Wave propagation in anisotropic layered media

The determination of the natural modes of wave propagation in an anisotropic layered medium requires the solution of a transcendental eigenvalue problem that is usually approached numerically with the aid of search techniques. Such computations require great effort. The method presented in this paper provides an alternate solution to this problem in terms of a quadratic eigenvalue problem involving tridiagonal matrices, for which the eigenvalues can be found with great speed and accuracy. The technique is then illustrated by means of an example involving a cross-anisotropic Gibson solid.     

Forbidden gaps in finite periodic and quasi-periodic cantor-like dielectric multilayers at normal incidence

Periodic and quasi-periodic Cantor-like bandgap structures that bordered upon a medium of refractive index n(0) are analyzed. An immersion model is used with the assumption that each layer is embedded between two identical regions of refractive index n(0) and thickness d(0), where d(0) is set equal to zero. Transmittance and group velocity are determined. Their dependence on n(0) is emphasized. Relations for the midgap value of the normalized group velocity are given. By use of these relations, diagrams are completed at different values of n(0), showing the pairs of quarter-wave-layer refractive indices at which there is an apparent superluminal tunneling through the finite periodic and quasi-periodic Cantor-like bandgap structures.     

On the propagation of waves in layered anisotropic media in generalized thermoelasticity

In view of the increased usage of anisotropic materials in the development of advanced engineering materials such as fibers and composite and other multilayered, propagation of thermoelastic waves in arbitrary anisotropic layered plate is investigated in the context of the generalized theory of thermoelasticity. Beginning with a formal analysis of waves in a heat-conducting N-layered plate of an arbitrary anisotropic media, the dispersion relations of thermoelastic waves are obtained by invoking continuity at the interface and boundary conditions on the surfaces of layered plate. The calculation is then carried forward for more specialized case of a monoclinic layered plate. The obtained solutions which can be used for material systems of higher symmetry (orthotropic, transversely isotropic, cubic, and isotropic) are contained implicitly in our analysis. The case of normal incidence is also considered separately. Some special cases have also been deduced and discussed. We also demonstrate that the particle motions for SH modes decouple from rest of the motion, and are not influenced by thermal variations if the propagation occurs along an in-plane axis of symmetry. The results of the strain energy distribution in generalized thermoelasticity are useful in determining the arrangements of the layer in thermal environment.     

Time-resolved line focus acoustic microscopy of layered anisotropic media: application to composites

This paper presents theoretical and experimental studies of the time-domain response of line focus acoustic microscopy from a layered anisotropic medium. A method for elastic constant reconstruction from acoustic microscopy signatures also is presented. The microscopy response is complicated by multiple reflections in the layers and by the anisotropic nature of the material. The model is based on a new, stable recursive stiffness matrix algorithm developed for a multilayered anisotropic medium, which is applied to the interpretation of the time-resolved acoustic microscopy signature. Specific examples are given for unidirectional and multidirectional graphite epoxy composites. It is shown that the fluid load has a significant effect on the leaky surface waves in these composites, increasing surface wave speed above that for the slow transverse wave. This results in its absence from the microscopy signature of the surface wave. The theoretical results are compared with experiments carried out using a line focus PVDF transducer developed at National Institute of Standards and Technology (NIST). Time-resolved acoustic microscopy has been applied to the determination of elastic constants of a unidirectional composite or of one lamina in a cross-ply composite. The lateral waves and multiple reflections of bulk waves appearing in the microscopy signatures are used for the elastic properties reconstruction. The reconstruction results are compared to data obtained by the self-reference double-through-transmission ultrasonic bulk wave method.     

Static stresses in a periodically layered anisotropic elastic composite containing a periodic array of planar cracks

Summary The problem of calculating the static elastic stresses in a periodically layered anisotropic composite containing a periodic array of planar cracks is considered. We formulate the problem in terms of a system of simultaneous finite-part singular integral equations which can be solved numerically using collocation techniques. The solution of the integral equations enables relevant quantities such as the stress intensity factors to be computed. Numerical results are obtained for specific cases of the problem.     

Mechanics of layered anisotropic poroelastic media with applications to effective stress for fluid permeability

The mechanics of vertically layered porous media has some similarities to and some differences from the more typical layered analysis for purely elastic media. Assuming welded solid contact at the solid-solid interfaces implies the usual continuity conditions, which are continuity of the vertical (layering direction) stress components and the horizontal strain components. These conditions are valid for both elastic and poroelastic media. Differences arise through the conditions for the pore pressure and the increment of fluid content in the context of fluid-saturated porous media. The two distinct conditions most often considered between any pair of contiguous layers are: (1) an undrained fluid condition at the interface, meaning that the increment of fluid content is zero (i.e., δζ = 0), or (2) fluid pressure continuity at the interface, implying that the change in fluid pressure is zero across the interface (i.e., δp_f = 0). Depending on the types of measurements being made on the system and the pertinent boundary conditions for these measurements, either (or neither) of these two conditions might be directly pertinent. But these conditions are sufficient nevertheless to be used as thought experiments to determine the expected values of all the poroelastic coefficients. For quasi-static mechanical changes over long time periods, we expect drained conditions to hold, so the pressure must then be continuous. For high-frequency wave propagation, the pore-fluid typically acts as if it were undrained (or very nearly so), with vanishing of the fluid increment at the boundaries being appropriate. Poroelastic analysis of both these end-member cases is discussed, and the general equations for a variety of applications to heterogeneous porous media are developed. In particular, effective stress for the fluid permeability of such poroelastic systems is considered; fluid permeabilities characteristic of granular media or tubular pore shapes are treated in some detail, as are permeabilities of some of the simpler types of fractured materials.     

Collinear periodic crack in anisotropic bimaterials

The problems of collinear periodic cracks in anisotropic bimaterials are examined in this paper. By means of Stroh formalism, conformal mapping and analytic continuation arguments, explicit full domain solutions for the periodic cracks are presented. Following the procedure used by Wu (1990), we also obtain the corresponding stress intensity factors. The solutions are valid not only to plane problems but also to antiplane problems and those problems whose inplane and antiplane deformations couple each other. This revised version was published online in August 2006 with corrections to the Cover Date.     

Path-independent integrals in anisotropic media

The concept proposed by the author for the construction of path-independent integrals (PI Is) in isotropic media is generalized for the construction of PIIs in anisotropic plane bodies weakened by a number of collinear cracks. The PIIs are classified into three classes satisfying well-defined restrictions. Using this classification about fifty general forms of PIIs are given, from which an infinity of new PI Is can be constructed. In many cases the form of the proposed integrals is simpler than the already known ones. This will facilitate their use in conjunction with finite element or experimental methods.A number of illustrative examples is also given.

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Résum'e L'auteur a proposé un concept pour construire des intégrals indépendantes du parcours dans les milieux isotropes. Il généralise à présent son concept pour construire ces intégrales dans le cas des corps plans anisotropes affaiblis par la présence d'un grand nombre de fissures colinéaires. Ces intégrales sont classées suivant trois catégories correspondant à des restrictions bien définies. En utilisant cette classification, près de cinquante formes générales d'intégrales indépendantes du parcours sont fournies, et, à partir d'elles, une infinité d'intégrales peuvent être construites. Dans de nombreux cas, la forme des intégrales proposées est plus simple que celles déjà connues. Ceci va faciliter leur utilisation, en association avec la méthode des éléments finis ou des methodes experimentales.On donne également plusieurs exemples d'application.

     

Cracks in anisotropic elastic media

A numerical method for 3D problems of cracks in anisotropic media is developed, and this is based on the variational approach to the crack opening problem. Properties of the pseudodifferential operator of the crack equilibrium problem are considered. Numerical examples are also presented.     

Collinear periodic cracks in an anisotropic medium

The problem of collinear periodic cracks in an anisotropic medium is examined in this paper. By means of Stroh formalism and the conformal mapping method, we obtain general periodic solutions for collinear cracks. The corresponding stress intensity factors, crack opening displacements and strain energy release rate are found.     

Deformation of an anisotropic layered reinforced cylinder

On the basis of the developed approach to the analysis of the stressed states of hollow thick-walled layered cylinders described by three-dimensional equations of the theory of elasticity, we study the influence of the inhomogeneity and anisotropy of the elastic properties of materials with regard for the type of fastening the layers to each other, fixtures of the ends, and loading modes on the level of stresses and deformability of reinforced cylinders. It is shown that a rational scheme of reinforcement can be chosen by changing the structure of the reinforcement and, hence, the characteristics of the entire material.     

Deformation of an anisotropic layered reinforced cylinder

On the basis of the developed approach to the analysis of the stressed states of hollow thick-walled layered cylinders described by three-dimensional equations of the theory of elasticity, we study the influence of the inhomogeneity and anisotropy of the elastic properties of materials with regard for the type of fastening the layers to each other, fixtures of the ends, and loading modes on the level of stresses and deformability of reinforced cylinders. It is shown that a rational scheme of reinforcement can be chosen by changing the structure of the reinforcement and, hence, the characteristics of the entire material. Translated from Problemy Prochnosti, No. 5, pp. 78–88, September–October, 1997.     

Acoustical vector solitons in anisotropic media

A theory of acoustical vector solitons of self-induced transparency in anisotropic media is developed. It is shown that, in these systems, a two-component vector soliton oscillating with the difference and sum of the frequencies in the vicinity of the frequency of a carrying acoustic wave may arise. Explicit analytical expressions for the form and parameters of a nonlinear wave depending on the direction of pulse propagation are given.     

Avalanches in anisotropic sheared granular media

We study the influence of particle shape anisotropy on the occurrence of avalanches in sheared granular media. We use molecular dynamic simulations to calculate the relative movement of two tectonic plates. Our model considers irregular polygonal particles constituting the material within the shear zone. We find that the magnitude of the avalanches is approximately independent of particle shape and in good agreement with the Gutenberg–Richter law, but the aftershock sequences are strongly influenced by the particle anisotropy yielding variations on the exponent characterizing the empirical Omori’s law. Our findings enable one to identify the presence of anisotropic particles at the macro-mechanical level only by observing the avalanche sequences of real faults. In addition, we calculate the probability of occurrence of an avalanche for given values of stiffness or frictional strength and observe also a significant influence of the particle anisotropy.     

Heat transfer in anisotropic metallic media

The temperature distribution over the cross-section of a metallic sample with anisotropic kinetic coefficients heated by an electric current in liquid helium has been studied.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 58, No. 4, pp. 670–675, April, 1990.     

An anisotropic layered material with a crack

Summary The problem of an anisotropic layered material which contains a plane crack in its interior is considered here. The problem is reduced to a set of Fredholm integral equations of the second kind which may be solved iteratively. Once these integral equations are solved, the crack tip stress intensity factors may be readily computed. Numerical results for some particular examples involving transversely isotropic materials are given here.     

层状周期介质中的非线性平面声波的传播

对于在非线性媒质中传播的有限幅度平面波,可以一维拉格朗日坐标中的一维时空函数来表示;任一单频简谐波通常展开到二阶的形式:     

Explicit eigenmodes for anisotropic media

An exact computational algorithm that solves steady-state Maxwell equations for fields produced by electric currents in the presence of slabs with biaxial anisotropy is developed. Eigenmodes are computed explicitly and are used to study unattenuated propagation and transverse modes     

轴向载荷周期结构梁的弯曲振动带隙特性

各种载荷广泛存在于结构振动中,影响结构的振动特性。利用传递矩阵法,建立了轴向载荷周期结构梁弯曲振动特性理论模型,能够计算轴向载荷周期结构梁弯曲振动的能带结构和传输特性。研究表明,轴向载荷周期结构梁弯曲振动存在带隙,并分析了轴向载荷对带隙频率范围和衰减的影响。通过调节载荷条件,可以实现了超低频带隙特性。通过调节轴向载荷的大小和方向可以提高带隙的适应性。     

Maxwell equations in Fourier space: fast-converging formulation for diffraction by arbitrary shaped, periodic, anisotropic media.

We establish the most general differential equations that are satisfied by the Fourier components of the electromagnetic field diffracted by an arbitrary periodic anisotropic medium. The equations are derived by use of the recently published fast-Fourier-factorization (FFF) method, which ensures fast convergence of the Fourier series of the field. The diffraction by classic isotropic gratings arises as a particular case of the derived equations; the case of anisotropic classic gratings was published elsewhere. The equations can be resolved either through classic differential theory or through the modal method for particular groove profiles. The new equations improve both methods in the same way. Crossed gratings, among which are grids and two-dimensional arbitrarily shaped periodic surfaces, appear as particular cases of the theory, as do three-dimensional photonic crystals. The method can be extended to nonperiodic media through the use of a Fourier transform.