Anti-plane shear waves in a fibre-reinforced composite with a non-linear imperfect interface

The propagation of non-linear elastic anti-plane shear waves in a unidirectional fibre-reinforced composite material is studied. A model of structural non-linearity is considered, for which the non-linear behaviour of the composite solid is caused by imperfect bonding at the “fibre–matrix” interface. A macroscopic wave equation accounting for the effects of non-linearity and dispersion is derived using the higher-order asymptotic homogenisation method. Explicit analytical solutions for stationary non-linear strain waves are obtained. This type of non-linearity has a crucial influence on the wave propagation mode: for soft non-linearity, localised shock (kink) waves are developed, while for hard non-linearity localised bell-shaped waves appear. Numerical results are presented and the areas of practical applicability of linear and non-linear, long- and short-wave approaches are discussed.     

BIFURCATIONS OF TRAVELLING WAVE SOLUTIONS IN VARIANT BOUSSINESQ EQUATIONS

The bifurcations of solitary waves and kink waves for variant Boussinesq equations are studied by using the bifurcation theory of planar dynamical systems. The bifurcation sets and the numbers of solitary waves and kink waves for the variant Boussinesq equations are presented. Several types explicit formulas of solitary waves solutions and kink waves solutions are obtained. In the end, several formulas of periodic wave solutions are presented.     

石英玻璃杆Taylor撞击实验的数值模拟

采用离散元方法模拟石英玻璃杆Taylor撞击问题,再现了其破坏过程:在撞击端,杆以压缩失效波的形式破坏;在自由端,出现了密集的拉伸层裂破坏. 分析表明:层裂是失效波阵面应力快速下降引起的追赶卸载波,与弹性压缩前驱波在自由端反射引起的迎面卸载波相互作用的结果;随着撞击速度的增大,撞击端失效波造成的压缩破坏区域损伤程度增大,反射端层裂破坏损伤区域减小. 进一步对失效波阵面的结构变化及其波速问题进行了研究,发现失效区域随着扩张变成一段裂纹逐渐由密到稀的区段,将此区段分为高损伤区和低损伤区,研究发现由稀疏微裂纹组成的低损伤区的前端面传播速度和弹性前驱波速基本相同,为固定值;而高损伤区前端面的裂纹密度随着传播距离的增加变稀,直至过渡为低损伤区,其传播具有显著的速度衰减、端面模糊直至停止的过程. 高损伤前端面的平均速度随着撞击速度的增大而增大,并逐渐趋近于弹性波速. 最后与已有实验做了对比,发现实验中高速摄影观察到的玻璃中"失效波"阵面实际上是高损伤前端面,而稀疏的低损伤微裂纹很难捕捉.      

Numerical analysis of quasi-static crack branching in brittle solids by a modified displacement discontinuity method

Mechanism of quasi-static crack branching in brittle solids has been analyzed by a modified displacement discontinuity method. It has been assumed that the pre-existing cracks in brittle solids may propagate at the crack tips due to the initiation and propagation of the kink (or wing) cracks. The originated wing cracks will act as new cracks and can be further propagated from their tips according to the linear elastic fracture mechanics (LEFM) theory. The kink displacement discontinuity formulations (considering the linear and quadratic interpolation functions) are specially developed to calculate the displacement discontinuities for the left and right sides of a kink point so that the first and second mode kink stress intensity factors can be estimated. The crack tips are also treated by boundary displacement collocation technique considering the singularity variation of the displacements and stresses near the crack tip. The propagating direction of the secondary cracks can be predicted by using the maximum tangential stress criterion. An iterative algorithm is used to predict the crack propagating path assuming an incremental increase of the crack length in the predicted direction (straight and curved cracks have been treated). The same approach has been used for estimating the crack propagating direction and path of the original and wing cracks considering the special crack tip elements. Some example problems are numerically solved assuming quasi-static conditions. These results are compared with the corresponding experimental and numerical results given in the literature. This comparison validates the accuracy and applicability of the proposed method.     

A computational study of local stress intensity factor solutions for kinked cracks near spot welds in lap-shear specimens

In this paper, the local stress intensity factor solutions for kinked cracks near spot welds in lap-shear specimens are investigated by finite element analyses. Based on the experimental observations of kinked crack growth mechanisms in lap-shear specimens under cyclic loading conditions, three-dimensional and two-dimensional plane-strain finite element models are established to investigate the local stress intensity factor solutions for kinked cracks emanating from the main crack. Semi-elliptical cracks with various kink depths are assumed in the three-dimensional finite element analysis. The local stress intensity factor solutions at the critical locations or at the maximum depths of the kinked cracks are obtained. The computational local stress intensity factor solutions at the critical locations of the kinked cracks of finite depths are expressed in terms of those for vanishing kink depth based on the global stress intensity factor solutions and the analytical kinked crack solutions for vanishing kink depth. The three-dimensional finite element computational results show that the critical local mode I stress intensity factor solution increases and then decreases as the kink depth increases. When the kink depth approaches to 0, the critical local mode I stress intensity factor solution appears to approach to that for vanishing kink depth based on the global stress intensity factor solutions and the analytical kinked crack solutions for vanishing kink depth. The two-dimensional plane-strain computational results indicate that the critical local mode I stress intensity factor solution increases monotonically and increases substantially more than that based on the three-dimensional computational results as the kink depth increases. The local stress intensity factor solutions of the kinked cracks of finite depths are also presented in terms of those for vanishing kink depth based on the global stress intensity factor solutions and the analytical kinked crack solutions for vanishing kink depth. Finally, the implications of the local stress intensity factor solutions for kinked cracks on fatigue life prediction are discussed.     

Nonlinear steady states of hyperelastic membrane tubes conveying a viscous non-Newtonian fluid

We study possible steady states of an infinitely long tube made of a hyperelastic membrane and conveying either an inviscid, or a viscous fluid with power-law rheology. The tube model is geometrically and physically nonlinear; the fluid model is limited to smooth changes in the tube’s radius. For the inviscid case, we analyse the tube’s stretch and flow velocity range at which standing solitary waves of both the swelling and the necking type exist. For the viscous case, we first analyse the tube’s upstream and downstream limit states that are balanced by infinitely growing upstream (and decreasing downstream) fluid pressure and axial stress caused by fluid viscosity. Then we investigate conditions that can connect these limit states by a single solution. We show that such a solution exists only for sufficiently small flow speeds and that it has a form of a kink wave; solitary waves do not exist. For the case of a semi-infinite tube (infinite either upstream or downstream), there exist both kink and solitary wave solutions. For finite-length tubes, there exist solutions of any kind, i.e. in the form of pieces of kink waves, solitary waves, and periodic waves.     

钢轨轨底垂直振动模式导波检测技术的实验研究

现有铁路钢轨超声探伤车技术无法检测线路钢轨轨底缺陷,给铁路运输安全带来很大隐患.本文开展了钢轨轨底超声导波传播特性和垂直振动模式导波检测技术研究,采用半解析有限元方法分析了我国60型钢轨轨底的各振动模态导波频散曲线和波结构.应用模态锤技术对自由状态钢轨轨底垂直振动模态导波传播特性进行了实验测量,结果表明,在0～100kHz频率范围内,钢轨轨底垂直振动模态优势模式与厚度为14 mm板中的A0模式兰姆波具有等效性.进一步研究了激励频率、激励脉冲周数、传播距离对轨底垂直振动模态导波传播的影响,设计了导波斜探头,选择合适的参数在钢轨轨底激励出垂直振动模态导波并检测出了轨底的人工缺陷.本文的研究结果为线路钢轨轨底的导波检测技术奠定了一定的基础.     

Lamb wave scattering by a symmetric pair of surface-breaking cracks in a plate

The scattering problem of a Lamb wave incident on a symmetric pair of surface-breaking transverse cracks in a plate is considered. The Lamb wave is assumed to be obliquely incident on the crack plane. Since the cracks are part-through, the scattered field will contain reflected as well as transmitted waves. The energy of the incoming wave is partitioned into reflected and transmitted wave modes. Energy coefficients of the reflected and transmitted waves are calculated as a function of incident frequency and crack depth. The incidence angle of the incoming wave is also treated as a parameter. Both the reflected and transmitted wave fields are considered as linear superpositions of all real and complex wave modes in the plate. Decomposition of modes is achieved with the help of an orthogonality condition based on the principle of reciprocal work. Continuity of displacement and stress fields is imposed at the crack plane. Energy coefficients for reflection and transmission are obtained from the mode amplitudes. Energy coefficients are shown to be a strong function of incident frequency and crack depth. Experiments are conducted with a PZT transducer network interacting with a symmetric pair of machined cracks in an aluminum plate. Trends predicted by the analysis are reflected in the experimental results.     

Can We Hear the Echos of Cracks?

The detection of cracks in mechanical engineering is mainly based on ultrasonic testing and Foucault currents. But even if they are efficient tools, this technology requires an important handling and is limited to the detection of cracks which are close to the source. Recently, several searchers have discussed the possibility of using waves as Lamb waves, for thin plates and shells, but also Love waves for bimaterials. In both cases the structure works as a wave guide and enables a long range propagation which is a promising possibility for detecting a crack quite far from the source. In this paper, we discuss the observability property of a small crack inside an open set using Love waves (the goal is to detect the beginning of the growth). It is proved that an adapted selection of these waves is necessary in order to avoid a black out which can occur for particular frequencies. This phenomenon is due to the fact that the crack has two extremities which can cancel their influence in a detection criterion. The main contribution of this paper is to discuss this point from a mathematical point of view, using an energy criterion requiring measurements quite far from the defect which should be detected.     

Nonlinear waves in electromigration dispersion in a capillary

We construct exact solutions to an unusual nonlinear advection–diffusion equation arising in the study of Taylor–Aris (also known as shear) dispersion due to electroosmotic flow during electromigration in a capillary. An exact reduction to a Darboux equation is found under a traveling-wave ansatz. The equilibria of this ordinary differential equation are analyzed, showing that their stability is determined solely by the (dimensionless) wave speed without regard to any (dimensionless) physical parameters. Integral curves, connecting the appropriate equilibria of the Darboux equation that governs traveling waves, are constructed, which in turn are shown to be asymmetric kink solutions (i.e., non-Taylor shocks). Furthermore, it is shown that the governing Darboux equation exhibits bistability, which leads to two coexisting non-negative kink solutions for (dimensionless) wave speeds greater than unity. Finally, we give some remarks on other types of traveling-wave solutions and a discussion of some approximations of the governing partial differential equation of electromigration dispersion.     

对称表面动载下有限块体的破裂过程

实验表明,受对称布置的表面爆炸载荷的脆性块体,会在通过载荷作用点连线的某一平面上破裂。为解释这一现象并进一步探讨利用类似方法破碎岩块的可能性,本文介绍了应用弹性动力学理论建立的计算模型以及所进行的动光弹和混凝土块模型试验。研究结果表明:在所述载荷条件下,应力波特别是自由界面反射的拉伸波对块体的破碎起重要作用;由于多向拉应力集中,在块体加载端面梭边中部最易产生径向裂隙,此后在侧面反射波的作用下裂隙延伸,与中部可能存在的裂纹贯通,从而将块体破开;对称加载使应力波在块体内多次叠加有利于块体充分破碎。     

SPH modeling of fluid–solid interaction for dynamic failure analysis of fluid-filled thin shells

This work concerns the prediction of failure of a fluid-filled tank under impact loading, including the resulting fluid leakage. A water-filled steel cylinder associated with a piston is impacted by a mass falling at a prescribed velocity. The cylinder is closed at its base by an aluminum plate whose characteristics are allowed to vary. The impact on the piston creates a pressure wave in the fluid which is responsible for the deformation of the plate and, possibly, the propagation of cracks. The structural part of the problem is modeled using Mindlin–Reissner finite elements (FE) and Smoothed Particle Hydrodynamics (SPH) shells. The modeling of the fluid is also based on an SPH formulation. The problem involves significant fluid–structure interactions (FSI) which are handled through a master–slave-based method and the pinballs method. Numerical results are compared to experimental data.     

Simulation of dynamic processes in three-dimensional layered fractured media with the use of the grid-characteristic numerical method

This paper touches upon the computer simulation of the propagation of elastic waves in three-dimensional multilayer fractured media. The dynamic processes are described using the defining system of equations in the partial derivatives of the deformed solid mechanics. The numerical solution of this system is carried out via the grid-characteristic method on curvilinear structural grids. The fractured nature of the medium is accounted for by explicitly selecting the boundaries of individual cracks and setting special boundary conditions in them. Various models of heterogeneous deformed media with a fractured structures are considered: a homogeneous medium, a medium with horizontal boundaries, a medium with inclined boundaries, and a medium curvilinear boundaries. The wave fields detected on the surface are obtained, and their structures are analyzed. It is demonstrated that it is possible to detect the waves scattered from fractured media even in the case of nonparallel (inclined and curvilinear) boundaries of geological layers.     

Mechanical wave momentum from the first principles

Axial momentum carried by waves in a uniform waveguide is considered based on the conservation laws and a kind of the causality principle. Specifically, we examine (without resorting to constitutive data) steady-state waves of an arbitrary shape, periodic waves which speed differs from the speed of its form and binary waves carrying self-equilibrated momentum. The approach allows us to represent momentum as a product of the wave mass and the wave speed. The propagating wave mass, positive or negative, is the excess of that in the wave over its initial value. This general representation is valid for mechanical waves of arbitrary nature and intensity. The finite-amplitude longitudinal and periodic transverse waves are examined in more detail. It is shown in particular, that the transverse excitation of a string or an elastic beam results in the binary wave. The closed-form expressions for the drift in these waves functionally reduce to the Stokes’ drift in surface water waves (a half the latter by the value). Besides, based on the general representation an energy–momentum relation is discussed and the physical meaning of the so-called “wave momentum” is clarified.     

Imperfection and burial-depth sensitivity of the initiation and development of kink folds in laminated rocks

The first objective is to study the influence of the burial depth and of an imperfection, in the form of a tilt in the inclination of the otherwise straight, laminated beam, on the conditions for the initiation and the development of kink folds. The beam, typical of sedimentary rocks, is layered with weak interfaces between the competent beds, promoting the onset of kinking by their slip. The results are analytical and based on the upper bound approach of the classical limit analysis, referred to as the maximum strength theorem in the absence of any discussion of plasticity. The weak interface strength is described by the Coulomb criterion, whereas the bulk material is also cohesive and frictional but with an additional closure in the compressive stress domain to depict the action of compacting deformation mechanisms. The new twist to the methodology is to extend its application to the development of the failure mode beyond the onset, assuming that the structure finite response is well described by the least upper bound solution. The second objective is to compare in terms of upper bounds three different failure mechanisms which are the compaction band, the reverse fault and the kink fold. Their respective domain of dominance is constructed in failure-mechanism maps in the space spanned by the imperfection angle and the burial depth.Compaction bands are predicted at the deepest end of the beam and the reverse fault and the kink fold at the shallower end. These depth differences are resulting from the geometrical imperfection. It is found that the kink-band mode at its onset, with compaction band dominant conditions, resembles to a slip-enhanced compaction band due to the weak interface activation and the compaction along the two parallel hinges. This hybrid mode migrates suddenly through the competent beam from the deepest towards the shallowest region and develops as a kink fold, after a negligible amount of shortening. The kink fold development, beyond the onset, occurs in two phases, the first corresponding to the rotation of the kink band and the second, to its widening. The associated least upper bound is first decreasing during the development and then increasing, the minimum being controlled more by the increase in the potential energy of the system than by the most favorable orientation of the frictional weak interfaces. It is finally found that the continuous activation of slip over the weak interfaces and the widening of the kink band prevent the rotation of the kink towards the large angles which are necessary to induce its locking. It is proposed that the introduction of damage along the hinges could palliate these two effects and prompt the locking observed experimentally and in the field.     

Travelling wave solutions for a second order wave equation of KdV type

The theory of planar dynamical systems is used to study the dynamical behaviours of travelling wave solutions of a nonlinear wave equations of KdV type.In different regions of the parametric space,sufficient conditions to guarantee the existence of solitary wave solutions,periodic wave solutions,kink and anti-kink wave solutions are given.All possible exact explicit parametric representations are obtained for these waves.     

Lamb wave mode decomposition using concentric ring and circular piezoelectric transducers

Lamb waves using surface-bonded piezoelectric transducers (PZTs) have been widely used for nondestructive testing (NDT). However, the identification of individual Lamb wave modes and the subsequent data interpretation are often difficult due to the dispersive and multimodal natures of Lamb waves. To tackle the problem, a Lamb wave mode decomposition technique using concentric ring and circular PZTs is proposed. Its advantages over the conventional approaches are that (1) PZTs need to be placed only a single surface of a specimen and (2) mode decomposition can be performed at any desired frequency without changing the PZT size and/or spacing configuration. The proposed mode decomposition technique is formulated by solving 3D Lamb wave propagation equations considering the PZT size and shape, and this technique requires a specially designed dual PZT composed of concentric ring and circular PZTs. The effectiveness of the proposed technique for the Lamb wave mode decomposition is investigated through numerical simulation and experimental tests performed on an aluminum plate.     

Modeling non-collinear mixing by distributions of clapping microcracks

Nonlinear scattering by distributions of clapping cracks in a non-collinear wave mixing setting is modeled. Features of the nonlinear response discriminating distributions of clapping cracks from quadratic nonlinear damage are investigated for distributions of cracks that are parallel to each other or randomly oriented. The effective properties of these distributions are recovered extending an existing model that applies to open cracks. The equation of motion is solved using a perturbation approach, and its solutions are evaluated numerically. Their dependence on the amplitude of the incident field is found to be linear, in contrast with the quadratic dependence characterizing quadratic nonlinearity. The spectrum of the scattered field is shown to contain an infinite number of higher harmonics already at the first order of perturbation. Grating-like structures due to the opening and closing of cracks are responsible for adding diffraction peaks to the directivity functions of waves scattered by open cracks. The locations of the most prominent peaks of these functions do not satisfy the selection rules controlling nonlinear scattering by quadratic nonlinearity. Examples of these are given, together with others showing the possibility of using at least one of several discrimination modalities offered by non-collinear wave mixing.     

含单排周期微裂纹平板结构中的弹性波传播

受损伤固体中含有的微裂纹或微孔洞往往具有周期性，对含周期性缺陷结构中的弹性波分析是力学研究中的重要课题，它直接关系到结构的强度和使用寿命。目前对损伤固体中弹性波散射与透射研究结果主要是弹性动力学平面问题。1995年。Scarpetta和Sumbatyan采用解析法研究了平面波在双周期裂纹弹性介质中的传播问题。并推出显式分析结果。本文基于弹性动力学理论，分析研究了含有单排横向周期裂纹的平板中弯曲波的反射与透射问题。给出了含单排裂纹时反射波与透射波系数的数值结果。对于多排裂纹情况，可采用具有退化核第一类Fredholm积分方程方法分析求解，在求解中给出相应的无量纲数，例如无量纲波数、裂纹尺寸比等。本文分析结果可望能在工程振动控制中应用。     

不同当量比下喷管对旋转爆震特性的影响研究

为研究不同当量比下喷管构型对旋转爆震特性的影响,以煤油预燃裂解气为燃料,氧气体积分数为30%的富氧空气为氧化剂,开展了无喷管、收敛喷管、扩张喷管和收敛扩张喷管等工况下旋转爆震特性实验研究。实验发现,当量比为0.73～1.30时旋转爆震可稳定工作。随着当量比和喷管构型的变化,爆震波出现了单波、不稳定的对撞双波和稳定的对撞双波等3种传播模态。喷管构型对模态转换和旋转爆震波速有重要影响,收敛和收敛扩张喷管会促使新波头的产生,导致爆震波主要以双波对撞模态传播;而扩张喷管工况下,爆震波主要以单波模态传播。收敛喷管和收敛扩张喷管会使得波速最大值偏离化学恰当比,收敛扩张喷管可以提升爆震波速。