The nonuniformly moving edge dislocation

The motion of an edge dislocation starting from rest and moving thereafter nonuniformly on its slip-plane is analyzed by means of Laplace transforms in space and time, with detailed treatment of the singularities involved. The stress and particle velocities are derived in the form of an integral over the history of the motion in the case of a general motion and in closed form in the special case of a dislocation starting from rest and moving with constant velocity thereafter.     

Ice cover perturbation by a dipole in motion within a liquid

The two-dimensional problem of ice cover perturbation by a dipole starting to move uniformly, rectilinearly, and horizontally in a liquid initially at rest is considered. It is shown that stationary waves of two different types can be established on the liquid/ice interface, depending on the ice thickness and the dipole velocity. Examples of the numerical investigation of these waves are presented.     

Propagation of converging and diverging shock waves under isothermal condition

In this article the flows of perfect gas behind converging and diverging strong shock waves under isothermal condition in the cases of spherical and cylindrical symmetry are examined. A diverging shock wave is formed by energy supply according to a power law. These waves propagate in a uniform medium at rest and all conservation laws hold at the fronts of these shock waves. It was established that in the case of converging waves for any value of the ratios of specific heats the solution of the problem under consideration exists and is unique. When the problem has more than one solution. In the case of diverging shock waves the solution exists and is unique for any from the interval and any value of power in the energy input law. Received 4 August 1996 / Accepted 28 May 1996     

Suppression of transients in wave-excited response testing

When a floating body in a wave tank has low hydrodynamic damping, for example in the heave mode, very long duration transient responses can arise if it is excited from a state of rest by sinusoidal waves. Such behaviour can be undesirable when steady state response characteristics are the object of investigation in a numerical tank, because of the consequential need for very long computations. The present paper develops a method for suppressing such transient behaviour in computational models. The success of the approach is demonstrated in the context of the heaving motion of a simple buoy. A linear model of such a buoy initially at rest in a wave tank, excited by propagating sinusoidal waves, is used here for a preliminary investigation of the removal of transients. The technique is then incorporated into a fully nonlinear potential flow simulation of the buoy, and the approach is shown to be effective.     

The supersonic motion of a rigid body in an elastic medium with friction

The plane problem of supersonic steady motion of a body in an elastic medium is solved. Two possible cases of body motion are considered depending on its velocity. In the first case, the body moves at a velocity greater than the velocity of transverse waves but smaller than the velocity of longitudinal waves. In the second case, the body moves at a velocity greater than the velocity of longitudinal waves. An analytic solution of the problem under study is obtained and analyzed. It is shown that friction substantially influences the penetration process.     

蚯蚓爬行的生物力学分析与数值计算

蚯蚓是典型的多体节动物。本文从生物力学的角度,分析了蚯蚓在静止和运动状态下的体壁应力,又分析了蚯蚓爬行过程中的变形以及与地面之间的摩擦力,给出了蚯蚓在地表爬行的动力学模型。进一步,又数值计算了一定质量范围的蚯蚓在静止和运动状态下体壁承受的最大应力和动力学模型方程,得到蚯蚓爬行的平均速度与质量的关系。计算结果与实验观测值基本一致。      

Biomechanical analysis and numerical calculation of earthworm crawling

蚯蚓是典型的多体节动物。本文从生物力学的角度,分析了蚯蚓在静止和运动状态下的体壁应力,又分析了蚯蚓爬行过程中的变形以及与地面之间的摩擦力,给出了蚯蚓在地表爬行的动力学模型。进一步,又数值计算了一定质量范围的蚯蚓在静止和运动状态下体壁承受的最大应力和动力学模型方程,得到蚯蚓爬行的平均速度与质量的关系。计算结果与实验观测值基本一致。     

Variational principles and operator equations for electromagnetic waves in inhomogeneous media

A variational characterization of the polarizations generated by electromagnetic waves in an inhomogeneous medium is developed, starting from more conventional variational principles which imply, in the static limit, the classical energy principles. Associated operator equations are generated and the Green's function kernels that appear in them are given explicitly for an infinite body. The formulation proceeds along a route directly parallel to one previously established by the author for elastodynamics.     

Shock and acceleration waves with large amplitudes in laminated composite plates

Propagation of shock and acceleration waves with large amplitudes is studied. The geometrical nonlinearity in the von Karman sense is included in deriving the plate equations. The dynamical conditions on the wave fronts are derived from the three-dimensional conditions in a way consistent with the derivation of the plate equations. General equations governing the propagation velocities are obtained. Solutions are presented for the case where the plates are initially at rest. It is found that, in this case, the large amplitude has a substantial effect only on the transverse shear shock wave. Finally, stability of the wave front is discussed.     

Unsteady motion of an elliptic cylinder under a free surface

A problem of generation of nonlinear unsteady waves on the surface of an ideal liquid in an infinitely deep fluid due to the motion of a submerged elliptic cylinder is considered. The initial formulation of the problem is reduced to an integrodifferential system of equations for the function defining the free surface shape and for the normal and tangential components of velocity on the free surface. The small-time asymptotics of the solution is constructed for the case of cylinder motion with a constant acceleration from the state at rest.     

Reduction of the sonic boom level by heating the flow in front of the body

A numerical study of the possibility of reducing the sonic boom level in the case of local heat release to a supersonic gas flow at Mach number equal to 2 ahead of a body is described. The computations are performed for a spherical heat supply zone located on the flight trajectory ahead of the tip of an axisymmetric thin body. For the numerical study the combined method of “phantom bodies” is used. Different magnitudes of heat supply to the incoming flow are tested. These calculations are performed with allowance for interaction of shock waves emanating from the heated gas region and from the body in the far field. The computational results show that the local heat supply to a supersonic gas flow ahead of a body can reduce the sonic boom level by more than 20 %. The reduction of the sonic boom level is ensured by changing the free-stream parameters ahead of the body and by preventing the coalescence of shock waves from the heat supply zone and from the body in the far field.     

Internal waves from a body accelerating in a thermocline

Many papers study the steady wave system around bodies moving in thermoclines but little attention has been given to unsteady wave systems. This paper concentrates on the unsteady wave systems around accelerating bodies in thermoclines. The wave shapes are calculated using a theory derived from a dispersion relation based on an exp-tanh density profile. All modes of oscillation can be determined and it is shown that for the lowest mode both oblique and transverse waves occur whereas for the higher modes the presence of transverse waves depends on the background conditions and on the speed of the body. Cauchy-Poisson impulsive start waves are included. The theoretical wave shapes compare quite well with those calculated using finite-difference formulations of the full Navier-Stokes equations when a body accelerates from rest.It is also shown how the dispersion relation =N sin together with the WKB approximation can produce the same plan-view wave forms as those obtained using the thermocline wave dispersion relation given by [17, 30].     

Wedging of an elastic medium with the formation of separation zones

The problem of motion of a rigid body in an elastic medium is solved analytically for the case when a separation zone caused by asymmetry is formed in front of the body. A scheme of flow around wedge-shaped and ogive bodies is given for the entire range of the velocities under consideration. It is shown that there exists a limit velocity such that the separation zone disappears when the body moves at a velocity greater than the velocity of transverse waves. The forces exerted on a wedge-shaped body and on an ogive body are the same in the case of the limit velocity.     

Analysis of plane waves in anisotropic thermoelastic diffusive medium

This paper concentrates on the study of the propagation of harmonic plane waves in a homogeneous anisotropic thermoelastic diffusive medium in the context of different theories of thermoelastic diffusion. It is found that five types of waves propagate in an anisotropic thermoelastic diffusive medium, namely a quasi-elastodiffusive (QED-mode), two quasi-transverse (QSH-mode and QSV-mode), a quasi-mass diffusive (QMD-mode) and a quasi-thermo diffusive (QTD-mode) wave. The governing equations for homogeneous transversely isotropic diffusive medium in different theories of thermoelastic diffusion are taken as a special case. It is noticed that when plane waves propagate in one of the planes of transversely isotropic thermoelastic diffusive solid, purely quasitransverse wave mode(QSH) decouples from rest of the motion and is not affected by the thermal and diffusion vibrations. On the other hand, when plane waves propagate along the axis of solid, two quasi-transverse wave modes (QSH and QSV) decouple from the rest of the motion and are not affected by the thermal and diffusion vibrations. From the obtained results, the different characteristics of waves like phase velocity, attenuation coefficient, specific loss and penetration depth are computed numerically and presented graphically for a single crystal of magnesium. The effects of diffusion and relaxation times on phase velocity, attenuation coefficient, specific loss and penetration depth has been studied. Some particular cases are also discussed.     

位势流动和非均匀介质中声波方程的36种形式

声波方程是对大多数声学问题进行数学描述的出发点. 那些得到 广泛应用的经典波动方程及对流波动方程都存在苛刻的适用条件, 即仅适用于描述处于静态或匀速运动状态的定常 均匀介质中的线性无耗散声波. 然而, 很多实际场合并不满足这些严格的适用条件. 本文对经典声波方程和对流声波 方程进行推广, 导出了编号为W1$\sim$W36的36种不同形式的声波方程, 涵盖了处于静止、势流或旋涡流状态下的非均匀 和/或非定常介质中的声波传播问题. 所考虑的声波传播情形包括: (1) 线性波, 即具有小梯度(小振幅)性质; (2)非线性波, 即具有陡峭梯度性质, 包括``波纹'(小振幅大梯度)或者大振幅波. 本文仅考虑非耗散声波, 即排除了由剪切、体积黏度及热传导所引起的耗散. 对具有匀熵或等熵(熵沿流线守恒)性质的均匀介质和非均匀介质中的声传播进行了研究但非等熵(即耗散)情况除外; 另外, 对非定常介质中的 声波问题也进行了分析. 所涉及的介质可以处于静止、匀速运动状态, 或者是非匀速的和/或非定常的平均流动, 包括: (1)低Mach数的势平均流(即不可压缩的平均态), 或高速势平均流(即非均匀可压缩的平均流); ② 变截面管 道中的准一维传播, 包括无平均流的号管和具有低或高Mach数平均流的喷管; 或③平面的、空间的、或轴对称的单 向剪切平均流. 本文没有探讨其他类型的旋涡平均流(将与耗散及其他情形一起留待下一步研究), 例如, 可能与剪切效应相结合的轴对称旋转平均流. 通过对流体力学的一般方程进行消元处理或根据声学变分原理, 导出了36种波动方程, 对一些波动方程还采用这两种方法进行相互校验. 尽管声波方程的36种形式没有涵盖非线性、非均匀与非定常及非匀速运动介质 这3个效应的所有可能的组合情形, 但它们的确包括了孤立状态下的各种效应, 并包括了多种多重效应组合的 情形. 虽然经典波动方程和对流波动方程仅适用于处于静止(或匀速运动)的均匀定常介质中的线性无耗散声波, 但它们在 相关文献中已被广泛采用; 本文给出的36种声波方程提供了它们多种有用的推广形式. 在许多实际应用中, 经典波动方 程和对流波动方程仅是粗略的近似, 声波方程的更一般形式可提供更令人满意的理论模型. 本文每节末尾给出了这些应用 的众多范例. 在这篇评论文章中引用了240篇参考文献.     

Comments on the relation between surface wave theory and the theory of reflection

The sextic Stroh formalism, previously extensively used in the analysis of subsonic phenomena, has been used for the analysis of reflection phenomena and leaky surface waves in the first transsonic range of velocities. In particular the behaviour of the reflection problem at the limiting velocity is studied. It is shown that when the condition of free surface can be satisfied without the inhomogeneous partial wave, a situation which would appear to be the natural limiting case of a surface wave of infinite penetration, the body wave alone satisfies the condition of free surface. This result illuminates the Barnett-Lothe existence theorem for subsonic surface waves. The close connection between the reflection problem and the leaky surface wave problem becomes very apparent in the formalism used. It is shown that for a point on a branch of leaky waves where the solution is undamped, the conditions for simple reflection, i.e. reflection only involving the two body waves, are also present. In the vicinity of such a point reflection is accompanied by resonance excitation of leaky waves. The paper concludes with some explicit calculations for transversely isotropic solids.     

Axisymmetric longitudinal wave propagation in a finite prestrained circular cylinder embedded in a finite prestrained compressible medium

Axisymmetric longitudinal wave propagation in a finite prestrained circular cylinder contained in a finite prestrained infinite body is investigated within the scope of the piecewise-homogeneous body model by employing the three-dimensional linearized theory of elastic waves in a prestressed body. It is assumed that the materials of the cylinder and infinite body are compressible and that their elastic relations are described by a harmonic potential. Numerical results are presented and discussed for the case where the elastic constants of the cylinder are greater than those of the surrounding infinite body     

On Small-Displacement Waves in Prestressed Bodies with Isotropic Incremental Elasticity Tensor

We consider a body at rest in a prestressed configurationwhich responds elastically to small incremental displacements fromthe incremental elasticity tensor is supposed isotropic. On the basis of the paper [1] we characterize the conditions for the propagation of longitudinal, transverse, and oblique small-displacement waves superimposed toFormulae for the propagation speeds of these waves are written in terms of the prestress components and Lamparameters. The amplitudes of longitudinal and transverse waves are eigenvectors for the prestress.