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。     

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     

Wave propagation along a non-principal direction in a compressible pre-stressed elastic layer

The dispersive behavior of small amplitude waves propagating along a non-principal direction in a pre-stressed, compressible elastic layer is considered. One of the principal axes of stretch is normal to the elastic layer and the direction of propagation makes an angle θ with one of the in-plane principal axes. The dispersion relations which relate wave speed and wavenumber are obtained for both symmetric and anti-symmetric motions by formulating the incremental boundary value problem for a general strain energy function. The behavior of the dispersion curves for symmetric waves is for the most part similar to that of the anti-symmetric waves at the low and high wavenumber limits. At the low wavenumber limit, depending on the pre-stress and propagation angle, it may be possible for both the fundamental mode and the next lowest mode to have finite phase speeds, while other higher modes have an infinite phase speed. At the high wavenumber limit, the phase speeds of the fundamental mode and the higher modes tend to the Rayleigh surface wave speed and the limiting wave speeds of the layer, respectively. Numerical results are presented for a Blatz–Ko material and the effect of the propagation angle is clearly illustrated.     

Time-harmonic wave propagation in a pre-stressed compressible elastic bi-material laminate

The dispersive behaviour of time-harmonic waves propagating along a principal direction in a perfectly bonded pre-stressed compressible elastic bi-material laminate is considered. The dispersion relation which relates wave speed and wavenumber is obtained by formulating the incremental boundary value problem and the use of the propagator matrix technique. At the low wavenumber limit, depending on the pre-stress, both the fundamental mode and the next lowest mode may have finite phase speeds. For the higher modes which have infinite phase speeds in the low wavenumber region, an expression to determine the cut-off frequencies is obtained. At the high wavenumber limit, the phase speeds of the fundamental mode and higher modes tend to phase speeds of the surface wave, the interfacial wave or the limiting phase speed of the composite. For numerical examples, either a two-parameter compressible neo-Hookean material or a two-parameter compressible Varga material is assumed.     

A mixture theory analysis for the surface-wave propagation in an unsaturated porous medium

The mixture theory is employed to the analysis of surface-wave propagation in a porous medium saturated by two compressible and viscous fluids (liquid and gas). A linear isothermal dynamic model is implemented which takes into account the interaction between the pore fluids and the solid phase of the porous material through viscous dissipation. In such unsaturated cases, the dispersion equations of Rayleigh and Love waves are derived respectively. Two situations for the Love waves are discussed in detail: (a) an elastic layer lying over an unsaturated porous half-space and (b) an unsaturated porous layer lying over an elastic half-space. The wave analysis indicates that, to the three compressional waves discovered in the unsaturated porous medium, there also correspond three Rayleigh wave modes (R1, R2, and R3 waves) propagating along its free surface. The numerical results demonstrate a significant dependence of wave velocities and attenuation coefficients of the Rayleigh and Love waves on the saturation degree, excitation frequency and intrinsic permeability. The cut-off frequency of the high order mode of Love waves is also found to be dependent on the saturation degree.     

On the behavior of stress waves in composite materials—I. A universal set of boundary conditions

In recent years experiments on uniaxially reinforced composites have revealed anomalous behavior in the stress-wave propagation characteristics of these materials. Whenever the exposed ends of both composite constituents were subjected to moderate pressures of a few kilobars the number of stable propagating waves generated within the composite exceeded by one the number of waves calculated through conventional composite models. This effect greatly increased the wave dispersion and rise-time in the experimentally observed stress wave.The key to the origin of this phenomenon is quite elementary. The composite debonds internally. When the bond between the reinforcing and matrix fails, the composite attains an additional degree of freedom which results in an additional stable propagating wave. Since conventional composite models do not allow for this debonding, they cannot account for the resulting wave. However, as was shown in an earlier paper, direct application of the theory of elasticity to this problem results in wave velocities and mode shapes for all of the waves.The solution to the total problem, including the determination of the various wave amplitudes, was previously hampered by an insufficient set of boundary conditions. The usual procedure was to impose continuity of stress and displacement at the boundary between the composite and the adjoining homogeneous material where the volumetric averages of stress and displacement were used for the composite. While these conditions are necessary and sufficient for the bonded composite problem, they are insufficient for the debonded composite problem. The additional degree of freedom in the debonded problem makes the use of an additional boundary condition necessary. This additional boundary condition is the subject of this paper.     

Anisotropic wave propagation and its applications to NDE of composite materials

This paper utilized anisotropic wave propagation theory to measure the elastic constants of a unidirectional fiber-reinforced composite specimen. For plane waves propagating in the composite specimen, the deviation of the propagational directions between the energy and phase velocities were measured. It is found that in such a sample, the deviations may be as large as 60 degrees. The measured energy velocities were transformed to the phase velocities of the plane waves by employing a numerical scheme. It is demonstrated that the elastic constants of a unidirectional fiber-reinforced composite can be determined by conducting ultrasonic experiments in two principal symmetry planes.     

Elastic Waves in Swelling Porous Media

Time harmonic waves in a swelling porous elastic medium of infinite extent and consisting of solid, liquid and gas phases have been studied. Employing Eringen’s theory of swelling porous media, it has been shown that there exist three dilatational and two shear waves propagating with distinct velocities. The velocities of these waves are found to be frequency dependent and complex valued, showing that the waves are attenuating in nature. Here, the appearance of an additional shear wave is new and arises due to swelling phenomena of the medium, which disappears in the absence of swelling. The reflection phenomenon of an incident dilatational wave from a stress-free plane boundary of a porous elastic half-space has been investigated for two types of boundary surfaces: (i) surface having open pores and (ii) surface having sealed pores. Using appropriate boundary conditions for these boundary surfaces, the equations giving the reflection coefficients corresponding to various reflected waves are presented. Numerical computations are performed for a specific model consisting of sandstone, water and carbon dioxide as solid, liquid and gas phases, respectively, of the porous medium. The variations of phase speeds and their corresponding attenuation coefficients are depicted against frequency parameter for all the existing waves. The variations of reflection coefficients and corresponding energy ratios against the angle of incidence are also computed and depicted graphically. It has been shown that in a limiting case, Eringen’s theory of swelling porous media reduces to Tuncay and Corapcioglu theory of porous media containing two immiscible fluids. The various numerical results under these two theories have been compared graphically.     

A knife-edge load traveling on the surface of an elastic halfspace

A load moving on the surface of an elastic halfspace forms a basic problem that is related to different fields of engineering, such as the subsoil response due to vehicle motion or the ultrasound field due to an angle beam transducer. Many numerical techniques have been developed to solve this problem, but these do not provide the fundamental physical insights that are offered by closed form solutions, which are very rare in comparison. This paper describes the development and analysis of the closed form space-time domain solution for a knife-edge load, i.e. a line segment of normal traction, moving at a constant speed on the surface of an elastic halfspace. The various contributions making up the exact solution, obtained with the Cagniard-De Hoop method, produce all the complicated wave patterns from this distributed type of loading. Examples are the transient wave field at the starting position of the load, angled conical and plane waves propagating into the solid, Rayleigh waves propagating along the surface, and head waves spreading and attenuating in specific directions from the loading path. The influence of the load speed on the wave field is investigated by considering the singularities in the relevant complex domains, for each sonic range relative to the bulk wave velocities. The characteristic wave fronts and wave patterns as exhibited by the particle displacements are evaluated for subsonic, transonic and supersonic load speeds.     

超声纯横波法测试45#钢的内部应力

声各向同性的金属材料在应力作用下,材料表现出声各向异性,这是用声弹性法分析材料内部应力的基础。本文用垂直于应力方向传播的超声纯横波对45#钢进行测试,测试时横波的偏振化方向分别平行和垂直于应力方向。实验结果表明:材料在拉、压应力作用下,相互正交的两超声纯横波的声速都发生了变化,且声各向异性因子与应力成线性关系。利用此关系可测试材料内部应力,提供了一种无损测试材料内部应力的方法,另外本实验方法也可以对材料内部残余应力进行评估。实验中利用回振法测量声速,可测量声速的微小变化,精度高。     

Wave–wave interactions in a periodic chain with quadratic nonlinearity

Two waves are studied using perturbation analysis for their interactions in an one-dimensional periodic structure with quadratic nonlinearity. A first-order multiple-scales analysis along with numerical simulations on the full chain are used to understand the interaction of two waves when one is the sub- or super-harmonic of the other. The strength of quadratic nonlinearity affects the rate at which the energy is exchanged between the two waves. Depending on parameters and energy states, the interactions between the waves are periodic or whirling and result in quasi-periodic combined propagating waves with either phase drifts or weakly phase-locking properties. The analysis suggests the possibility of the existence of emergent wave harmonics. Due to quadratic nonlinearity, a very small amplitude subharmonic or superharmonic wave mode can drift in its phase, and then burst out with a larger amplitude as it circumnavigates a separatrix. Depending on the parameters and wave numbers, the amplitude of this emergent wave burst can have varying significance.     

Boundary element modeling for defect characterization potential in a wave guide

Wave scattering analysis implemented by boundary element methods (BEM) and the normal mode expansion technique is used to study the sizing potential of two-dimensional shaped defects in a wave guide. Surface breaking half-elliptical shaped defects of three opening lengths (0.3, 6.35 and 12.7 mm) and through-wall depths of 10–90% on a 10 mm thick steel plate were considered. The reflection and transmission coefficients of both Lamb and shear horizontal (SH) waves over a frequency range 0.05–2 MHz were studied. A powerfully practical result was obtained whereby the numerical results for the S₀ mode Lamb wave and n₀ mode SH wave at low frequencies showed a monotonic increase in signal amplitude with an increase in the defect through-wall depth. At high frequency (usually above the cut-off frequency of the A₁ mode for Lamb waves and the n₁ mode for SH waves, respectively), the monotonic trend does not hold in general due to the energy redistribution to the higher order wave modes. Guided waves impinging onto an internal stringer-like an inclusion were also studied. Both the Lamb and SH waves were shown to be insensitive to the stringer internal inclusions at low frequency. Experiments with piezoelectric Lamb wave transducers and non-contact SH wave electro-magnetic acoustic transducers (EMAT) verified some of the theoretical results.     

Inhomogeneous waves at the boundary of a generalized thermoelastic anisotropic medium

The Christoffel equation is derived for the propagation of plane harmonic waves in a generalized thermoelastic anisotropic (GTA) medium. Solving this equation for velocities implies the propagation of four attenuating waves in the medium. The same Christoffel equation is solved into a polynomial equation of degree eight. The roots of this equation define the vertical slownesses of the eight attenuating waves existing at a boundary of the medium. Incidence of inhomogeneous waves is considered at the boundary of the medium. A finite non-dimensional parameter defines the inhomogeneity of incident wave and is used to calculate its (complex) slowness vector. The reflected attenuating waves are identified with the values of vertical slowness. Procedure is explained to calculate the slowness vectors of the waves reflected from the boundary of the medium. The slowness vectors are used, further, to calculate the phase velocities, phase directions, directions and amounts of attenuations of the reflected waves. Numerical examples are considered to analyze the variations of these propagation characteristics with the inhomogeneity and propagation direction of incident wave. Incidence of each of the four types of waves is considered. Numerical example is also considered to study the propagation and attenuation of inhomogeneous waves in the unbounded medium.     

Waves in Nonlocal Elastic Solid with Voids

In this paper, the governing relations and equations are derived for nonlocal elastic solid with voids. The propagation of time harmonic plane waves is investigated in an infinite nonlocal elastic solid material with voids. It has been found that three basic waves consisting of two sets of coupled longitudinal waves and one independent transverse wave may travel with distinct speeds. The sets of coupled waves are found to be dispersive, attenuating and influenced by the presence of voids and nonlocality parameters in the medium. The transverse wave is dispersive but non-attenuating, influenced by the nonlocality and independent of void parameters. Furthermore, the transverse wave is found to face critical frequency, while the coupled waves may face critical frequencies conditionally. Beyond each critical frequency, the respective wave is no more a propagating wave. Reflection phenomenon of an incident coupled longitudinal waves from stress-free boundary surface of a nonlocal elastic solid half-space with voids has also been studied. Using appropriate boundary conditions, the formulae for various reflection coefficients and their respective energy ratios are presented. For a particular model, the effects of non-locality and dissipation parameter (\(\tau \)) have been depicted on phase speeds and attenuation coefficients of propagating waves. The effect of nonlocality on reflection coefficients has also been observed and shown graphically.     

多铁性扇环截面柱体中的波传播

论文基于线性磁电弹性理论,研究了具有扇环形截面的多铁性柱形波导中的弹性波传播问题.利用波动势函数法,解析推导获得波动特征方程,进而得到弥散关系.通过算例研究了波传播的关键特性,深入分析了弥散曲线、相速度曲线和截止频率变化情况.结果显示,波的相速度和截止频率非常依赖于波导结构的扇环截面半顶角、内外径比和层合界面的弱界面系数,对于给定材料的波导结构,这些参数也是控制其弥散特性的重要影响因素.值得指出的是,在柱面应力自由的边界条件下相速度曲线中存在独特的频率带隙,而这通常是在周期结构中才会出现.     

基于积分方程方法的弹性波多重散射计算

运用积分方程方法计算了含多个随机分布椭圆柱型孔洞的随机非均匀介质中相干波的速度和衰减系数,分析了这种介质的频散特性。首先,建立了散射位移场满足的积分方程,推导了单个椭圆柱孔洞的散射截面计算公式。接着分析了在含多个随机分布椭圆柱型孔洞的随机非均匀介质中弹性波的多重散射,给出在统计平均意义下的相干波的波速和衰减系数计算公式。然后用Matlab进行了编程,给出了一个数值算例,并将计算结果与波函数展开法进行了比较,分析了随机空隙介质的频散特征及其孔洞椭圆偏心率和材料空隙率的影响。     

“Anomalous” nonlinear wave phenomena in a supersonic boundary layer

Nonlinear evolution of high-amplitude periodic disturbances in a boundary layer on a flat plate for Mach numberM=2 is studied. An anomalous downstream evolution of the disturbances is found, quasi-two-dimensional disturbances being most unstable. The obtained phase velocities of the waves are 30–40% greater than the phase velocities of the Tollmien-Schlichting waves. The nonlinear evolution of vortex waves is accompanied by an increase in steady disturbances from the source of controlled vibrations. High-frequency disturbances decay, and a periodic wave train degenerates downstream into a quasiharmonic wave train. Institute of Theoretical and Applied Mechanics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 5, pp. 91–98, September–October, 1999.     

The propagation of elastic surface waves along cylindrical cavities of general cross section

The existence of surface wave modes, propagating along an infinite cylindrical cavity of arbitrary constant cross section in an elastic medium, is investigated theoretically. A general secular equation is derived using the null-field approach and global expansions of the surface displacements. Numerical results for the phase velocities, surface displacements and cut-off frequencies are presented for elliptic cross sections. The largest eccentricity considered is 0.99995 and it is inferred that the flexural mode exists at all frequencies for any eccentricity of the cross section.     

Nonlinearwaves in a liquid film-gas flow system

The instability and regular nonlinear waves in the film of a heavy viscous liquid flowing along the wall of a round tube and interacting with a gas flow are investigated. The solutions for the wave film flows are numerically obtained in the regimes from free flow-down in a counter-current gas stream to cocurrent upward flow of the film and the gas at fairly large gas velocities. Continuous transition from the counter-current to the cocurrent flow via the state with a maximum amplitude of nonlinear waves and zero values of the liquid flow rate and the phase velocity is investigated. The Kapitsa-Shkadov method is used to reduce a boundary value problem to a system of evolutionary equations for the local values of the layer thickness and the liquid flow rate.     

Transition to detonation in dynamic phase changes

Subsonically propagating phase boundaries (kinks) can be modelled by material discontinuities which satisfy integral conservation laws plus an additional jump condition governing the phase-change kinetics. The necessity of an additional jump condition distinguishes kinks from the conventional shocks which satisfy the Lax criterion. We study stability of kinks with respect to the breakup (splitting) into a sequence of waves. We assume that all conventional shocks are admissible and that admissible kinks are selected by a prescribed kinetic relation. As we show, regardless of a particular choice of the kinetic relation, sufficiently fast-phase boundaries are unstable. The mode of instability includes an emission of a centered Riemann wave followed by a sonic shock (Chapman-Jouguet type phase boundary).