Mandal, Palas. „Moving semi-infinite mode-III crack inside the semi-infinite elastic media“. Journal of Theoretical and Applied Mechanics 58, Nr. 3 (15.07.2020): 649–59. http://dx.doi.org/10.15632/jtam-pl/117813.

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3

Nougaoui, A., und B. Djafari Rouhani. „Elastic waves in periodically layered infinite and semi-infinite anisotropic media“. Surface Science 185, Nr. 1-2 (Juni 1987): 125–53. http://dx.doi.org/10.1016/s0039-6028(87)80618-0.

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4

Nougaoui, A., und B. Djafari Rouhani. „Elastic waves in periodically layered infinite and semi-infinite anisotropic media“. Surface Science Letters 185, Nr. 1-2 (Juni 1987): A243. http://dx.doi.org/10.1016/0167-2584(87)90304-5.

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5

Lin, Yuan, und Timothy C. Ovaert. „Thermoelastic Problems for the Anisotropic Elastic Half-Plane“. Journal of Tribology 126, Nr. 3 (28.06.2004): 459–65. http://dx.doi.org/10.1115/1.1760553.

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By applying the extended version of Stroh’s formalism, the two-dimensional thermoelastic problem for a semi-infinite anisotropic elastic half-plane is formulated. The steady-state heat transfer condition is assumed and the technique of analytical continuation is employed; the formulation leads to the Hilbert problem, which can be solved in closed form. The general solutions due to different kinds of thermal and mechanical boundary conditions are obtained. The results show that unlike the two-dimensional thermoelastic problem for an isotropic media, where a simply-connected elastic body in a state of plane strain or plane stress remains stress free if the temperature distribution is harmonic and the boundaries are free of traction, the stress within the semi-infinite anisotropic media will generally not equal zero even if the boundary is free of traction.

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Choi, Hyung Jip, und S. Thangjitham. „Stress Analysis of Multilayered Anisotropic Elastic Media“. Journal of Applied Mechanics 58, Nr. 2 (01.06.1991): 382–87. http://dx.doi.org/10.1115/1.2897197.

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The stress analysis of multilayered anisotropic media subjected to applied surface tractions is performed within the framework of linear plane elasticity. The solutions are obtained based on the Fourier transform technique together with the aid of the stiffness matrix approach. A general solution procedure is introduced such that it can be uniformly applied to media with transversely isotropic, orthotropic, and monoclinic layers. As an illustrative example, responses of the semi-infinite media composed of unidirectional and angle-ply layers to a given surface traction are presented.

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Zhang, Mei, Bo Tang und Hongjun Li. „Construction and application of adaptive semi-Infinite boundary element with dynamic problems on half-plane“. E3S Web of Conferences 165 (2020): 06049. http://dx.doi.org/10.1051/e3sconf/202016506049.

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For thedynamic problem ofhalf-plane, if the radiation condition at the semi-infinite boundary is not taken into account in the numerical calculation, the accuracy of the result will be affected.In this paper, the basic theory of time-domain boundary element method (TD-BEM) and the propagation characteristics of stress waves in elastic media are used to transform a semi-infinite boundary into a semi-infinite boundary element which can adjust the size of the element automatically with time-space parameters.Enablingthe element to simulate radiative damping effects in the far field.At last, the efficiency of theelement is verified with a half-plane example under dynamic load by comparing its results with the results of the finite element method (FEM). Theverificationshows thatthe adaptive semi-infinite element can effectively simulate the radiation conditions in the far area. And it is convenient to use TD-BEM to solve the half-plane dynamics problem.

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Zeng, Xiaogang, J. Bielak und R. C. MacCamy. „Stable Variational Coupling Method for Fluid-Structure Interaction in Semi-Infinite Media“. Journal of Vibration and Acoustics 114, Nr. 3 (01.07.1992): 387–96. http://dx.doi.org/10.1115/1.2930274.

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An energy-based symmetric coupled finite element and boundary integral method valid for all frequencies has been developed recently by the authors (Zeng et al., 1990; Bielak et al., 1991), for analyzing scattering problems for an inhomogeneous deformable body immersed in an infinite acoustic medium. Here we extend the methodology to a halfspace with a free surface via the method of images. Numerical examples are presented for an infinitely long radially inhomogeneous elastic cylinder with its centroidal axis parallel to the free surface and subjected to an incident plane wave perpendicular to this axis, in order to illustrate the applicability of the new procedure; its accuracy at critical frequencies is assessed with a rigid cylinder.

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Zeng, Xian Wei, und Xi Luo. „Analysis of Crack-Inclusion Interaction in an Anisotropic Medium by Eshelby Equivalent Inclusion Method“. Advanced Materials Research 268-270 (Juli 2011): 72–75. http://dx.doi.org/10.4028/www.scientific.net/amr.268-270.72.

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The problem of a semi-infinite crack in anisotropic medium interacting with a near-tip inclusion is analyzed by the Eshelby equivalent inclusion method. The change of mode I stress intensity factor due to crack-inclusion interaction is evaluated using a novel analytical solution for the model I stress intensity factor at the tip of a semi-infinite crack due to near-tip eigenstrains. Numerical results of the mode I stress intensity factor due to the presence of a near-tip circular inclusion are presented to show the influence of the elastic stiffness of an inclusion on the near-tip elastic field. The present scheme can be applied to calculate the stress intensity at a crack-tip in anisotropic media due to the interaction of inclusions with arbitrary shapes.

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Madan, Dinesh K., und Naveen Kumar. „Propagation of Rayleigh Wave in Sandy Media with Imperfect Interface“. SAMRIDDHI : A Journal of Physical Sciences, Engineering and Technology 15, Nr. 01 (14.01.2023): 78–82. http://dx.doi.org/10.18090/samriddhi.v15i01.27.

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In the present study, the propagation of Rayleigh wave in a sandy layer overlying a sandy semi-infinite media is investigated, with the interface considered imperfect. Expressions for displacement components are obtained. The dispersion frequency equation is derived using suitable boundary conditions. In particular cases, when interface is perfect and elastic media replace sandy media are also discussed. The effects of imperfectness and sandy parameter on the Rayleigh waves’ phase velocity are investigated using MATLAB software. The theoretical results obtained may find useful applications in geophysics, civil engineering and soil mechanics

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Ashayeri, Iman, Mahnoosh Biglari und Majid Rezaie Sefat. „Elastic wave theory for propagation of Rayleigh waves at surface of unsaturated semi-infinite media“. Japanese Geotechnical Society Special Publication 2, Nr. 10 (2016): 446–50. http://dx.doi.org/10.3208/jgssp.irn-09.

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CELA, J. J. LÓPEZ, A. R. PIRIZ, M. C. SERNA MORENO und N. A. TAHIR. „Numerical simulations of Rayleigh-Taylor instability in elastic solids“. Laser and Particle Beams 24, Nr. 3 (September 2006): 427–35. http://dx.doi.org/10.1017/s0263034606060599.

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Numerical simulations of the Rayleigh-Taylor instability in the interface of two semi-infinite media have been performed based on the finite element method. Two different interfaces have been considered: elastic solid/elastic solid and elastic solid/viscous fluid. The results have been compared with previously published analytical models. In particular, the asymptotic growth rate has been compared with the model by Terrones (2005) while the initial transient phase is compared with the model by Piriz et al. (2005). Finally, some examples show the importance of such an initial transient phase if more realistic material laws (for example, elastoplastic behavior) are taken into account.

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Madan, Dinesh Kumar, Naveen Kumar und Annu Rani. „Rayleigh wave propagation in isotropic sandy layer sliding over isotropic sandy semi-infinite medium with sliding contact“. International Journal of Applied Mechanics and Engineering 28, Nr. 1 (01.03.2023): 58–70. http://dx.doi.org/10.59441/ijame-2023-0006.

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The present study aims to investigate Rayleigh wave propagation in an isotropic sandy layer overlying an isotropic sandy semi-infinite medium, with interface considered to be imperfect (slide contact and dislocation like model). Expressions for displacement components are obtained using the variable separation method. The dispersion frequency equation for the Rayleigh wave propagating in sandy media is derived using suitable boundary conditions. Particular cases, such as when the interface is in smooth contact and when sandy media are replaced by elastic media, are also discussed. Using MATLAB software, the effects of the imperfectness parameter (slide contact and dislocation like model) and sandy parameter on the Rayleigh waves’ phase velocity are investigated and compared with the already obtained results of the dislocation like model. The present study may find useful applications in geophysics, civil engineering and soil mechanics.

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Goldsberry, Benjamin M., Samuel P. Wallen und Michael R. Haberman. „Nonreciprocal acoustic scattering from an elastic plate with spatiotemporally modulated material properties“. Journal of the Acoustical Society of America 151, Nr. 4 (April 2022): A156. http://dx.doi.org/10.1121/10.0010958.

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Acoustic and elastic metamaterials with space- and time-dependent material properties have received great attention recently as a means to realize nonreciprocal wave propagation. The nonreciprocal behavior of propagating waves in a spatiotemporally modulated infinite medium is usually characterized by directional bandgaps present in the frequency-wavenumber spectrum. However, less attention has been given to acoustic scattering from spatiotemporally modulated media. In this work, we consider nonreciprocal reflection and transmission from a spatiotemporally modulated, infinite elastic plate excited by a plane wave at oblique incidence. A semi-analytical approach is developed that considers the coupling between the acoustic waves and the displacement of the plate. The reflection and transmission response of the plate for each generated frequency harmonic as a function of the incident angle are reported. Finally, we find conditions on the modulation parameters that yield a large degree of nonreciprocity. The present analysis leads to potential applications in acoustic communications, such as directional wave sensing.

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Xia, Muming, Hui Zhou, Hanming Chen, Qingchen Zhang und Qingqing Li. „A rectangular-grid lattice spring model for modeling elastic waves in Poisson’s solids“. GEOPHYSICS 83, Nr. 2 (01.03.2018): T69—T86. http://dx.doi.org/10.1190/geo2016-0414.1.

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The lattice spring model (LSM) combined with the velocity Verlet algorithm is a newly developed scheme for modeling elastic wave propagation in solid media. Unlike conventional wave equations, LSM is established on the basis of micromechanics of the subsurface media, which enjoys better dynamic characteristics of elastic systems. We develop a rectangular-grid LSM scheme for elastic waves simulation in Poisson’s solids, and the direction-dependent elastic constants are deduced to keep the isotropy of the discrete grid. The stability condition and numerical dispersion properties of LSM are discussed and compared with other numerical methods. The 2D and 3D numerical simulations are carried out using the rectangular-grid LSM, as well as the second- and fourth-order accuracy staggered finite-difference method (FDM). Wavefields obtained by LSM are fairly similar with those by analytical solution and FDM, which demonstrates the correctness of the proposed scheme and its capability of modeling elastic wave propagation in heterogeneous media. Moreover, we perform plane P-wave simulation through a semi-infinite cavity model via LSM and FDM, the recorded wavefield snapshots indicate that our proposed rectangular-grid LSM obtains more reasonable wavefield details compared with those of FDM, especially in media with high compliance and structure complexity. Our main contribution lies in offering an alternative simulation scheme for modeling elastic wave propagation in media with some kinds of complexities, which conventional FDM may fail to simulate.

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Kumar, Rajneesh, und Rajeev Kumar. „Analysis of wave motion in transversely isotropic elastic material with voids under a inviscid liquid layer“. Canadian Journal of Physics 87, Nr. 4 (April 2009): 377–88. http://dx.doi.org/10.1139/p09-020.

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The present investigation is to study the surface wave propagation in a semi-infinite transversely isotropic elastic material with voids under a homogeneous inviscid liquid layer. The frequency equation is derive after developing the mathematical model. The dispersion curves giving the phase velocity and attenuation coefficients versus wave numbers are plotted graphically to depict the effects of voids for (i) a transversely isotropic elastic half-space with voids under a homogeneous inviscid liquid layer and (ii) a transversely isotropic elastic half-space with voids. The particle path is also obtained for Rayleigh wave propagation in a transversely isotropic elastic half-space with voids, i.e., case (ii). The amplitudes of the displacements, the volume fraction field, and the normal stresses in both the media are obtained and are shown graphically for a particular model to depict the voids and anisotropy effects. Some special cases are also deduced from the present investigation.

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17

Fan, Hui, und L. M. Keer. „Two-Dimensional Contact on an Anisotropic Elastic Half-Space“. Journal of Applied Mechanics 61, Nr. 2 (01.06.1994): 250–55. http://dx.doi.org/10.1115/1.2901437.

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The two-dimensional contact problem for a semi-infinite anisotropic elastic media is reconsidered here by using the formalism of Es he I by et al. (1953) and Stroh (1958). The approach of analytic function continuation is employed to investigate the half-space contact problem with various mixed boundary conditions applied to the half-space. A key point of the solution procedure suggested in the present paper is its dependence on a general eigenvalue problem involving a Hermitian matrix. This eigenvalue problem is analogous to the one encountered when investigating the behavior of an interface crack (Ting, 1986). As an application, the interaction between a dislocation and a contact strip is solved. The compactness of the results shows their potential for utilization to solve the problem of contact of a damaged anisotropic half-space.

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Komvopoulos, K., und N. Ye. „Three-Dimensional Contact Analysis of Elastic-Plastic Layered Media With Fractal Surface Topographies“. Journal of Tribology 123, Nr. 3 (25.07.2000): 632–40. http://dx.doi.org/10.1115/1.1327583.

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Three-dimensional rough surfaces were generated using a modified two-variable Weierstrass-Mandelbrot function with fractal parameters determined from real surface images. The number and size of truncated asperities were assumed to follow power-law relations. A finite element model of a rigid sphere in normal contact with a semi-infinite elastic-plastic homogeneous medium was used to obtain a constitutive relation between the mean contact pressure, real contact area, and corresponding representative strain. The contact model was extended to layered media by modifying the constitutive equation of the homogeneous medium to include the effects of the mechanical properties of the layer and substrate materials and the layer thickness. Finite element simulations of an elastic-plastic layered medium indented by a rigid sphere validated the correctness of the modified contact model. Numerical results for the contact load and real contact area are presented for real surface topographies resembling those of magnetic recording heads and smooth rigid disks. The model yields insight into the evolution of elastic, elastic-plastic, and fully plastic deformation at the contact interface in terms of the maximum local surface interference. The dependence of the contact load and real contact area on the fractal parameters and the carbon overcoat thickness is interpreted in light of simulation results obtained for a tri-pad picoslider in contact with a smooth thin-film hard disk.

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Yaremko, Oleg, und Natalia Yaremko. „Matrix Fourier Transforms for Consistent Mathematical Models“. Chinese Journal of Mathematics 2016 (31.08.2016): 1–10. http://dx.doi.org/10.1155/2016/1975493.

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We create a matrix integral transforms method; it allows us to describe analytically the consistent mathematical models. An explicit constructions for direct and inverse Fourier matrix transforms with discontinuous coefficients are established. We introduce special types of Fourier matrix transforms: matrix cosine transforms, matrix sine transforms, and matrix transforms with piecewise trigonometric kernels. The integral transforms of such kinds are used for problems solving of mathematical physics in homogeneous and piecewise homogeneous media. Analytical solution of iterated heat conduction equation is obtained. Stress produced in the elastic semi-infinite solid by pressure is obtained in the integral form.

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Gupta, Shishir, Mostaid Ahmed und Abhijit Pramanik. „Shear waves in elastic medium with void pores welded between vertically inhomogeneous and anisotropic magnetoelastic semi-infinite media“. Acta Geophysica 65, Nr. 1 (10.02.2017): 139–49. http://dx.doi.org/10.1007/s11600-017-0012-2.

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Shuvalov, A. L., O. Poncelet und S. V. Golkin. „Existence and spectral properties of shear horizontal surface acoustic waves in vertically periodic half-spaces“. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 465, Nr. 2105 (25.02.2009): 1489–511. http://dx.doi.org/10.1098/rspa.2008.0457.

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The paper is concerned with the propagation of shear horizontal surface waves (SHSW) in semi-infinite elastic media with vertically periodic continuous and/or discrete variation of material properties. The existence and spectral properties of the SHSW are shown to be intimately related to the shape of the properties variation profile. Generally, the SHSW dispersion branches represent randomly broken spectral intervals on the ( ω , k ) plane. They may, however, display a particular regularity in being confined to certain distinct ranges of slowness s = ω / k , which can be predicted and estimated directly from the profile shape. The SHSW spectral regularity is especially prominent when the material properties at the opposite edge points of a period are different. In particular, a unit cell can be arranged so that the SHSW exists within a single slowness window, narrow in the measure of material contrast between the edges, and does not exist elsewhere or vice versa. Explicit analysis in the ( ω , k ) domain is complemented and verified through the numerical simulation of the SH wave field in the time–space domain. The results also apply to a longitudinally periodic semi-infinite strip with a homogeneous boundary condition at the faces.

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Kaganova, I. M., und M. L. Litinskaia. „Singularities of the dynamical Green function for semi-infinite isotropic elastic media subjected to time and position dependent normal surface force“. Physics Letters A 200, Nr. 5 (Mai 1995): 365–74. http://dx.doi.org/10.1016/0375-9601(95)00153-t.

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23

Prasad, Ratan Mani, Santimoy Kundu und Shishir Gupta. „Propagation of torsional surface wave in sandy layer sandwiched between a non-homogeneous and a gravitating anisotropic porous semi-infinite media“. Journal of Vibration and Control 23, Nr. 11 (18.08.2015): 1768–81. http://dx.doi.org/10.1177/1077546315600112.

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The present paper attempts to study the propagation of torsional surface waves in a pre-stressed dry sandy layer sandwiched by a pre-stressed non-homogeneous semi-infinite medium and an anisotropic porous half-space under gravity. The non-homogeneity in the non-homogeneous layer is caused by the quadratic variation in rigidity, density and initial stress. The inhomogeneity has been assumed as hyperbolic variation in the dry sandy layer. The dispersion equation of motion has been derived under suitable boundary conditions in a close form, which shows the variation of phase velocity of the corresponding wave number. The velocities of torsional waves are calculated numerically as a function of kH and presented in a number of graphs where k is the wave number and H is the thickness of the sandy layer. The effect of inhomogeneity in the elastic modulus of rigidity, pre-stress, density, gravity and porosity depicted by means of graph, using MATLAB software. The study reveals that the torsional waves propagate in the pre-stress dry sandy layer sandwiched between the considered media. This work may be useful to understand the nature of seismic wave propagation during earthquakes.

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Danoyan, Z. N., L. H. Atoyan, S. L. Sahakyan und N. Z. Danoyan. „Love waves in а layered elastic media consisting of two semi-infinite half-spaces with inhomogeneous layers and homogeneous layer between them.“ Mechanics - Proceedings of National Academy of Sciences of Armenia 67, Nr. 3 (2014): 49–55. http://dx.doi.org/10.33018/67.3.6.

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Bescond, C., und M. Deschamps. „Erratum: “Dynamical surface response of a semi-infinite anisotropic elastic media to an impulsive force” [J. Acoust. Soc. Am. 103, 114–124 (1998)]“. Journal of the Acoustical Society of America 104, Nr. 1 (Juli 1998): 599. http://dx.doi.org/10.1121/1.423280.

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Afanasyev, Andrey, und Ivan Utkin. „Modelling ground displacement and gravity changes with the MUFITS simulator“. Advances in Geosciences 54 (19.10.2020): 89–98. http://dx.doi.org/10.5194/adgeo-54-89-2020.

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Abstract. We present an extension of the MUFITS reservoir simulator for modelling the ground displacement and gravity changes associated with subsurface flows in geologic porous media. Two different methods are implemented for modelling the ground displacement. The first approach is simple and fast and is based on an analytical solution for the extension source in a semi-infinite elastic medium. Its application is limited to homogeneous reservoirs with a flat Earth surface. The second, more comprehensive method involves a one-way coupling of MUFITS with geomechanical code presented for the first time in this paper. We validate the accuracy of the development by considering a benchmark study of hydrothermal activity at Campi Flegrei (Italy). We investigate the limitations of the first approach by considering domains for the geomechanical problem that are larger than those for the fluid flow. Furthermore, we present the results of more complicated simulations in a heterogeneous subsurface when the assumptions of the first approach are violated. We supplement the study with the executable of the simulator for further use by the scientific community.

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Radjen, Anthony, Gabriele Gradoni und Richard Tew. „Reflection and transmission of high-frequency acoustic, electromagnetic and elastic waves at a distinguished class of irregular, curved boundaries“. IMA Journal of Applied Mathematics 84, Nr. 6 (Dezember 2019): 1203–19. http://dx.doi.org/10.1093/imamat/hxz029.

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Abstract Reflection and transmission phenomena associated with high-frequency linear wave incidence on irregular boundaries between adjacent acoustic or electromagnetic media, or upon the irregular free surface of a semi-infinite elastic solid, are studied in two dimensions. Here, an ‘irregular’ boundary is one for which small-scale undulations of an arbitrary profile are superimposed upon an underlying, smooth curve (which also has an arbitrary profile), with the length scale of the perturbation being prescribed in terms of a certain inverse power of the large wave-number of the incoming wave field. Whether or not the incident field has planar or cylindrical wave-fronts, the associated phase in both cases is linear in the wave-number, but the presence of the boundary irregularity implies the necessity of extra terms, involving fractional powers of the wave-number in the phase of the reflected and transmitted fields. It turns out that there is a unique perturbation scaling for which precisely one extra term in the phase is needed and hence for which a description in terms of a Friedlander–Keller ray expansion in the form as originally presented is appropriate, and these define a ‘distinguished’ class of perturbed boundaries and are the subject of the current paper.

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Braun, Stefan, Helmut Nowotny, Ewald Benes und Martin Gröschl. „Layered piezoelectric structures with arbitrary acoustic termination impedances“. Journal of the Acoustical Society of America 153, Nr. 3 (März 2023): 1733–53. http://dx.doi.org/10.1121/10.0017600.

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Multilayer piezoelectric transducers and resonators are widely used for generating propagating and standing acoustic waves as well as for sensor devices. More recently, layered piezoelectric structures based on thin film technology became increasingly important for electromechanical filters used in mobile phones. As a consequence, analytical mathematical modeling of such structures is of high interest. In this paper, a general rigorous transfer matrix description for one-dimensional (1D) layered structures consisting of piezoelectric, visco-elastic, and dielectric layers of arbitrary number is introduced to characterize the electrical and mechanical behavior of a general piezoelectric transducer or resonator with two electrodes and arbitrary acoustic termination impedances (Rig-1D-model). This model is the most general 1D analytical description of layered piezoelectric structures available and can be used for the characterization of various composite transducer and resonant sensor applications. Considered in detail are layered structures with the technically important cases of only one electromechanically coupled mode, and the structure at one or both outer surfaces is in contact with semi-infinite media. For such devices, it is shown how the frequency dependence of the total electrical admittance and spatial dependence of the displacements can be calculated.

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Voytko, M. V., O. B. Trishchuk und D. B. Kuryliak. „Estimation of the stress intensity factor of an interface crack by the scattered SH-far field“. Information extraction and processing 2023, Nr. 51 (14.12.2023): 19–22. http://dx.doi.org/10.15407/vidbir2023.51.019.

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The diffraction of the plane elastic SH-wave from a semi-infinite interface crack on junction of two elastic semi-infinite media is studied. The crack is modelled by the mathematical cut with no stress on its faces. The displacement and the stress fields are continuous outside of the crack. The wave diffraction problem is reduced to the solution of the mixed boundary value problem for Helmholtz equation. We search the solution which satisfies the Neumann boundary condition on the crack faces and the continuity condition for the stress and displacement fields outside of the crack. The radiation condition at the infinity and the Meixners condition at the crack tip must be also satisfied. Using the Fourier integral transform, the mixed boundary value problem is reduced to the Wiener-Hopf functional equation which is valid in the given strip of regularity in the complex plane. The method of factorization and decomposition, as well as the Liouvilles theorem, are used to solve this equation. Its kernel function is factorized and represented as a product of two split functions that are regular in the overlapping half-planes. These ones allow for the simple poles outside of the regularity regions. The solution of the Wiener-Hopf equation is presented in analytical form. The scattered displacement field is found for an arbitrary frequency and sounding angle by applying an inverse Fourier integral transform to the solution. The asympŹtotic formula for the stress intensity factor (SIF) at the crack tip is obtained. The correlation between complex amplitude of the SH-wave far scattered displacement field and the SIF caused by this field is obtained for an arbitrary radiation angle, frequency and medium parameters. This allows us to express the SIF through the amplitude of the far field if the radiation frequency, sounding angle as well as the physical characteristics of materials are known. It is shown that in the plane that is normal to the tip of the crack the ratio of SIF for the given junction and two fixed values of the sounding angle or two sounding frequencies is proportional to the ratio of the scattered fields. It is found that under above mentioned condition the proportionality rate does not depend on material properties. The obtained relations can be applied for estimation of the SIF with changing frequency and sounding angle.

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Bouare, Hamed, Arnaud Mesgouez und Gaëlle Lefeuve-Mesgouez. „Contribution to the modeling and the mechanical characterization of the subsoil in the LSBB environment“. E3S Web of Conferences 88 (2019): 06001. http://dx.doi.org/10.1051/e3sconf/20198806001.

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The present research work aims at better characterizing the specific underground environment of the LSBB (Low Noise Inter-Disciplinary Underground Science and Technology, Rustrel, France) using mechanical wave propagation information. The LSBB experimental environment is characterized by a system of cylindrical galleries, some of them presenting a concrete layer. In the global project, three steps are considered : firstly the construction of an efficient forward mechanical wave propagation model to calculate the displacement vector and stress tensor components; secondly a sensitivity analysis to extract the pertinent parameters in the configurations and models under study (viscoelastic or poroviscoelastic media with potential anisotropy); and lastly an inversion strategy to recover some of the pertinent parameters. In this proposal, the first step, under progress, is described. The work carried out is in the continuity of the work presented by Yi et al. (2016) [1] who studied the harmonic response of a cylindrical elastic tunnel, impacted by a plane compressional wave, embedded in an infinite elastic ground. The interface between the rock mass and the linen is an imperfect contact modeled with two spring parameters, Achenbach and Zhu (1989) [2]. We choose a semi-analytical approach to calculate the two-dimensional displacement and stress fields in order to get a fast tool, from the numerical point of view. The main steps of the theoretical approach are : use of the Helmholtz decomposition, solving the wave equation based on the separation method and the expansion in Bessel function series in the harmonic domain. The harmonic results are validated by comparison with Yi et al. (2016) [1] and new ones are presented. Moreover, the transient regime case obtained with the use of a Fourier transform on the time variable, is under progress.

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Pavlov, I. S., und A. V. Muravieva. „A 3D HIGHER-ORDER GRADIENT MODEL FOR A HALF-SPACE GEOMEDIUM“. Problems of Strength and Plasticity 84, Nr. 4 (2022): 480–92. http://dx.doi.org/10.32326/1814-9146-2022-84-4-480-492.

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In this paper, a structural model of a geomedium (a soil) is proposed in the form of a simple cubic lattice of spherical particles (blocks) possessing three translational and three rotational degrees of freedom. The force and couple interactions between the particles are modeled by elastic springs of five types. A long-wavelength continuum mathematical model of the soil has been elaborated by the method of structural modeling. An analytical relationship between its macroconstants and microstructure parameters has been found. It is shown that the obtained model differs from the model of the reduced Cosserat medium, which is often employed to describe granular media. In the low-frequency approximation, it can be reduced to the equations of the higher-order gradient theory of elasticity, which are similar to the Cosserat continuum equations with constrained rotation of particles. These equations contain both terms with mixed derivatives with respect to time and coordinate that take into account the inertia of particles rotation in the medium and lead to the wave dispersion, and terms proportional to the spatial derivatives of the fourth order, which describe the contribution of stresses caused by bending of the medium to the potential energy. In the framework of the higher-order gradient model, expressions for the classical and couple stresses in the considered geomedium are found. Boundary conditions are set that consist in the absence of normal and shear stresses on the upper platform of a half-space medium. A condition for the microstructure parameters has been revealed, under which the couple stresses can be neglected. The proposed here higher-order gradient model with given boundary conditions can be used to investigate the propagation and interaction of elastic waves in a semi-infinite geomedium, which are generated by the high-speed movement of trains, as well as to identify and study potentially dangerous effects caused by such movement.

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Han, Zejun, Mi Zhou, Xiaowen Zhou und Linqing Yang. „Dynamic Response of 3D Surface/Embedded Rigid Foundations of Arbitrary Shapes on Multi-Layered Soils in Time Domain“. International Journal of Structural Stability and Dynamics 19, Nr. 09 (28.08.2019): 1950106. http://dx.doi.org/10.1142/s0219455419501062.

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Significant differences between the predicted and measured dynamic response of 3D rigid foundations on multi-layered soils in the time domain were identified due to the existence of uncertainties, which makes the issue a complicated one. In this study, a numerical method was developed to determine the dynamic responses of 3D rigid surfaces and embedded foundations of arbitrary shapes that are bonded to a multi-layered soil in the time domain. First, the dynamic stiffness matrices of the rigid foundations in the frequency domain are calculated via integral domain transformation. Secondly, a dynamic stiffness equation for rigid foundations in the time domain is established via the mixed variables formulation, which is based on the discrete dynamic stiffness matrices in the frequency domain. The proposed method can be applied to the treatment of systems with multiple degrees of freedom without losing the true information that concerns the coupling characteristics. Numerical examples are presented to demonstrate the accuracy of the proposed method for predicting the horizontal, vertical, rocking, and torsional vibrations. Further, a parametric study was carried out to provide insight into the dynamic behavior of the soil–foundation interaction (SFI) while considering soil nonhomogeneity. The results indicate that the elastic modulus of the soil has a significant impact on the dynamic responses of the rigid foundation. Finally, a numerical example of a rigid foundation resting on a six-layered, semi-infinite soil demonstrates that the proposed method can be used to deal with multi-layered media in the time domain in a relatively easy way.

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Srinivasan, M. A., und K. Dandekar. „An Investigation of the Mechanics of Tactile Sense Using Two-Dimensional Models of the Primate Fingertip“. Journal of Biomechanical Engineering 118, Nr. 1 (01.02.1996): 48–55. http://dx.doi.org/10.1115/1.2795945.

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Tactile information about an object in contact with the skin surface is contained in the spatiotemporal load distribution on the skin, the corresponding stresses and strains at mechanosensitive receptor locations within the skin, and the associated pattern of electrical impulses produced by the receptor population. At present, although the responses of the receptors to known stimuli can be recorded, no experimental techniques exist to observe either the load distribution on the skin or the corresponding stress-state at the receptor locations. In this paper, the role of mechanics in the neural coding of tactile information is investigated using simple models of the primate fingertip. Four models that range in geometry from a semi-infinite medium to a cylindrical finger with a rigid bone, and composed of linear elastic media, are analyzed under plane strain conditions using the finite element method. The results show that the model geometry has a significant influence on the surface load distribution as well as the subsurface stress and strain fields for a given mechanical stimulus. The elastic medium acts like a spatial low pass filter with the property that deeper the receptor location, the more blurred the tactile information. None of the models predicted the experimentally observed surface deflection profiles under line loads as closely as a simple heterogeneous waterbed model that treated the fingerpad as a membrane enclosing an incompressible fluid (Srinivasan, 1989). This waterbed model, however, predicted a uniform state of stress inside the fingertip and thus failed to explain the spatial variations observed in the neural response. For the cylindrical model indented by rectangular gratings, the maximum compressive strain and strain energy density at typical receptor locations emerged as the two strain measures that were directly related to the electrophysiologically recorded response rate of slowly adapting type I (SAI) mechanoreceptors. Strain energy density is a better candidate to be the relevant stimulus for SAIs, since it is a scalar that is invariant with respect to receptor orientations and is a direct measure of the distortion of the receptor caused by the loads imposed on the skin.

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Khandelwal, Ratnesh, und J. M. Chandra Kishen. „Thermal Weight Functions and Stress Intensity Factors for Bonded Dissimilar Media Using Body Analogy“. Journal of Applied Mechanics 78, Nr. 6 (09.09.2011). http://dx.doi.org/10.1115/1.4003911.

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In this study, an analytical method is presented for the computation of thermal weight functions in two dimensional bi-material elastic bodies containing a crack at the interface and subjected to thermal loads using body analogy method. The thermal weight functions are derived for two problems of infinite bonded dissimilar media, one with a semi-infinite crack and the other with a finite crack along the interface. The derived thermal weight functions are shown to reduce to the already known expressions of thermal weight functions available in the literature for the respective homogeneous elastic body. Using these thermal weight functions, the stress intensity factors are computed for the above interface crack problems when subjected to an instantaneous heat source.

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Zhang, Yijing, und Alexander F. Vakakis. „High-Frequency Dynamic Overshoot in Linear and Nonlinear Periodic Media“. Journal of Computational and Nonlinear Dynamics 12, Nr. 1 (01.09.2016). http://dx.doi.org/10.1115/1.4034272.

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We study the transient responses of linear and nonlinear semi-infinite periodic media on linear elastic foundations under suddenly applied, high-frequency harmonic excitations. We show that “dynamic overshoot” phenomena are realized whereby, due to the high-rate of application of the high-frequency excitations, coherent traveling responses are propagating to the far fields of these media; and this, despite the fact that the high frequencies of the suddenly applied excitations lie well within the stop bands of these systems. For the case of a linear one-dimensional (1D) spring-mass lattice, a leading-order asymptotic approximation in the high frequency limit of the suddenly applied harmonic excitation shows that the transient dynamic overshoot is expressed in terms of the Green's function at its free end. Then, a two-dimensional (2D) strongly nonlinear granular network is considered, composed of two semi-infinite, ordered homogeneous granular lattices mounted on linear elastic foundations and coupled by weak linear coupling terms. A high-frequency harmonic excitation is applied to one of the granular lattices—designated as the “excited lattice”, with the other lattice designated as the “absorbing” one. The resulting dynamic overshoot phenomenon consists of a “pure” traveling breather, i.e., of a single propagating oscillatory wavepacket with a localized envelope, resulting from the balance of discreteness, dispersion, and strong nonlinearity. The pure breather is asymptotically studied by a complexification/averaging technique, showing nearly complete but reversible energy exchanges between the excited and absorbing lattices as the breather propagates to the far field. Verification of the analytical approximations with direct numerical simulations is performed.

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„Plane strain fracture in poroelastic media“. Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences 434, Nr. 1892 (09.09.1991): 605–33. http://dx.doi.org/10.1098/rspa.1991.0116.

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The effect of fully coupled poroelasticity on an impulsively loaded crack in plane strain is investigated. A formally exact solution for a semi-infinite crack in a linear, isotropic, poroelastic medium with a prescribed internal stress is considered; the solution is obtained using Laplace and Fourier transforms in time and space respectively and then using the Wiener-Hopf technique to solve the resulting functional equations. The stress intensity factor is found as a function of the Laplace variable s and is evaluated explicitly for small times and numerically for all times. The problem of a finite length crack embedded in a poroelastic medium under uniform impulsively applied tension at infinity is solved using the method of matched asymptotic expansions for small times. The formal solution for a steadily propagating semi-infinite crack under tension is outlined, the crack-tip fields are examined and the crack-tip stress intensity factors are found as functions of the crack velocity. Analytical solutions for the pore pressure and stress ahead of the crack are obtained and their relevance to the retardation of fracture discussed. The results extend the range of possible solutions of the fully coupled poroelastic equations to mixed boundary-value problems in fracture mechanics. These are fundamental to the study of the interaction between a diffusing pore fluid and the solid elastic skeleton. In particular, time dependent solutions to the symmetric problems of impulsive loadings and explicit solutions to the steady problems are considered.

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Kaplunov, J., D. A. Prikazchikov und L. Prikazchikova. „On non-locally elastic Rayleigh wave“. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 380, Nr. 2231 (18.07.2022). http://dx.doi.org/10.1098/rsta.2021.0387.

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The Rayleigh-type wave solution within a widely used differential formulation in non-local elasticity is revisited. It is demonstrated that this wave solution does not satisfy the equations of motion for non-local stresses. A modified differential model taking into account a non-local boundary layer is developed. Correspondence of the latter model to the original integral theory with the kernel in the form of the zero-order modified Bessel function of the second kind is addressed. Asymptotic behaviour of the model is investigated, resulting in a leading-order non-local correction to the classical Rayleigh wave speed due to the effect of the boundary layer. The suitability of a continuous set-up for modelling boundary layers in the framework of non-local elasticity is analysed starting from a toy problem for a semi-infinite chain. This article is part of the theme issue ‘Wave generation and transmission in multi-scale complex media and structured metamaterials (part 1)’.

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Makeev, Maxim A., und Anupam Madhukar. „Stress and strain fields from an array of spherical inclusions in semi-infinite elastic media: Ge nanoinclusions in Si“. Physical Review B 67, Nr. 7 (26.02.2003). http://dx.doi.org/10.1103/physrevb.67.073201.

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Kumar, Amit, und Santosh Kapuria. „Finite element simulation of axisymmetric elastic and electroelastic wave propagation using local-domain wave packet enrichment“. Journal of Vibration and Acoustics, 24.08.2021, 1–28. http://dx.doi.org/10.1115/1.4052244.

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Abstract A local-domain wave packet enriched multiphysics finite element (FE) formulation is employed for accurately solving axisymmetric wave propagation problems in elastic and piezoelastic media, involving complex wave modes and sharp jumps at the wavefronts, which pose challenges to the conventional FE solutions. The conventional Lagrangian interpolations for displacement, temperature and electric potential fields are enriched with the element-domain sinusoidal functions which satisfy the partition of unity condition. The extended Hamilton's principle is employed to derive the coupled system of equations of motion which is solved using the simple Newmark-beta direct time integration scheme without resorting to any remeshing near the wavefronts or post-processing. The performance of the enrichment is assessed for the axisymmetric problems of impact waves in elastic and piezoelectric cylinders and elastic half-space, bulk and Rayleigh waves in the semi-infinite elastic domain and ultrasonic Lamb wave actuation and propagation in plate-piezoelectric transducer system. The element shows significant improvement in the computational efficiency and accuracy over the conventional FE for all problems, including those involving multiple complex wave modes and sharp discontinuities in the fields at the wavefronts.

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Liu, Zhiwei, und Hui Qi. „Dynamic anti-plane behavior of rare earth giant magnetostrictive medium with a circular cavity defect in semi-space“. Scientific Reports 11, Nr. 1 (29.06.2021). http://dx.doi.org/10.1038/s41598-021-92841-5.

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AbstractAn analytical solution to the anti-plane dynamics problem of semi-space rare earth giant magnetostrictive media with circular cavity defects near the horizontal boundary under the action of SH wave is studied. Based on the Helmholtz theorem and the theory of complex function, the elastic-magnetic dynamic equation of magnetostrictive medium is established, and the semi-space incident wave field is written. In addition, based on the theory of complex function and the method of wave function expansion, the expression of the wave function of the scattered displacement field and the corresponding magnetic potential of the scattered wave under the condition of no stress and magnetic insulation of the horizontal boundary are obtained. Then, based on the conditions of free boundary stress, continuous magnetic induction intensity and continuous magnetic potential around the circular cavity, the infinite linear algebraic equations are established. Finally, the analytical expressions of dynamic stress concentration factor and magnetic field intensity concentration factor around circular cavity in semi-space rare earth giant magnetostrictive medium are obtained. Numerical examples show that the analysis results depend on the following parameters: permeability, dimensional-piezomagnetic coefficient, frequency of the incident wave, incident angle, distance between the circular cavity and horizontal boundary. These results have certain reference value for the study of non-destructive testing and failure analysis of rare earth giant magnetostrictive materials.

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Panchenko, Borys, Liudmyla Bukata und Denys Bahachuk. „MATHEMATICAL MODEL OF THE INTERACTION OF STATIONARY SH-WAVES WITH A SYSTEM OF CURVILINEAR CRACKS IN A HALF-SPACE“. Інфокомунікаційні та комп’ютерні технології, 2023, 73–84. http://dx.doi.org/10.36994/2788-5518-2023-01-05-09.

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A method for solving mathematical physics problems is proposed for semi-infinite media containing systems of curved crack-slits. Most of the studies known from the literature relate to the problems of diffraction of elastic waves on straight and circular cuts. However, in reality, the crack is usually not straight or circular. Studies have shown that the curvature of a crack significantly affects the value of the dynamic stress intensity coefficients. The value of this parameter also depends on the proximity of the defects to each other, since they always fall within the range of the reflected wave. The stress-strain state of media with complex properties can be effectively modeled by computing complexes in combination with software systems. Most studies are devoted to the development of the finite element method. However, the method of integral equations is very effective for solving anti-planar problems of diffraction theory. The advantage of this method is the reduction in the number of spatial variables, the high speed of convergence, and the possibility of using various efficient numerical solution methods. The method also has the ability to build efficient parallel computing schemes. A unified approach to solving the problem is developed on the basis of singular integral equations (SIEs). The corresponding dynamic boundary value problems for a clamped and force-free half-plane are investigated. The influence of the defect curvature, their interaction, and the proximity of the boundary on the magnitude and nature of the dynamic stress intensity coefficients is studied. Parallel algorithms allow to significantly reduce the computation time and analyse the characteristics of the wave field in more detail. The combination of the SIE method, which reduces the dimensionality of the problem by one, and provides significant savings in computing time due to the parallelization of computational procedures, leads to a significant increase in the efficiency of the proposed algorithm. The method can be used to assess the influence of various mechanical or geometric factors on the strength of bodies with defects.

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Selvadurai, P. A., R. Wu, P. Bianchi, Z. Niu, S. Michail, C. Madonna und S. Wiemer. „A Methodology for Reconstructing Source Properties of a Conical Piezoelectric Actuator Using Array-Based Methods“. Journal of Nondestructive Evaluation 41, Nr. 1 (21.02.2022). http://dx.doi.org/10.1007/s10921-022-00853-6.

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AbstractWe investigated the force produced by a conical piezoelectric (PZT, lead zirconate titanate) transducer actuated by high voltage pulses (HVP) in contact with a steel transfer plate. Using elastic wave propagation theory in a semi-infinite plate, we aimed to quantify the magnitude and estimate the shape of the force–time function via the body waves produced in the transfer plate using the displacement field recorded on an array of 20 absolutely calibrated PZT receivers. We first calibrated the receiver array using glass capillary fracture. We proceeded to use a conical PZT transducer to actively produce a source at the origin, allowing us to study the displacement field produced on the now calibrated PZT receiver array. We studied two types of HVP: An impulsive and step source. The calibrated receiver array was used to estimate the general shape of the force–time functions for each type of HVP. From our hypothesized force–time functions we were able to estimate the peak force produced by the PZT actuator: The impulsive source generated a force of $$f_{peak} = 2.90 \pm 0.42$$ f peak = 2.90 ± 0.42 N and the step source generated $$f_{peak} = 1.79 \pm 0.30$$ f peak = 1.79 ± 0.30 N, respectively, for a peak applied voltage of 273 V. This translates to an applied force of $$\sim $$ ∼ 0.011 N/V and 0.007 N/V for the impulse and step force–time functions, respectively, which is similar to estimates found in the literature for other conical transducers in contact with metallic transfer media. This measurement was verified directly by independent measurements of the peak force $$f_{peak}$$ f peak using a dynamic force transducer. We found that our methodology correctly estimated the magnitude of the force but is limited to transducers with incident angles $$\theta<$$ θ < 53$$^{\circ }$$ ∘ . Beyond this angle, overestimates of the force were observed due to the lack of body wave energy produced by the source. These results allow us to quantitatively determine the forces produced by active PZT techniques using only the measurement of the displacement field captured on a calibrated conical PZT array. Quantitative understanding of active PZT sources additionally constrains the transfer functions approach, which is commonly used in the non-destructive testing of materials and in other fields, such as rock physics and laboratory seismology.

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