The propagation of elastic stress waves in a conical shell under axial impulsive loading

The propagation of elastic stress waves in a conical shell subjected to axial impulsive loading is studied in this paper by means of the finite element calculation and model experiments. It is shown that there are two axisymmetrical elastic stress waves propagating with different velocities, i.e., the longitudinal wave and the bending wave. The attenuation of these waves while propagating along the shell surface is discussed. It is found in experiments that the bending wave is also generated when a longitudinal wave reflects from the fixed end of the shell, and both reflected waves will separate during the propagation due to their different velocities. Southwest Institute of Structural Mechanics     

SH-type waves dispersion in an isotropic medium sandwiched between an initially stressed orthotropic and heterogeneous semi-infinite media

The present paper studies the propagation of shear waves (SH-type waves) in an homogeneous isotropic medium sandwiched between two semi infinite media. The upper half-space is considered as orthotropic medium under initial stress and lower half-space considered as heterogeneous medium. We have obtained the dispersion equation of phase velocity for SH-type waves. The propagation of SH-type waves are influenced by inhomogeneity parameters and initial stress parameter. The velocity of SH-type wave has been computed for different cases. We have also obtained the dispersion equation of phase velocity in homogeneous media in the absence of initial stress. The velocities of SH-type waves are calculated numerically as a function of kH (non-dimensional wave number) and presented in a number of graphs. To study the effect of inhomogeneity parameters and initial stress parameter we have plotted the velocity of SH-type wave in several figure. We have observed that the velocity of wave increases with the increase inhomogeneity parameters. We found that in both homogeneous and inhomogeneous media the velocity of SH-type wave increases with the increase of initial stress parameter. The results may be useful for the study of seismic waves propagation during any earthquake and artificial explosions.     

Stress waves in pyramids by photoelasticity

The propagation of stress waves in pyramids was studied photoelastically with the application of a laser-photomultiplier tube system and an internal polariscope for recording moving fringes. Dispersion and attenuation of stress waves were considered in a straight bar, a 5-deg pyramid, and a 20-deg pyramid made of Hysol 4290 epoxy plastic. In the straight bar and 5-deg pyramid, longitudinal waves propagate without any dispersion even though the waves attenuate as they progress down the models; in the 20-deg pyramid, however, the dispersion of the stress waves is quite significant. The distributions of the axial and radial stresses and the photoelastic fringe patterns obtained on the 20-deg pyramid show that the stress wave front is spherical with the maximum stress along the central axis of the pyramid. A one-dimensional theory of wave propagation without correction factors in a small-angle infinite cone compares well with the experimental results.     

轴向冲击载荷作用下锥壳中弹性应力波传播的计算和实验研究

本文利用有限元分析和模型实验研究了在轴向冲击载荷作用下,锥壳中弹性应力波的传播、计算和实验结果表明,结构中存在着弹性纵波和弹性弯曲波的传播,它们传播的速度各不相同,使壳面承受不同的应力状态;讨论了纵波和弯曲波随壳面的衰减;实验指出,由于边界的影响,即使纵波的反射也会产生新的反射弯曲波沿锥面传播。     

同震断层三维裂纹扩展波动时域超奇异积分法

应用波动时域超奇异积分法将P波、S波和磁电热弹多场耦合作用下同震断层任意形状三维裂纹扩展问题转化为求解以广义位移间断率为未知函数的超奇异积分方程组问题;定义了广义应力强度因子,得到裂纹前沿广义奇异应力增量解析表达式;应用波动时域有限部积分概念及体积力法,为超奇异积分方程组建立了数值求解方法,编制了FORTRAN程序,以三维矩形裂纹扩展问题为例,通过典型算例,研究了广义应力强度因子随裂纹位置变化规律;分析了同震断层裂纹扩展中力、磁、电场辐射规律.      

界面上应力波传播规律的动态光弹性试验研究

采用动态光弹性方法,对应力波在杆-杆和板-板双材料连接界面上的反射和透射传播规律展开研究．通过对双材料粘接模型施加冲击载荷作用,采集和分析等差线条纹,计算出最大剪应力值．对于两种试验模型应力波在界面上都以透射为主,对应力波的阻隔作用不明显,这与接触式界面对应力波有较强的阻隔作用有较大区别,在应用界面减弱应力波的作用时应注意区分．试验结果与理论计算结果基本保持一致,并由此证明采用动态光弹性法研究应力波在界面上传播规律的可行性．     

Relection of elastic waves at the elastically supported boundary of a couple stress elastic half-space

The relection elastic waves at the elastically supported boundary of a couple stress elastic half-space are studied in this paper. Different from the classical elastic solid, there are three kinds of elastic waves in the couple stress elastic solid, and two of them are dispersive. The boundary conditions of a couple stress elastic half-space include the couple stress vector and the rotation vector which disappear in the classical elastic solids. These boundary conditions are used to obtain a linear algebraic equation set, from which the amplitude ratios of relection waves to the incident wave can be determined. Then, the relection coeficients in terms of energy lux ratios are calculated numerically, and the normal energy lux conservation is used to validate the numerical results. Based on these numerical results,the inluences of the boundary parameters, which relect the mechanical behavior of elastic support, on the relection energy partition are discussed. Both the incident longitudinal wave(the P wave) and incident transverse wave(the SV wave) are considered.     

薄壁管预扭冲击拉伸实验装置的研制

材料在复合应力下的拉压或扭转行为常常与单轴拉压或者单轴扭转应力下不同,拉压以及扭转常体现出相互影响的特点。而复合应力下的塑性波可以有效地反映材料在复合应力下的本构行为特点。本文通过对霍普金森压杆进行改造,建立了一套薄壁管预扭冲击拉伸的实验装置,可以在薄壁管内产生拉扭耦合塑性波,并对率相关材料304不锈钢进行了薄壁管预扭拉伸实验研究,得到了该材料的拉扭耦合塑性波。结果表明,304不锈钢薄壁管的拉扭耦合塑性波具有明显的耦合快波和耦合慢波的双波结构,并且快波慢波之间没有恒值区间隔。同时也表明,该装置可以实现预期效果,并且可以有效避免薄壁管屈曲的产生。     

Determination of the minimum entropy configuration and velocity surfaces for elastic–plastic wave scattering at grain boundaries

A recent model based on full elastic anisotropy and crystal plasticity predicted the existence of multiple wave configurations during the interaction of stress waves with grain boundaries. Since the multiple wave configuration scenario cannot exist in nature, the principle of minimum entropy production is applied in the current work to find the most probable configuration. A large amplitude transmitted quasi-longitudinal wave is predicted for the given bicrystal orientation studied due to the wave propagating near a [001] direction and thus requiring large stress given the very low Schmid factor in this direction (for nickel aluminide (NiAl) as a model material). Anisotropic elastic–plastic velocity surfaces for quasi-longitudinal and quasi-shear waves in NiAl have also been constructed to gain an understanding of the general nature of plastic waves as a function of crystallographic direction.     

Effects of initial stress on the reflection and transmission waves at the interface between two piezoelectric half spaces

The effects of initial stress on the reflection and transmission waves at the interface between two piezoelectric half spaces are studied in this paper. First, the secular equations in the traverse isotropic piezoelectric half space are derived from the general dynamic equation with initial stress taken into consideration. Then, the interface conditions that displacement, stress, electric potential, and electric displacement are continuous across interface are required to be satisfied by three sets of coupled waves, namely, quasi-longitudinal wave, quasi-transverse wave and the electric–acoustic wave. The algebraic equations resulting from the interface conditions are solved to obtain the amplitude ratio of various waves and furthermore the energy reflection and transmission coefficients of various waves. The numerical results are shown graphically and the effects of initial stress are discussed.     

应力波传播与屈曲耦合情况下结构动力屈曲控制方程探讨

从应力波作用下结构动力屈曲的特点出发,指出应力波作用下结构动力屈曲与结构中应力波传播的耦合导致时间成为结构动力屈曲的参变量,从而应力波作用下结构动力屈曲问题中结构的真实运动与邻近运动是不同时刻、不同扰动区域的比较,这使得其动力屈曲控制方程的建立不宜采用传统的等时积分变分原理;以压应力波作用下弹性直杆为例,应用能量守恒原理,根据屈曲时刻结构能量的转换关系,建立了弹性压应力波作用下半无限长直杆的动力屈曲控制方程,并得到了波前附加约束条件;最后,讨论了波前附加约束条件的物理意义,指出波前附加约束条件出现的根本原因是轴向应力波的传播与屈曲不能解耦。     

Torsional surface waves in heterogeneous anisotropic half-space under initial stress

The present paper is concerned with the propagation of torsional surface waves in a heterogeneous anisotropic half-space under the initial compressive stress. The heterogeneity in the half-space is caused by the linear variation in rigidity, initial compressive stress and density. The solution part of the problem involves the use of Whittaker function. The dispersion equation has been obtained in a closed form, which shows the variation of phase velocity with corresponding wave number. Effects of anisotropy and initial stress have been shown by the means of graphs for different anisotropic materials. It has found that the phase velocity of torsional waves decreases with increment in initial stress and inhomogeneity. Obtained phase velocity of torsional surface wave is found to be less than the shear wave velocity, which agrees with the standard result.     

Rayleigh lamb waves in micropolar isotropic elastic plate

The propagation of waves in a homogeneous isotropic micropolar elastic cylindrical plate subjected to stress free conditions is investigated. The secular equations for symmetric and skew symmetric wave mode propagation are derived. At short wave limit, the secular equations for symmetric and skew symmetric waves in a stress free circular plate reduces to Rayleigh surface wave frequency equation. Thin plate results are also obtained. The amplitudes of displacements and microrotation components are obtained and depicted graphically. Some special cases are also deduced from the present investigations. The secular equations for symmetric and skew symmetric modes are also presented graphically.     

Resonance in Polyurea-Based Multilayer Structures Subjected to Laser-Generated Stress Waves

We report resonance associated with polyurea layers sandwiched between identical acrylic and polycarbonate plates when subjected to laser-generated stress waves of several nanoseconds in duration. Transmitted stress wave amplitudes almost 16 times the incident stress wave amplitudes are observed. An elastodynamics simulation identified the thickness of the polyurea layer as the key parameter controlling the amplitude of the transmitted stress wave. This resonance effect was found absent when the polyurea was sandwiched between the steel and aluminum plates of similar thickness. However, for these samples, a dramatic reduction in the amplitudes of the transmitted stress waves was recorded. A finite element analysis of the wave propagation through the sandwiched polyurea layer in these samples tied the large amplitude reduction to the large acoustic impedance mismatch and the viscoelastic dissipation within the polyurea layer.     

核爆X光辐照铝靶产生的脉冲应力波的简化解析估算

高空核爆炸大约有７０％的能量以Ｘ射线形式向外辐射，高能通量密度的Ｘ射线辐照在空间结构物上，在其表面的能量沉积将产生脉冲应力波（通常又称为热击波），这样的脉冲应力波可造成壳体材料的动力学破坏。对于试验研究人员来说希望采用简化解析模型对于其参数作出直观、快速的预测。并以简化模型估算了核爆Ｘ射线谱的特征、Ｘ光辐照铝靶产生的脉冲应力波的初始参数及其沿铝靶厚度的衰减特性。     

应力波在变截面体中的传播特性

对应力波在变截面体中的传播特性进行了理论研究和数值分析。以杆中一维纵波波动理论和谐波分析法为基础，研究截面变化所导致的应力波的波形弥散和波幅变化。推导了与截面变化相关的应力波演化因子，并对由于截面变化所造成的几何弥散等二维效应进行了分析，同时计算了变截面体的几何特征参数和截面变化等因素影响应力波演化规律的特点。     

Wave front analysis of a plane compressional pulse scattered by a cylindrical elastic inclusion

The plane-strain problem of a stress pulse striking an elastic circular cylindrical inclusion embedded in an infinite elastic medium is treated. The method used determines dominant stress singularities that arise at wave fronts from the focusing of waves refracted into the interior. It is found that a necessary and sufficient condition for the existence of a propagating stress singularity is that the incident pulse has a step discontinuity at its front. The asymptotic wave front behavior of the first few P and SV waves to focus are determined explicitly and it is shown that the contribution from other waves are less important. In the exterior, it is found that in most composite materials the reflected waves have a singularity at their wave front which depends on the angle of reflection. Also the wave front behavior of the first few singular transmitted waves is given explicitly.The analysis is based on the use of a Watson-type lemma, developed here, and Friedlander's method [5]. The lemma relates the asymptotic behavior of the solution at the wave front to the asymptotic behavior of its Fourier transform on time for large values of the transform parameter. Friedlander's method is used to represent the solution in terms of angularly propagating wave forms. This method employs integral transforms on both time and θ, the circumferential coordinate. The θ inversion integral is asymptotically evaluated for large values of the time transform parameter by use of appropriate asymptotics for Bessel and Hankel functions and the method of stationary phase. The Watson-type lemma is then used to determine the behavior of the solution at singular wave fronts.The Watson-type lemma is generally applicable to problems which involve singular loadings or focusing in which wave front behavior is important. It yields the behavior of singular wave fronts whether or not the singular wave is the first to arrive. This application extends Friedlander's method to an interior region and physically interprets the resulting representation in terms of ray theory.     

Acoustoelastic determination of residual stress with laser doppler velocimetry

The main object of this study is to develop a new technique for stress nondestructive measurement. A noncontact measurement technique of ultrasonic wave velocity is proposed. In the measurement system, a laser Doppler velocimeter, which is noncontact, is used to detect wave motions due to Rayleigh waves instead of a piezoelectric transducer. The noncontact measurement technique is applied to determine the stress-acoustic coefficient of Rayleigh waves for aluminum 5052 and a structural steel, and the results are in good agreement with those obtained using knife-edge piezoelectric transducers. The technique is also used to evaluate residual stress existing in an H-section rolled beam of the structural steel. The distribution of residual stress is reasonable.     

Spall Characterization in Epoxy Via Laser Spallation

Background: The strength of materials under extreme dynamic loading conditions, such as in the case of shock wave loading, is assessed from their spallation characteristics. Under laboratory conditions, flyer plate impact, or sometimes laser-induced stress waves, is employed to instigate spall in a material. These methods are often combined with velocity interferometer system for any reflector (VISAR) technique for performing transient measurements. Although the VISAR can record the velocity of extremely fast-moving surfaces, it requires a complex optical setup and a specialized data reduction technique. Objective: In this study, a simpler approach is adopted by extending laser spallation method to determine the spall strength of epoxy, while performing in situ interferometric measurements, directly on top of thick epoxy films. Methods: The glass/epoxy test samples are prepared by transferring an aluminum coating on top of epoxy layers with different thicknesses. Laser-induced stress waves transmit across the substrate/film interface and induce subsurface failure in the epoxy at sufficiently high incident laser energy. The nature and magnitude of the waves are deciphered from the out-of-plane displacement histories of the top reflective sample surfaces, which are recorded by using a Michelson interferometer. Results: The interferometric data reveal the development of two (temporally) well-separated stress waves: an ablation-induced high-amplitude short-duration longitudinal pulse, which is referred to as the primary wave, and a secondary wave, which travels at a comparatively slower speed. The complex constructive interaction of the two waves develops a high-magnitude tensile stress region in the epoxy layer. The spall strength is quantified by superimposing the two stress wave histories associated with the critical energy fluence. Conclusions: The spall depths predicted from spatiotemporal wave travel analyses are in excellent agreement with the experimental observations. The newly adopted methodology estimates the spall strength of epoxy as 260?±?20 MPa.