Thermal radio emission of a homogeneous half-space with a rough boundary

Khar'kov State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 32, No. 8, pp. 927–932, August, 1989.     

Coefficient of friction between a rigid conical indenter and a model elastomer: Influence of local frictional heating

We investigate the coefficient of friction between a rigid cone and an elastomer with account of local heating due to frictional dissipation. The elastomer is modeled as a simple Kelvin body and an exponential dependency of viscosity on temperature is assumed. We show that the coefficient of friction is a function of only two dimensionless variables depending on the normal force, sliding velocity, the parameter characterizing the temperature dependence as well as shear modulus, viscosity at the ambient temperature and the indenter slope. One of the mentioned dimensionless variables does not depend on velocity and determines uniquely the form of the dependence of the coefficient of friction on velocity. Depending on the value of this controlling variable, the cases of weak and strong influence of temperature effects can be distinguished. In the case of strong dependence, a generalization of the classical “master curve” procedure introduced by Grosch is suggested by using both horizontal and vertical shift factors.     

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.

     

Reflection of radiofrequency waves by a two-layer medium with randomly rough boundaries

Using perturbation theory, we have investigated the electromagnetic field reflected by a two-layer medium with rough boundaries. To first order in perturbation theory with respect to the asperities on the boundaries, we consider the scattering fading effect. To a second approximation, we have obtained analytical expressions for the perturbations of the mean field reflected and transmitted into the medium, and also analytical expressions for the second moment of the field with orthogonal polarization scattered in the plane of incidence. We have investigated the dependences of the second moment of the field on the character of the asperity spectrum, the frequency of the radiation, and the layer thickness.Scientific-Research Institute of Physics at Rostov University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 37, No. 12, pp. 1483–1498, December, 1994.     

Applying the method of dimensionality reduction to calculate the friction force between a rotationally symmetric indenter and a viscoelastic half-space

The method of dimensionality reduction is applied to the tangential contact between an elastomer and a rotationally symmetric indenter. The resulting equations are solved analytically, and numerical methods are discussed. The dependence of the normal and tangential force on the indentation depth and velocity is indicated.     

Scattering of radio waves by a two-layer medium with a weakly reflecting rough boundary

The average reflected field and the second moment of the scattered field of the main polarization are found and analyzed in the approximation of a small jump of the dielectric constant when a horizontally polarized wave is reflected by a two-layer medium with a rough upper boundary. It is shown that the oscillations due to frequency changes predicted by perturbation theory do not exist when the scattering parameter is large. Sounding at close angles of incidence and scattering is the most efficient method of layer thickness determination by the scattered radiation. Institute of Physics, State University, Rostov-on-Don, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 41, No. 7, pp. 889–903, July, 1998.     

Green's functions for a volume source in an elastic half-space

Green's functions are derived for elastic waves generated by a volume source in a homogeneous isotropic half-space. The context is sources at shallow burial depths, for which surface (Rayleigh) and bulk waves, both longitudinal and transverse, can be generated with comparable magnitudes. Two approaches are followed. First, the Green's function is expanded with respect to eigenmodes that correspond to Rayleigh waves. While bulk waves are thus ignored, this approximation is valid on the surface far from the source, where the Rayleigh wave modes dominate. The second approach employs an angular spectrum that accounts for the bulk waves and yields a solution that may be separated into two terms. One is associated with bulk waves, the other with Rayleigh waves. The latter is proved to be identical to the Green's function obtained following the first approach. The Green's function obtained via angular spectrum decomposition is analyzed numerically in the time domain for different burial depths and distances to the receiver, and for parameters relevant to seismo-acoustic detection of land mines and other buried objects.     

Influence of indenter tip geometry on elastic deformation during nanoindentation

Nanoindentation with a Berkovich indenter is commonly used to investigate the mechanical behavior of small volumes of materials. To date, most investigators have made the simplifying assumption that the tip is spherical. In reality, indenter tips are much more complex. Here, we develop a new method to describe the tip shape using the experimentally determined area function of the indenter at small depths (0-100 nm). Our analysis accurately predicts the elastic load-displacement curve and allows the theoretical strength of a material to be determined from pop-in data. Application of our new method to single crystal Cr3Si shows that the predicted theoretical strengths are within 12% of the ideal strength G/2pi, where G is the shear modulus.     

Normal contact problem between a cylindrical indenter and a half-space with long-range adhesion: Study with the method of dimensionality reduction

Adhesive contact with exponential adhesive interaction is simulated with the use of the method of dimensionality reduction. The developed procedure is illustrated with an example of adhesion of a cylindrical punch and an elastic half space. However, it is general and can be used for any form of interaction potential and any form of indenter.     

Vibrations of an elastic strip with a rough boundary

A plane problem of steady-state forced vibrations of an elastic strip whose lower boundary contains a rough segment is considered. Using Green’s functions for a strip, the problem is reduced to a system of integral equations with integrals over the rough boundary, which is solved by the boundary-element method. The inverse problem of determining the shape of the rough boundary segment from the data on the displacement field of a certain part of the upper boundary is formulated. By the linearization procedure, the inverse problem is reduced to a Fredholm integral equation of the first kind with a smooth kernel, which is solved by Tikhonov’s regularization method.     

Scatter of a plane elastic wave by a rough crack edge

The aim of this paper is to investigate the effect of roughness of the crack edge on the reliability of ultrasonic NDE (nondestructive evaluation). The rough crack face has been modeled by earlier authors as a mosaic of large triangular facets and the effect of this roughness has been simulated using the Kirchhoff approximation. We now augment this model by the rough crack edge that is a polygonal line. We then model the scattered field using the Isakovich approach, originally developed for modeling scatter from rough surfaces, also with the help of the Kirchhoff approximation.     

Forced torsional vibrations of a cylindrical rod connected to an elastic half-space

An analysis is presented of the forced torsional vibrations of a cylindrical rod connected to an elastic half-space under the condition that the circumferential displacement at the free end of the rod, where the disturbing moment is applied, varies proportionally with the distance from the rod axis. Both the Pochhammer-Chree and elementary theory are utilized. The response curve of the rotational amplitude at the free end of the rod, obtained from the Pochhammer-Chree theory, and that obtained from the elementary theory almost coincide with each other except in the case where the rod and the half-space are of the same material. The amplitude attenuation is largest when the rod and the half-space are of the same material. The maximum values of half-space displacement distribution at the interface lie within the rod edge.     

粗糙界面板Lamb波的传播特征

弹性波在粗糙界面板中的传播问题对无损检测、地震波传播等问题有实际意义,但是多年来的研究限于相屏近似等方法。本文从严格的理论出发,把粗糙界面起伏看作空间位置变量的随机过程,在粗糙表面起伏很小的条件下,用多次散射相互独立假设得到了平均意义下的Rayleigh-Lamb频散方程。通过对方程进行求解,得到了Lamb波在粗糙界面板中传播时的衰减。结果表明Lamb波的衰减和界面的粗糙起伏方差近似成正比,和粗糙起伏相关长度关系不大。在理论分析的基础上,进行了实验验证。     

Adhesion between an elastic body and a randomly rough hard surface

I have developed a theory of adhesion between an elastic solid and a hard randomly rough substrate. The theory takes into account that partial contact may occur between the solids on all length scales. I present numerical results for the case where the substrate surface is self-affine fractal. When the fractal dimension is close to 2, complete contact typically occurs in the macro-asperity contact areas, while when the fractal dimension is larger than 2.5, the area of (apparent) contact decreases continuously when the magnification is increased. An important result is that even when the surface roughness is so high that no adhesion can be detected in a pull-off experiment, the area of real contact (when adhesion is included) may still be several times larger than when the adhesion is neglected. Since it is the area of real contact which determines the sliding friction force, the adhesion interaction may strongly affect the friction force even when no adhesion can be detected in a pull-off experiment. Received 3 April 2002     

Acoustic scattering by a three-dimensional elastic object near a rough surface

The ensemble-averaged field scattered by a smooth, bounded, elastic object near a penetrable surface with small-scale random roughness is formulated. The formulation consists of combining a perturbative solution for modeling propagation through the rough surface with a transition (T-) matrix solution for scattering by the object near a planar surface. All media bounding the rough surface are assumed to be fluids. By applying the results to a spherical steel shell buried within a rough sediment bottom, it is demonstrated that the ensemble-averaged "incoherent" intensity backscattered by buried objects illuminated with shallow-grazing-angle acoustic sources can be well enhanced at high frequencies over field predictions based on scattering models where all environmental surfaces are planar. However, this intensity must compete with the incoherent intensity scattered back from the interface itself, which can defeat detection attempts. The averaged "coherent" component of the field maintains the strong evanescent spectral decay exhibited by flat interface predictions of shallow-angle measurements but with small deviations. Nevertheless, bistatic calculations of the coherent field suggest useful strategies for improving long-range detection and identification of buried objects.     

Excitation of an elastic half-space by a buried line source of conical waves

A formal solution is obtained to the problem of a buried line source of conical waves propagating at a constant phase velocity c in an isotropic elastic half space. By applying the boundary conditions at the free surface, it is determined that the reflected field, in addition to the incident field, requires addition of a scalar potential and two components of the vector potential. The latter is in contrast to the case of cylindrical waves where only one component of the vector potential is needed. The formal solution for the conical wave source goes over to that for the two dimensional cylindrical wave case in the limit of infinite phase velocity c.