On strike-slip Somigliana dislocations in a layered elastic half-space

Summary We consider a vertical strike-slip fault which is embedded in an elastic layer overlying an elastic half-space. The layer and the half-space have different rigidities. In such a model, dislocations on the fault are usually taken to occur with uniform slip, due to the difficulty of solving analytically the general problem of variable-slip (Somigliana) dislocations in this case. We adopt the Somigliana dislocation representing a crack in a homogeneous half-space and examine under which conditions this can be considered a good approximation to a crack in the layered medium. Better approximations can be obtained by super-positions of Chebyshev polynomials of the first kind and odd degree.

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Riassunto Si considera una faglia verticale a scorrimento orizzontale, situata in uno strato elastico sovrastante un semispazio elastico di rigidità diversa Nell'àmbito di questo modello, sono state di solito considerate dislocazioni con scorrimento uniforme su tutta la faglia, a causa della difficoltà di risolvere analiticamente il problema della dislocazione a scorrimento variabile (dislocazione di Somigliana). Nel presente lavoro si adotta la dislocazione di Somigliana che rappresenta una frattura in un semispazioomogeneo e si studiano le condizioni in cui questa può essere considerata una buona approssimazione alla soluzione nel mezzo stratificato. Approssimazioni migliori possono ottenersi per sovrapposizione di polinomi di Chebyshev del primo tipo e grado dispari.

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Резйме Мы рассматриваем вертикалыу дефект проскалъзования, которыю внедрен в упручию слою, расположенныю над упрутим полупространством. Слою и полупространство имейт разлибные модули сдвича. В таком модели дислокации обыгно возникают при равномерном проскалъзовахии. Мы принимаем, гто дислокация представляет треЩину в однорном полупространстве, и исследуем, при каких условиях дислокация может рассматриватщся как трещина в слоистой среде. Наилугжее приближение может вытъ полугено с помощью суперпозиции полиномов Чебышева первого рода и нечетною степени.

     

分层半空间表面非线性瑞利波的激发*

针对非线性瑞利波在均匀分层半空间结构中的激发和传播规律进行研究。根据摄动理论和模态分解将分层半空间结构中瑞利波的二次谐波声场表示为二倍频瑞利波模式的线性组合,经由互易关系得到各模式的展开系数表达式。对不同分层半空间结构中瑞利波二次谐波的激发和传播特性进行讨论,结果表明相速度匹配的瑞利波模式其二次谐波分量随传播距离线性增长,非匹配模式的二次谐波分量则沿传播方向周期震荡传播。此外,文中定义非线性参数表征瑞利波模式产生的非线性程度,这有利于选择出具有明显非线性效应的匹配点,为后续检测工作提供理论依据,具有指导意义。     

A two-dimensional generalized thermo-hydro-mechanical-coupled problem for a poroelastic half-space

ABSTRACT

This study investigated the effects of coupled thermo-hydro- mechanical dynamics on an isotropic, uniform, fully saturated, and poroelastic half-space subgrade whose surface is subjected to either mechanical force or thermal load. In this paper, our formulation is deduced in the context of two theories of generalized thermoelasticity: the Lord-Shulman theory and the Green-Lindsay theory. We then deduce the general relationships among non-dimensional vertical displacement, excess pore water pressure, vertical stress, and temperature distribution using Normal Mode Analysis (NMA) and depict them graphically. NMA is a method using weighted residuals to derive analytical solutions and can thus solve partial differential equations more quickly compared to other methods. This study continues our work of applying NMA to derive theoretical results in the multi-field coupling of soil. Following the analysis, the theoretical results are illustrated with a numerical example and a Maple program is developed. Furthermore, the differences between the coupled thermo-hydro-mechanical dynamic model (THMD) and the thermo-elastic dynamic model (TED) are presented. This proposed derivation method can be widely applied in the geotechnical engineering field, especially with regard to the mechanical and thermal behaviors of commercial buildings, high-speed railways, and highway energy foundations.     

On diffusion-elastic instabilities in a solid half-space

A model of the diffusion-elastic instability that appears in an ensemble of non-equilibrium atomic defects in unbounded condensed media as well as on the free surface of a half-space is introduced and studied. The dynamical model developed here is based on coupled evolution equations for the elastic displacement of the medium and atomic defect density fields. The idea of an instability model is related to a drift of atomic defects under the influence of elastic fields. It is shown that the development of this instability creates ordered structures of coupled strain and defect-concentration fields. Dispersion relationships for the growth increment of these structures are derived and their characteristic scales are obtained.     

On the theory of layered high-temperature superconductors: Finite temperature properties

We extend the study of a model for layered high-temperature superconductors to finite temperatures. The model assumes Fermi liquid properties for the carriers, which form a narrow tight-binding band. The carriers are subject to on-site intralayer and nearest neighbor interlayer interactions. The previous studies of the zero temperature properties, revealing remarkable agreement with experimental data, are extended to finite temperatures. These properties include the tunneling conductance for diffuse and specular transmission in a normal isolator superconductor junction, specific heat, nuclear spin relaxation time and the London penetration depth. Our results are compared with experimental findings.     

On dynamic properties of gravitational fields

Using a theory for the individualization of points of a Riemannian space and introduction or corresponding comoving reference systems for the gravitational field in classical general relativity expressions are obtained for the field energy density as a four-dimensional scalar and a field energy-momentum tensor of rank 2 (not pseudoscalar and pseudotensor, respectively). The results relate to all types of vacuum Riemannian space in agreement with the classifications of A. Z. Petrov and R. Penrose.     

On the problem of coupling of ultrasonic receivers to layered structures for process control

Different layers in the construction of ultrasonic receiving transducers have been identified as a significant factor in the frequency response of these transducers. The discussion has been extended to the reception of signals through the layers of a process vessel-wall to determine whether the resulting system can be made independent of frequency over a significant spectral range and whether a system can be identified that is essentially independent, in its spectral response, to the thickness of one of the layers (the couplant to the vessel). While the present results are limited to a frequency range of 0–2 MHz, they can readily be extended to other frequency ranges. These computations have as variables the backing material, the transducer material, a wear plate, one or two quarter wavelength layers, the couplant and the structure of the vessel wall. The effect of thin bonding layers for the quarter wavelength plates is also briefly considered. As may have been expected each extra layer introduced into the system produces its own series of resonances. The case of a number of quarter wavelength layers can give a flat frequency response over almost a megahertz of bandwidth but great care needs to be taken with the bonding layers. A system in which the thickness of the couplant had little effect on the overall spectral response was not found.     

Contact problem for a transversely isotropic half-space with an unknown contact region

A three-dimensional contact problem with an unknown contact region for a transversely isotropic half-space, when the isotropy planes are perpendicular to the half-space boundary, is investigated. The method described makes it possible to evaluate effectively the Brinell and Vickers hardness and the contact strength of materials, the near-surface properties of which can substantially depend on the direction (titanium, zinc, beryllium, cobalt, aluminum and zinc oxides, graphite, wood, temoral bone, sapphire, etc; five elastic constants). We use the fact that the kernel of the integral equation of a contact problem can be represented in a form free of quadratures. Such a form of the kernel, in view of the simplicity of its regularization in singular points, makes it possible to apply the method of nonlinear boundary integral equations developed by Galanov to solve the contact problem with an unknown contact region. To debug the computer program, an exact solution of the contact problem for a stamp shaped like an elliptic paraboloid is used. Calculations are made for various materials with the incorporation of the stamp shaped as a rectangular pyramid. The contact regions, pressures, and the values of the impressing force with the specified stamp immersion are determined.     

一种计算分层半空间上方导线瞬态响应的新方法

提出了一种将时域积分方程(time domain integral equation, TDIE)方法和时域有限差分(finite differnce time domain, FDTD)方法相结合计算分层有耗半空间上方导线瞬态电磁响应的新方法.其中,一维FDTD方法用于计算入射电磁波经分层半空间反射的时域波形.TDIE用于求解细导线在加入两个激励源(直接入射电磁波和经分层半空间反射的电磁波)时的瞬态响应.相关计算理论和数值模拟结果说明了本文方法是一种解决了分层有耗介质上方水平放置导线瞬态响应的高效解决方案. 关键词： 时域积分方程 时域有限差分 细导线 分层半空间     

On the high-frequency measurement of the dynamic properties of nano-particle colloids

Measurement of the magnetic complex susceptibility, χ(ω)=χ′(ω)−iχ″(ω) by means of the transmission line technique, is a well established method for the determination of the dynamic properties of nano-particle colloids, such as magnetic fluids. From polarising studies one can obtain accurate data on the anisotropy constant, K, anisotropy field, H_A, gyromagnetic constant γ, and the damping parameter, α. From data on χ(ω), one can determine the loss tangent, tan δ, of the samples and also a value of the precessional decay time, τ₀. From polarized studies, one can investigate the presence of any hysteresis. The technique is also suitable for the investigation of the magnetic properties of composite samples. In this paper a review of the above mentioned topics are presented with examples of results obtained for a number of magnetic fluids.     

On reflection from a suddenly created plasma half-space: transientsolution

The reflection by a suddenly created plasma half-space of a time-harmonic plane electromagnetic wave propagating in free space is considered. The problem involves a temporal discontinuity, a spatial discontinuity, and a dispersive medium. The steady-state solution is obtained by considering the basic features of the scattering processes due to each of the discontinuities in terms of analogous transmission-line models. The electric field of the reflected wave consists of two components. One component (called component A) is of the same frequency as the incident wave frequency and is due to the spatial discontinuity. The other component (called component B) is of a different frequency and arises because of the temporal discontinuity. The B component is damped out even if the plasma is only slightly lossy. The damping rate of the B component is calculated. The transient solution is obtained through the use of Laplace transforms. The solution is given in terms of Bessel-like functions. The limiting value of this solution is shown to agree with the steady-state solution. Numerical results illustrating the transient effects are for two typical cases     

Elastic properties of layered crystals

The characteristic features of the elastic properties of layered crystals and their dependence on temperature and pressure are analyzed. The relations between the elastic constants of hexagonal layered crystals are given. It is shown that the anomalous behavior of the elastic constants in the temperature region of a phase transition affects both the magnitude and sign of the thermal expansion coefficients of layered crystals. From analyzing the pressure and temperature dependences of the elastic constants, it is found that the anharmonicity of the bonding forces between the layers is much greater than the anharmonicity of the intralayer forces. The contribution from thermal expansion to the variations of the elastic constants with temperature is estimated.     

On the acoustic field in a Pekeris waveguide with attenuation in the bottom half-space

The acoustic field in a Pekeris channel with an attenuating basement is critically examined, based on contour integrations of the wave number integrals for the two domains. In both regions, the field consists of a finite sum of proper (square integrable) normal modes plus a branch line integral around a hyperbolic cut. For low bottom attenuation, only "trapped" modes exist but as the loss increases additional "dissipation" modes contribute to the mode sum. A Newton-Raphson iterative procedure is introduced for finding the complex eigenvalues of the modes and a new expression is derived which shows that the total number of proper (trapped plus dissipation) modes supported by the waveguide increases essentially linearly with rising bottom attenuation. Approximations for the complex shape functions of the modes in the water column and the basement are developed and compared with the exact shape functions determined from the Newton-Raphson procedure. An expression derived for the modal attenuation coefficient scales in proportion to the square of the mode number and inversely with the square of the frequency. Stationary-phase approximations for the branch line integrals for both domains are developed, which serve to illustrate the asymptotic range dependence of the lateral wave but otherwise have little utility.