SECOND ORDER EFFECTS IN AN ELASTIC HALF－SPACE ACTED UPON BY A NON－UNIFORM NORMAL LOAD

ＳＥＣＯＮＤＯＲＤＥＲＥＦＦＥＣＴＳＩＮＡＮＥＬＡＳＴＩＣＨＡＬＦ－ＳＰＡＣＥＡＣＴＥＤＵＰＯＮＢＹＡＮＯＮ－ＵＮＩＦＯＲＭＮＯＲＭＡＬＬＯＡＤＬｉｕＹｏｕ－ｗｅｎ（刘又文）（ＤｅｐａｒｔｍｅｎｔｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓａｎｄＭｅｃｈ...     

三维粘弹性层状半空间埋置集中荷载动力格林函数求解—修正刚度矩阵法

针对三维粘弹性层状半空间埋置集中荷载作用下动力响应计算,在柱面坐标下,结合径向Hankel和周向Fourier变换,提出了一种新的求解方法修正刚度矩阵法.方法首先固定荷载所在层的上下界面,在空间波数域内,由波动方程的特解和齐解叠加得到“固端”反力.进而放松两“固端约束”,利用直接刚度法容易求得各层面位移.荷载作用层内反应另需叠加上该“固定层”内解,其中特解部分积分由全空间解析解代替,由此解决了当接收点和源点作用水平面接近时异常积分收敛问题.算例分析表明,对于低频(可退化为静力状态)和高频问题,论文方法均具有很高的计算效率和精度.     

The axisymmetrical elastic field of an ellipsoidal inclusion with a slipping interface

This paper is concerned with the axisymmetrical elastic fields caused by an ellipsoidal inclusion with a slipping interface which undergoes a uniform eigenstrain. The problem is solved under a revolving ellipsoidal coordinate with the aid of Papkovich-Neuber general dipacement formula. In contrast to the perfectly bonded interface, when the interface between the inclusion and the matrix cannot sustain shear stress, and is free to slip, the solution cannot be expressed in closed form and involves infinite series. Therefore, the results are illustrated by numerical examples.     

Rayleigh waves in an isotropic elastic half-space coated by a thin isotropic elastic layer with smooth contact

In the present paper, we are interested in the propagation of Rayleigh waves in an isotropic elastic half-space coated with a thin isotropic elastic layer. The contact between the layer and the half space is assumed to be smooth. The main purpose of the paper is to establish an approximate secular equation of the wave. By using the effective boundary condition method, an approximate, yet highly accurate secular equation of fourth-order in terms of the dimensionless thickness of the layer is derived. From the secular equation obtained, an approximate formula of third-order for the velocity of Rayleigh waves is established. The approximate secular equation and the formula for the velocity obtained in this paper are potentially useful in many practical applications.     

On the possibility of local buckling of the surface of an elastic half-space under compression

The possibility of local buckling of the free surface of the lower half-plane under compression is studied in a static formulation within the framework of plane deformation. It is shown that in some media small subcritical strains can lead to local buckling of the half-plane surface. It is found that two forms of local surface buckling correspond to one critical compression load. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 3, pp. 149–152, May–June, 2005.     

Scattering far field solution of SH-wave by movable rigid cylindrical interface inclusion

The Green's function is used to solve the scattering far field solution of SH-wave by a movable rigid cylindrical interface inclusion in a linear elastic body. First, a suitable Green's function is developed, which is the fundamental displacement solution of an elastic half space with a movable rigid half-cylindrical inclusion impacted by out-of-plane harmonic line source loaded at any point of its horizontal surface. By using the Green's function, a series of Fredholm integral equations of the first kind which determine the scattering far field can be set up. Then the paper gives the expressions on the far field including the displacement mode of scattering wave and the solution of scattering cross-section. Finally, some examples and numerical results are discussed to analyze the influence of the combination of different media parameters on the answer of far field.     

Using complex potentials to determine the reaction of a prestressed two-layer elastic half-space to a moving load

Complex potentials in common form for compressible and incompressible elastic bodies are used to formulate and solve the problem of stationary motion of a prestressed two-layer elastic half-space under a moving surface load. The results presented are similar to those obtained earlier using the Fourier transform __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 5, pp. 3–15, May 2008.     

Surface waves generated by a line load on a half-space with depth-dependent properties

The reciprocity theorem of elastodynamics is used in this paper to determine the surface waves that are radiated from a time-harmonic line load applied at the surface of a solid body, whose elastic moduli and mass density depend on the distance from the surface. In a high-frequency approximation, the surface wave velocity and expressions for the displacement and stresses of free surface waves are employed in the reciprocity theorem. The general expressions for the surface wave radiated by the oscillating line load, together with a virtual free surface wave, when employed in the reciprocity theorem, yield relatively simple expressions for the amplitude factor of the radiated surface wave. Results show the amplitude factor as a function of the wavenumber.     

On certain bounds for the in-plane translational stiffness of a disc inclusion at a bi-material elastic interface

This paper presents a set of bounds that can be used to estimate the in-plane translational stiffness of a rigid circular disc inclusion that is embedded at the interface between two dissimilar elastic half-space regions.     

The multi-parameter inversion of elastic wave in half-space

The multi-parameter inverse scattering problem of elastic wave equation with single frequency is investigated within Born approximation. By use of a wideband measuring scheme in which both transmitters and receivers scan over the half-space surface, the formula of the scattering field of elastic wave is derived. Four types of mode conversion of elastic wave (P→P,P→S,S→P,S→S) are separated from the scattering field. These components contain sufficient information for us to reconstruct the configurations of the density and Lamé parameters of the medium. The inverse formulas have the form of filtered back-propagation as in the acoustic diffraction tomography. Computer simulations are also obtained. Supported by Foundation of Ph.D Program of the State Education Commission of China.     

Flexural vibrations of a thin circular elastic inclusion in an unbounded body under the action of a plane harmonic wave

The interaction of a plane harmonic longitudinal wave with a thin circular elastic inclusion is considered. The wave front is assumed to be parallel to the inclusion plane. Since the inclusion is thin, the matrix-inclusion interface conditions (perfect bonding) are formulated on the mid-plane of the inclusion. The bending displacements of the inclusion are determined from the bending equation for a thin plate. The problem is solved using discontinuous Lamé solutions for harmonic vibrations. Therefore, the problem can be reduced to the Fredholm equation of the second kind for a function associated with the discontinuity of normal stresses on the inclusion. The equation obtained is solved by the method of mechanical quadratures using Gaussian quadrature formulas. Approximate formulas for the stress intensity factors are derived. Results from a numerical analysis of the dependence of the SIFs on the dimensionless wave number and the stiffness of the inclusion are presented __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 5, pp. 16–21, May 2008.