On the application of the Wiener–Hopf technique to problems in dynamic elasticity

Many problems in linear elastodynamics, or dynamic fracture mechanics, can be reduced to Wiener–Hopf functional equations defined in a strip in a complex transform plane. Apart from a few special cases, the inherent coupling between shear and compressional body motions gives rise to coupled systems of equations, and so the resulting Wiener–Hopf kernels are of matrix form. The key step in the solution of a Wiener–Hopf equation, which is to decompose the kernel into a product of two factors with particular analyticity properties, can be accomplished explicitly for scalar kernels. However, apart from special matrices which yield commutative factorizations, no procedure has yet been devised to factorize exactly general matrix kernels.

This paper shall demonstrate, by way of example, that the Wiener–Hopf approximant matrix (WHAM) procedure for obtaining approximate factors of matrix kernels (recently introduced by the author in [SIAM J. Appl. Math. 57 (2) (1997) 541]) is applicable to the class of matrix kernels found in elasticity, and in particular to problems in QNDE. First, as a motivating example, the kernel arising in the model of diffraction of skew incident elastic waves on a semi-infinite crack in an isotropic elastic space is studied. This was first examined in a seminal work by Achenbach and Gautesen [J. Acoust. Soc. Am. 61 (2) (1977) 413] and here three methods are offered for deriving distinct non-commutative factorizations of the kernel. Second, the WHAM method is employed to factorize the matrix kernel arising in the problem of radiation into an elastic half-space with mixed boundary conditions on its face. Third, brief mention is made of kernel factorization related to the problems of flexural wave diffraction by a crack in a thin (Mindlin) plate, and body wave scattering by an interfacial crack.     

PLIF技术测量浓度场及其二维数字校正

推导了ＰＬＩＦ技术测量浓度场时液地内荧光强度的分布，提出了ＰＬＩＦ技术的二维数字校正方程和校正方法来消除激光片光的高斯分布和沿光程衰减的影响．在此基础上，对圆形紊动射流的浓度场进行了测量和校正．此外，还将测量结果与前人的半经验理论进行了分析和比较。     

井下巷道围岩变形的散斑分析法

通过对散斑计量法原理分析、数学描述及观测实例的论述，证明激光散斑法是研究煤矿地下结构物相似模型变形状态的一种新的无损检测技术，若采用白光作为光源，该项技术可用于二维变形场的实地测试。     

一种最优控制的胞映射算法

由Hsu提出的利用胞映射进行最优控制的方法可以发展成实用的工程控制技术.本文以研究算法为出发点,利用胞映射的特性,结合实际的计算与可能,作了一系列旨在提高计算速度和节省内存的改进;并给出了简单有效的区分同耗最优控制对的统一的方法.使用平常的微型计算机也能有效地解决实际工程问题的最优控制.     

Mode III fracture analysis by Trefftz boundary element method

This paper presents a hybrid Trefftz (HT) boundary element method (BEM) by using two indirect techniques for mode III fracture problems. Two Trefftz complete functions of Laplace equation for normal elements and a special purpose Trefftz function for crack elements are proposed in deriving the Galerkin and the collocation techniques of HT BEM. Then two auxiliary functions are introduced to improve the accuracy of the displacement field near the crack tips, and stress intensity factor (SIF) is evaluated by local crack elements as well. Furthermore, numerical examples are given, including comparisons of the present results with the analytical solution and the other numerical methods, to demonstrate the efficiency for different boundary conditions and to illustrate the convergence influenced by several parameters. It shows that HT BEM by using the Galerkin and the collocation techniques is effective for mode III fracture problems. The project supported by the National Natural Science Foundation of China(10472082). The English text was polished by Keren Wang.     

Nonstationary deformation of an elastic plate with a notch under the action of a shock wave

The behavior of a thin elastic plate with a rectilinear notch under the action a weak shock wave in air is studied experimentally. A technique is developed for this purpose. The effect of the notch on the strain state of the plate is analyzed __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 11, pp. 99–104, November 2007.     

A lattice Boltzmann method for KDV equation

We prepose a 5-bit lattice Boltzmann model for KdV equation. Using Chapman-Enskog expansion and multiscale technique, we obtained high order moments of equilibrium distribution function, and the 3rd dispersion coefficient and 4th order viscosity. The parameters of this scheme can be determined by analysing the energy dissipation. The project supported by the Foundation of the Laboratory for Nonlinear Mechanics of Continuous Media, Institute of Mechanics, Chinese Academy of Sciences     

集成光芯片的电光性能测试方法

为了提高中低精度光纤陀螺工程化批产过程中的一致性和合格率,降低筛选成本,初步定量研究了铌酸锂集成光芯片的附加损耗、光克尔效应、分光比和偏振效应等重要参数对陀螺性能的影响和优化方法,并提出了电光性能的具体测试方法。通过输入特定方波、锯齿波、方波加阶梯波,可从输出波形上进行直观的判断,并可进一步给出性能优劣的量化指标,能够较为准确地进行芯片筛选,提高工艺水平。此项研究成果对铌酸锂集成光芯片的相关标准进行了补充,不仅可以帮助光纤陀螺的制作单位进行更合理可行的器件筛选,还可以帮助芯片的生产单位完善相应的参数测试工作,提高合格率。     

用地面模拟试验识别卫星太阳电池翼伸展运动的各种阻尼参数

本文利用Lagnrange方程建立了卫星太阳电池翼伸展运动的数学模型.这是一个包含摩擦阻尼、结构阻尼和空气阻尼参数的非线性微分方程组.在用气垫消除了重力影响但存在空气阻尼的地面环境中,对实尺太阳电池翼模型进行了伸展运动的模拟试验并用频闪摄影技术记录了运动的时间历程.再利用最小p乘优化方法识别出该系统的各个阻尼参数.通过对系统运动方程进行数值积分求得的太阳电池翼的伸展运动历程与实测值相当吻合.取空气阻尼等于零,得出了太阳电池翼在无空气阻尼的太空中的伸展运动规律.     

Influence of gas injection on phase inversion in an oil–water flow through a vertical tube

An experimental study has been made of the influence of gas injection on the phase inversion between oil and water flowing through a vertical tube. Particular attention was paid to the influence on the critical concentration of oil and water where phase inversion occurs and on the pressure drop increase over the tube during phase inversion. By using different types of gas injectors also the influence of the bubble size of the injected gas on the phase inversion was studied. It was found that gas injection does not significantly change the critical concentration, but the influence on the pressure drop is considerable. For mixture velocities larger than 1 m/s, the pressure drop over the tube increases with decreasing bubble size and at inversion can become even larger than the pressure drop during the flow of oil and water without gas injection.