Head-on collision of normal shock waves in dusty gases

The head-on collision of normal shock waves in dusty gases has been investigated numerically, using the modified random-choice method. The results concerning the various flow field properties as well as the waves configuration were compared with those of a pure gas case.     

On shapes of body waves in periodically inhomogeneous, magnetostrictive, dielectric materials

The shapes of shear body waves in periodically inhomogeneous, magnetostrictive, dielectric media are studied with emphasis on the partial (elastic and magnetostrictive) wave motions coupled to produce magnetoelastic waves __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 7, pp. 57–63, July 2006.     

浅埋的圆柱形孔洞对SH波的散射与地震动

研究了浅埋的圆柱形孔洞对以任意方向入射的平面SH波的散射与地震动问题。利用复变函数和多极坐标方法构造了问题的位移解。当入射波的波长与圆孔的半径相比较小时,地震动将受到较大的影响。影响地震动有三个主要参数:(1)SH波的入射角0;(2)入射波波数,即圆柱形孔洞的半径与入射波半波长之比;(3)h/R,即圆柱形孔洞至表面的距离与圆孔半径之比。当较大时,地震动幅值变化激烈,位移幅值可出现跳动和放大的现象。当h/R增大至10～12时,位移幅值变化恢复至半空间的情况,表明圆柱形孔洞的影响可被忽略。     

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.     

Wave propagation in multi-wire strands by wavelet-based laser ultrasound

Methods based on guided ultrasonic waves are gaining increasing attention for the non-destructive inspection and condition monitoring of multi-wire strands used in civil structures such as prestressing tendons and cable stays. In this paper we examine the wave propagation problem in seven-wire strands at the level of the individual wires comprising the strand. Through a broad-band, laser ultrasonic setup and a time—frequency wavelet transform processing, longitudinal and flexural waves are characterized in terms of dispersive velocity and frequency-dependent attenuation. These vibrating frequencies propagating with minimal losses are identified as they are suitable for long-range inspection of the strands. In addition, the wave transmission spectra are found to be sensitive to the load level, suggesting the potential for continuous load monitoring in the field.     

Plane waves in a semi-infinite fluid saturated porous medium

The field equations governing the propagation of waves in an incompressible liquid-saturated porous medium are investigated and a general solution is presented. It has been revealed that coupled longitudinal and transverse waves propagate in the porous medium. The propagation of transverse waves in the fluid phase is completely due to the interaction between the solid and fluid phases. The dispersion relationship and attenuation features are discussed. Unlike other investigations, all explicit forms of the arguments are derived. The reflection of the plane harmonic waves at the plane, traction-free boundary, which shows the influence of the dissipation on the velocity, and the attenuation coefficients of the reflected waves is studied. It is of interest that pore pressure is produced in the process of reflection, even in the case of the incidence of transverse waves.     

双原子正方晶格光子晶体边界模式的光传输特性

利用平面波展开法,发现双原子正方晶格光子晶体中ΓM方向边界面存在着快慢两类边界模式,并且通过计算色散关系和电场分布研究了边界参量对这两类边界模式传输特性的影响.依据两种模式的色散关系,计算了群指数和群速度色散参量,结果表明边界参量的变化对第一类边界模式传输特性的影响较小,该模式的平均群指数始终维持在5.0左右;第二类边界模式与第一类模式明显不同,边界参量的变化能够有效地影响到这种模式的传输特性,该模式的最大平均群指数可达178左右.利用时域有限差分法记录了不同时刻电场强度在边界附近的分布及监测点处的电场幅度变化情况,结果表明,两类模式都能够被限制在边界附近并向前传播,时域有限差分法得到的群速度与平面波展开法的结果完全吻合.     

Interactions of delta shock waves for the relativistic Chaplygin Euler equations with split delta functions

In this article, we are concerned with the interactions of delta shock waves with contact discontinuities for the relativistic Euler equations for Chaplygin gas by using split delta functions method. The solutions are obtained constructively and globally when the initial data consists of three piecewise constant states. The global structure and large time‐asymptotic behaviors of the solutions are analyzed case by case. During the process of the interaction, the strengths of delta shock waves are computed completely. Moreover, it can be found that the Riemann solutions are stable for such small perturbations with special initial data by letting perturbed parameter ε tends to zero. Copyright © 2014 John Wiley & Sons, Ltd.     

A system of coupled partial differential equations exhibiting both elevation and depression rogue wave modes

Analytical solutions are obtained for a coupled system of partial differential equations involving hyperbolic differential operators. Oscillatory states are calculated by the Hirota bilinear transformation. Algebraically localized modes are derived by taking a Taylor expansion. Physically these equations will model the dynamics of water waves, where the dependent variable (typically the displacement of the free surface) can exhibit a sudden deviation from an otherwise tranquil background. Such modes are termed ‘rogue waves’ and are associated with ‘extreme and rare events in physics’. Furthermore, elevations, depressions and ‘four-petal’ rogue waves can all be obtained by modifying the input parameters.