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41.
D. N. Mikhailov 《Fluid Dynamics》2006,41(1):112-120
The problem of the propagation of longitudinal Biot waves in a porous medium saturated with a weakly compressible liquid (water) or a gas is considered theoretically. The frequency dependence of the phase velocities and damping coefficients is investigated numerically. It is shown that for a certain relationship between the parameters of the porous medium and the saturating fluid there is a “critical” frequency at which the properties of longitudinal waves of both kinds are identical. An analytical expression for this “critical” frequency is obtained. It is shown that for a gas-saturated porous medium, at a certain frequency, in both longitudinal waves the relative gas-matrix motion changes type. Assuming that the saturating-gas behavior corresponds to an adiabatic equation of state, an estimate is obtained for the threshold pore pressure necessary for the restructuring of the relative motion. The wave associated with matrix deformation is shown to have a high damping coefficient in a porous medium saturated with a weakly compressible liquid (water in the case considered) but to be only weakly damped in a gas-saturated porous medium. 相似文献
42.
Herein we consider Rayleigh waves propagating along the free surface of a macroscopically homogeneous, anisotropic, prestressed half-space. We adopt the formulation of linear elasticity with initial stress and assume that the deviation of the prestressed anisotropic medium from a comparative ‘unperturbed’, unstressed and isotropic state, as formally caused by the initial stress and by the anisotropic part of the incremental elasticity tensor, be small. No assumption, however, is made on the material anisotropy of the incremental elasticity tensor. With the help of the Stroh formalism, we derive a first-order perturbation formula for the shift of phase velocity of Rayleigh waves from its comparative isotropic value. Our perturbation formula does not agree totally with that which was derived some years ago by Delsanto and Clark, and we provide another argument as further support for our version of the formula. According to our first-order formula, the anisotropy-induced velocity shifts of Rayleigh waves, taken in totality of all propagation directions on the free surface, carry information only on 13 elastic constants of the anisotropic part of the incremental elasticity tensor. The remaining eight elastic constants are those which would become zero if were monoclinic with the two-fold symmetry axis normal to the free surface of the material half-space in question. 相似文献
43.
The tomographic reconstruction of supersonic flows faces two challenges. Firstly, techniques used in the past, such as the
direct Fourier method (DFM) (Gottlieb and Gustafsson in On the direct Fourier method for computer tomography, 1998; Morton
in Tomographic imaging of supersonic flows, 1995) or various backprojection (Kak and Slaney in Principles of computerized
tomographic imaging, vol. 33 in Classics in Applied Mathematics, 2001) techniques, have only been able to reconstruct areas
of the flow which are upstream of any opaque objects, such as a model. Secondly, shock waves create sharp discontinuities
in flow properties, which can be difficult to reconstruct both in position and in magnitude with limited data. This paper
will present a reconstruction method, matrix inversion using ray-tracing and least squares conjugate gradient (MI-RLS), which uses geometric ray-tracing and a sparse matrix iterative solver (Paige and Saunders in ACM Trans. Math. Softw.
8(1):43–71, 1982) to overcome both of these challenges. It will be shown, through testing with a phantom object described
in tomographic literature, that the results compare favourably to those produced by the DFM technique. Finally, the method
will be used to reconstruct three-dimensional density fields from interferometric shock layer images, with good resolution
(Faletič in Tomographic reconstruction of shock layer flows, 2005).
This paper was based on work that was presented at the 3rd International Symposium on Interdisciplinary Shock Wave Research,
Canberra, Australia, March 1–3, 2006. 相似文献
44.
Some of the main progress on the investigation of the mechanism of the wave formation in explosive welding at the Institute
of Mechanics is summarized and others' previous works are reviewed. Our systematic experiments and analysis do not substantiate
the theory of wave formation based on Karman vortex-street analogy or Helmholtz instability. On the contrary, they show that
material strength insensitive to strain rate plays an important role. A simple hydro-plastic model is presented to explain
the main features regarding the interfacial wave formation and to estimate the magnitude of wave length. The result is in
broad agreement with experiment. 相似文献
45.
H.?J.?HupkesEmail author S.?M.?Verduyn?Lunel 《Journal of Dynamics and Differential Equations》2005,17(3):523-572
We present a variant of Newton’s method for computing travelling wave solutions to scalar bistable lattice differential equations. We prove that the method converges to a solution, obtain existence and uniqueness of solutions to such equations with a small second order term and study the limiting behaviour of such solutions as this second order term tends to zero. The robustness of the algorithm will be discussed using numerical examples. These results will also be used to illustrate phenomena like propagation failure, which are encountered when studying lattice differential equations. We finish by discussing the broad application range of the method and illustrate that higher dimensional systems exhibit richer behaviour than their scalar counterparts. 相似文献
46.
L. A. Tkacheva 《Fluid Dynamics》2005,40(2):282-296
The problem of the behavior of an elastic floating plate in the form of a strip under the action of a periodic surface load is solved using the Wiener-Hopf technique. The shortwave approximation is found in explicit form. The effect of the frequency and nature of the acting load on the vibration amplitudes of the fluid and the plate is investigated numerically. It is found that for certain loads no waves propagate in the fluid and the vibrations of the plate are localized in the neighborhood of the acting load. Conditions under which local vibration can be realized are found.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, 2005, pp. 132–146.Original Russian Text Copyright © 2005 by Tkacheva. 相似文献
47.
In this paper, based on the theory of multiple scattering of elastic waves, employing wave functions expansion method, multiple scattering and strain energy density in semi-infinite functional graded materials with a circular cavity are investigated, the analytical solution of the problem is derived, and the numerical solution of the strain energy density factors around the cavity is also presented. The effects of the distance between the cavity and the edge of the materials, the wave number and the non-homogeneous parameter of materials on strain energy density factors are analyzed. From analysis, it can be seen that when the non-homogeneous parameter of materials is less than zero, it has less influence on the maximum strain energy density factor around the cavity; however, it has greater influence on the distribution of strain energy density factors around the cavity. When the non-homogeneous parameter of materials is greater than zero, it has greater influence on both the maximum strain energy density factor and the distribution of strain energy density factor around the cavity, especially in the case that the distance between the cavity and the edge is comparatively little. 相似文献
48.
We study edge waves propagating along the edge of an asymmetrically laminated elastic plate for which the out-of-plane component of displacement is coupled with the in-plane components. A Stroh-like formulation is used to show that such a plate can support at most two edge waves. An efficient method for computing the edge-wave speeds is proposed and explained through examples. 相似文献
49.
50.
Mild-slope (MS) type equations are depth-integrated models, which predict under appropriate conditions refraction and diffraction of linear time-harmonic water waves. By using a streamfunction formulation instead of a velocity potential one, the complementary mild-slope equation (CMSE) was shown to give better agreement with exact linear theory compared to other MS-type equations. The main goal of this work is to extend the CMSE model for solving two-layer flow with a free-surface. In order to allow for an exact reference, an analytical solution for a two-layer fluid over a sloping plane beach is derived. This analytical solution is used for validating the results of the approximated MS-type models. It is found that the two-layer CMSE model performs better than the potential based one. In addition, the new model is used for investigating the scattering of linear surface water waves and interfacial ones over variable bathymetry. 相似文献