共查询到19条相似文献,搜索用时 78 毫秒
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本文讨论了饱和多孔介质的粘弹体本构关系。把Lee的弹性和粘弹性比拟理论,拓展到饱和多孔介质领域内。用比拟理论解出了饱和粘性土的常载和变载的一维固结问题,并利用比拟理论的属性,可以由简单的粘弹性本构关系来推求复杂的本构关系,得到了粘弹性地基上的粘弹性梁板问题的解答。由此初步形成了饱和多孔介质粘弹性比拟法的完整理论。 相似文献
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各向异性介质中有衬砌的非圆形结构与SH波的相互作用 总被引:4,自引:0,他引:4
本文利用复变函数方法求解各向异性介质中有衬砌的非圆形结构与SH波的相互作用问题.各向异性介质可以用来模拟结构周围的地质条件.利用作者在文献[5,7]中的方法决定介质和衬砌结构中的散射波,结合Savin在文献[6]中求解有衬砌结构所采用的对结构轮廓线进行近似处理的方法,并利用结构与介质的连续性条件与衬砌内边界上的边界条件,对问题进行求解.作为算例.本文讨论了在同一种各向异性介质中,两种不同材料组成的正方形有衬砌的结构与SH波的相互作用问题.给出了数值分析结果. 相似文献
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本文考虑了一个带有非线性阻尼项的粘弹性方程组.通过使用扰动能量的方法,我们得到了整体解的能量泛函依据松弛函数的衰减速率按指数衰减或者多项式衰减. 相似文献
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研究了扭转表面波在一个半无限非均匀半空间中的传播,半空间上覆盖着具有初始应力的各向异性多孔弹性层,弹性层的刚度和密度线性地变化,造成了界面的不规则性.半空间中界面的不规则性,用一个矩形形式表示.可以发现,扭转表面波在这样假定的介质中传播,得到了没有不规则性时的扭转表面波的速度方程.还可以发现,对于均匀半空间覆盖的层状介质,扭转表面波的速度与Love波的速度相一致. 相似文献
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横观各向同性含液饱和多孔介质中应力波传播的特征分析 总被引:2,自引:0,他引:2
根据广义特征理论,对横观各向同性含液饱和多孔介质中应力波传播特性进行了特征分析.给出了特征曲面的微分方程以及沿次特征线的相容条件,得到了波阵面的解析表达式.详细地讨论了应力波在横观各向同性含液饱和多孔介质中传播时,其速度曲面和波阵面的形状及性质.分析结果亦表明,纯固体中应力波传播的特征方程,是含液饱和多孔介质中应力波特征方程的特例. 相似文献
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各向异性介质中带衬砌的圆形结构与SH波相互作用 总被引:1,自引:0,他引:1
本文利用复变函数方法求解各向异性介质中带衬砌的圆形结构与SH波的相互作用问题。各向异性介质可以用来模拟地质条件。利用文献[5]中的方法则可决定介质中的散射波,再利用圆形结构上给出的边界条件,则可对问题进行求解,作为算例,本文给出了在一种各向异性介质中,二种不同材料组成的圆形带衬砌的结构与SH波相互作用问题的数值分析结果,并予以讨论。 相似文献
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通过运用扰动能量方法研究了一类具有弱非线性耗散项粘弹性波方程解的能量衰减性,其中耗散项显依赖于时间t,得到解的衰减率依赖于阻尼的增长速度和t的函数. 相似文献
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The paper deals with finite–difference (f-d) approach to simulation of elastic waves' propagation in anisotropic elastic media with general symmetry. Any implementation of this approach claims resolution of two key problems:
- construction of an effective f-d scheme itself; we propose to use the Lebedev's scheme (LS) being a natural generalization of Virieux staggered grid scheme (VS) widely used for isotropy; we prove that LS possesses better dispersion properties in comparison with well known Rotated Staggered Grids Scheme (RSGS).
- stable domain distension. The Perfectly Matched Layers(PML) useful for isotropic problems can be unstable in the case of anisotropy. Lebedev scheme allows one to use Optimal Grids (OG) which gives a possibility to implement efficient and low cost domain distension.
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Z. A. Yanson 《Journal of Mathematical Sciences》2003,117(2):4049-4063
The Love waves concentrated near the surface of an anisotropic elastic body are studied. A uniform asymptotics of the wave field is constructed with the use of the nonstationary caustic expansion (Yu. A. Kravtsov's ansatz) in the form of a space-time ray series. Using three types of waves, which propagate along any direction in an elastic medium, as a vector basis, sufficient conditions for the existence of a nonzero asymptotic solution of the problem under study are obtained. The procedure for constructing asymptotic series is illustrated with the model of a transversely isotropic medium. Bibliography: 9 titles. 相似文献
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Mariana Haragus 《偏微分方程通讯》2013,38(5):791-815
We investigate corners and steps of interfaces in anisotropic systems. Starting from a stable planar front in a general reaction-diffusion-convection system, we show existence of almost planar interior and exterior corners. When the interface propagation is unstable in some directions, we show that small steps in the interface may persist. Our assumptions are based on physical properties of interfaces such as linear and nonlinear dispersion, rather than properties of the modeling equations such as variational or comparison principles. We also give geometric criteria based on the Cahn–Hoffman vector, that distinguish between the formation of interior and exterior corners. 相似文献
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Doklady Mathematics - The problem of seismic wave propagation in a heterogeneous geological medium is considered. The dynamic behavior of the medium is described by the linear elastic system of... 相似文献
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We consider electromagnetic waves propagating in a periodic medium characterized by two small scales. We perform the corresponding homogenization process, relying on the modelling by Maxwell partial differential equations. 相似文献
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L. A. Molotkov 《Journal of Mathematical Sciences》2006,132(1):69-82
The propagation of seismic waves in block two- and three-dimensional fluid media is investigated. For these media, effective
models, which are anisotropic fluids, are established. Formulas for the velocities of wave propagation in these fluid media
are derived and analyzed. Special investigation is conducted in the cases where blocks with different fluids alternate along
the coordinate axes or where blocks filled with a fluid are surrounded by blocks with another fluid. In both cases, the dependence
of the wave velocities in the entire medium on the differences of the densities and the wave velocities in fluid blocks is
studied. Bibliography: 9 titles.
Dedicated to P. V. Krauklis on the occasion of his seventieth birthday
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 308, 2004, pp. 124–146. 相似文献
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The problem of transformation of the front of a plane longitudinal shock wave by curvilinear interfaces of layered anisotropic elastic media with different mechanical properties is considered. To solve the nonlinear Snell equations, the approach based on a synthesis of the Newton method and the algorithm of parametric continuation of a solution is used. The cases of focusing and scattering of rays by convex and concave interfaces of layered composite media and by convex lenses are investigated. Numerical examples are given for various ratios between the parameters of the elastic media. 相似文献
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L. A. Molotkov 《Journal of Mathematical Sciences》2005,127(6):2469-2481
An approach of averaging block elastic-fluid media is proposed, and an effective model for a block medium in which every cell consists of three elastic blocks and one fluid block is constructed. An investigation of the model equations shows that in this model two longitudinal waves and one wave with a concave front set propagate. The limiting cases where the fluid block is narrowed down to a point or where the fluid block occupies the whole cell are considered in the paper. Bibliography: 10 titles.__________Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 297, 2003, pp. 230–253. 相似文献
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L. A. Molotkov 《Journal of Mathematical Sciences》2005,127(6):2482-2491
A two-dimensional medium consisting of alternating elastic and fluid blocks along the x and z axes is considered. For this block medium, an effective model described by a system of equations is constructed by the method of matrix averaging. An investigation of the equations of this model enables one to separate two body waves from the wave field, to construct their fronts, and to obtain expressions for their velocities along the axes. The effective model is considered in the cases where the block medium is converted to a layered elastic-fluid medium, where all the blocks are of the same size, and where an elastic or a fluid medium occupies the entire volume. Bibliography: 7 titles.__________Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 297, 2003, pp. 254–271. 相似文献