Transient Green’s Tensor for a Layered Solid Half-Space With Different Interface Conditions

Pulsed ultrasonic techniques can be and have been used to examine the interface conditions of a bonded structure. To provide a theoretical basis for such testing techniques we model the structure as a layer on top of a half-space, both of different elastic properties, with various interface bonding conditions. The exact dynamic Green’s tensor for such a structure is explicitly derived from the three-dimensional equations of motion. The final solution is a series. Each term of the series corresponds to a successive arrival of a “generalized ray” and each is a definite line integral along a fixed path which can be easily computed numerically. Willis’ method is used in the derivation. A new scheme of automatic generation of the arrivals and ray paths using combinatorial analysis, along with the summation of the corresponding products of reflection coefficients is presented. A FORTRAN code is developed for computation of the Green’s tensor when both the source and the detector are located on the top surface. The Green’s tensor is then used to simulate displacements due to pulsed ultrasonic point sources of known time waveform. Results show that the interface bonding conditions have a great influence on the transient displacements. For example, when the interface bonding conditions vary, some of the first few head waves and regular reflected rays change polarities and amplitudes. This phenomenon can be used to infer the quality of the interface bond of materials in ultrasonic nondestructive evaluation. In addition the results are useful in the study of acoustic microscopy probes, coatings, and geo-exploration.     

斜入射平面SH波在层状饱和半空间中沉积谷地 周围的三维散射

为研究层状饱和场地中沉积谷地对斜入射地震波的三维散射问题,建立了求解问题的2.5维间接边界元方法。通过沿沉积谷地轴线方向的傅里叶变换将三维问题降为二维问题,进而在沉积谷地的截面内进行边界单元的离散和求解,求得沉积谷地截面内的动力响应,然后再将截面内计算结果沿沉积谷地轴线方向进行波数展开即可求得任意位置动力响应。通过与弹性情况的比较验证了方法的正确性,并以均匀饱和半空间和基岩上单一饱和土层中沉积谷地对斜入射平面SH波的三维散射为例进行了数值计算和分析。研究发现沉积谷地对SH波的三维散射与二维散射之间存在显著差异;饱和情况(透水或不透水)与干土情况沉积谷地附近地表位移的差别很大;另外层状饱和半空间中沉积谷地和均匀饱和半空间中沉积谷地对斜入射SH波的放大作用也存在显著差别。     

无限长水平圆柱体半空间电场问题

建立一个双极坐标系。双极坐标系中的拉普拉斯方程与极坐标系中的形式相同。解双极坐标下拉氏方程得出半空间中无限长水平圆柱体电场问题的解析解。由此计算出水平圆柱体中梯装置视电阻率、等位体电位和梯度异常。     

Soil seismic analysis for 2D oblique incident waves using exact free-field responses by frequency-based finite/infinite element method

The seismic analysis of a viscoelastic half-space under two-dimensional (2D) oblique incident waves is carried out by the finite/infinite element method (FIEM). First, the frequency-domain exact solutions for the displacements and stresses of the free field are derived in general form for arbitrary incident P and SV waves. With the present formulation, no distinction needs to be made for SV waves with over-critical incident angles that make the reflected P waves disappear, while no critical angle exists for P waves. Next, the equivalent seismic forces of the earthquake (Taft Earthquake 1952) imposed on the near-field boundary are generated by combining the solutions for unit ground accelerations with the earthquake spectrum. Based on the asymmetric finite/infinite element model, the frequency-domain motion equations for seismic analysis are presented with the key parameters selected. The results obtained in frequency and time domain are verified against those of Wolf’s, Luco and de Barros’ and for inversely computed ground motions. The parametric study indicated that distinct phase difference exists between the horizontal and vertical responses for SV waves with over-critical incident angles, but not for under-critical incident angles. Other observations were also made for the numerical results inside the text.     

Reflection of plane waves at the free surface of a fibre-reinforced elastic half-space

The propagation of plane waves in fibre-reinforced, anisotropic, elastic media is discussed. The expressions for the phase velocity of quasi-P (qP) and quasi-SV (qSV) waves propagating in a plane containing the reinforcement direction are obtained as functions of the angle between the propagation and reinforcement directions. Closed form expressions for the amplitude ratios for qP and qSV waves reflected at the free surface of a fibre-reinforced, anisotropic, homogeneous, elastic half-space are obtained. These expressions are used to study the variation of amplitude ratios with angle of incidence. It is found that reinforcement has a significant effect on the amplitude ratios and critical angle     

饱和弹性半空间在低频谐和集中力下的积分形式解

本文采用解耦联合方程组，算子法解回代方程，推导饱和土低频Ｌａｍｅｂ积分形式解，并退化为一般弹性半空间的积分形式解，为饱和土动孔隙水压力和动力响应的计算提供了方法。算例证实本文推导的可靠性，其结论对工程有指导意义。     

Analytical solution for the electric potential due to a point source in an arbitrarily anisotropic half-space

A very large class of important theory and applications in geophysics requires analytical solutions for the determination of the electric potential due to a point source in an arbitrarily anisotropic half-space. In this paper, a very clear and simple solution to the half-space problem has been developed from consideration of an arbitrarily anisotropic whole space. For the first time, the method of images is used to generate the solution for an arbitrarily anisotropic three dimensional half-space. Based on traditional extreme value theory the image source point has been determined and calculated for the half-space case.     

一款水声通信换能器研究

随着声呐技术的迅速发展,水声通信在海洋科学研究及海洋开发中发挥着非常重要的作用,水声通信换能器是水声通信设备中负责电声转换的重要部件。研究了一款带底座的溢流圆管换能器,通过有限元仿真计算了换能器发送电压响应和方向性等参数,优化了换能器中的陶瓷元件和底座的结构尺寸,制作并测量得到一款半空间指向性的水声通信换能器,换能器的工作频段为11~23 k Hz,带内起伏为3 d B,最大发送电压响应为133 d B,-3 d B垂直开角大于180°。     

对地基弹性均压系数与基础底面积关系的研究

根据各向同性的均质的弹性半空间理论,地基的弹性均压系数Cz与基底面积的平方根F成反比。但这一理论结果与大量的试验结果不符。在分析产生这种差异根本原因的基础上,提出在理论上假定地基在半空间范围内为各向同性的均质的弹性体是不符合实际的结论。并指出随着深度的增加,土体的弹性模量也在不断增加。考虑这一因素后,地基土的弹性均压系数Cz的变化比之随F的变化速率要缓慢得多。同时还指出,《动力机器基础设计规范》(GB 50040-96)对分层地基条件下确定地基弹性均压系数Cz的不合理性。