三层介质超声谐振模式随材料和界面粘接性能变化的演变规律

在用超声波谐振对粘接材料的粘接强度进行无损评估时, 不同模式对粘接强度的敏感程度受到众多因素和参数的影响, 对检测结果的可靠性至关重要. 基于多层介质中声传播和界面弱粘接边界条件的理论模型, 将一个上下非对称的金属-粘接剂-金属三层结构的平面波反射系数函数中的谐振模式看作是上下铝金属层各自的Lamb波频散模式通过夹心粘接剂层相互耦合后叠加组成. 改变影响结构粘接强度的因素, 即粘接剂的性能参数(声阻抗、密度、厚度)和界面切向劲度系数k_t来分析三层结构谐振模式耦合方式的变化,得出结论: 粘接结构粘接性能的变化基本上不改变与被粘铝层相关的固有部分的Lamb波模式, 而它们的耦合模式则在谐振频率上产生平移并会与固有模式进行交换和替代; 不同参数的变化引起的模式演变有各自的规律, 大多可彼此区分.     

Natural beam focusing of non-axisymmetric guided waves in large-diameter pipes

The propagation of non-axisymmetric guided waves in larger diameter pipes is studied in this paper by treating the guided waves as corresponding Lamb waves in an unwrapped plate. This approximation leads to a simpler method for calculating the phase velocities of hollow cylinder guided waves, which reveals a beam focusing nature of non-axisymmetric guided waves generated by a partial source loading. The acoustic fields in a pipe generated by a partial-loading source includes axisymmetric longitudinal modes as well as non-axisymmetric flexural modes. The circumferential distribution of the total acoustic field, also referred as an angular profile, diverges circumferentially while guided waves propagate with dependence on such factors as mode, frequency, cylinder size, propagation distance, etc. Exact prediction of the angular profile of the total field can only be realized by numerical calculations. In particular cases, however, when the wall thickness is far less than the cylinder diameter and the wavelength is smaller than or comparable to the pipe wall thickness, the acoustic field can be analyzed based on the characteristics of Lamb waves that travel along a periodic unwrapped plate. Based on this assumption, a simplified model is derived to calculate the phase velocities of non-axisymmetric flexural mode guided waves. The model is then applied to discussions on some particular characteristics of guided-wave angular profiles generated by a source loading. Some features of flexural modes, such as cutoff frequency values are predicted with the simpler model. The relationship between the angular profiles and other factors such as frequency, propagation distance, and cylinder size is obtained and presented in simple equations. The angular profile rate of change with respect to propagation distance is investigated. In particular, our simplified model for non-axisymmetric guided waves predicts that the wave beam will converge to its original circumferential shape after the wave propagates for a certain distance. A concept of "natural focal point" is introduced and a simple equation is derived to compute the 1st natural focal distance of non-axisymmetric guided waves. The applicable range of the simplified equation is provided. Industrial pipes meet the requirement of wall thickness being far less than the pipe diameter. The approximate analytical algorithms presented in this paper provides a convenient method enabling quick acoustic field analysis on large-diameter industrial pipes for NDE applications.     

Guided waves in a stratified half-space

The dispersion and excitation mechanisms and the energy distribution of guided waves in a stratified half-space are studied. All possible guided waves excited by a symmetric point source in two or three-layer medium models and their relation to the medium parameters are analyzed in detail. The excitation and propagation characteristics, as well as the energy distribution along the depth direction, of all modes of the surface waves and trapped waves are numerically investigated and analyzed thoroughly not only in the case when the shear wave velocity increases from up to down layers but also when a low-velocity layer is contained in halfspace, especially when the shear wave velocity decreases from up to down layers. It is found that there exist many guided wave modes in the case where the shear wave velocity of each layer increases from up to down layers. However, there is less than one guided wave mode in the case where the shear wave velocity of each layer decreases from up to down layers. The trapped waves exist and propagate along the low-velocity structure in the stratified half-space. It is also found that the characteristic of a mode is related to the source frequency. It is possible that a surface wave at one value of frequency is like a trapped wave at another value of frequency. Finally, the relation of the characteristics of all guided waves (surface waves and trapped waves) to the parameters of media is studied.     

Calculation of leaky Lamb waves with a semi-analytical finite element method

A semi-analytical finite element method (SAFE) has been widely used for calculating dispersion curves and mode shapes of guided waves as well as transient waves in a bar like structures. Although guided wave inspection is often conducted for water-loaded plates and pipes, most of the SAFE techniques have not been extended to a plate with leaky media. This study describes leaky Lamb wave calculation with the SAFE. We formulated a new solution using a feature that a single Lamb wave mode generates a harmonic plane wave in leaky media. Dispersion curves obtained with the SAFE agreed well with the previous theoretical studies, which represents that the SAFE calculation was conducted with sufficient accuracy. Moreover, we discussed dispersion curves, attenuation curves, and displacement distributions for total transmission modes and leaky plate modes in a single side and both two side water-loaded plate.     

Correlation between helical surface waves and guided modes of an infinite immersed elastic cylinder

Scattering of obliquely incident plane acoustic waves from immersed infinite solid elastic cylinders is a complex phenomenon that involves generation of various types of surface waves on the body of the cylinder. Mitri [F.G. Mitri, Acoustic backscattering enhancement resulting from the interaction of an obliquely incident plane wave with an infinite cylinder, Ultrasonics 50 (2010) 675-682] recently showed that for a solid aluminum cylinder, there exist acoustic backscattering enhancements at a normalized frequency of ka?0.1. The incidence angle α_c at which these enhancements are observed lies between the first (longitudinal) and second (shear) coupling angles of the cylinder. He also confirmed the observations previously reported by the authors that there exist backscattering enhancements of the dipole mode at large angles of incidence where no wave penetration into the cylinder is expected. In this paper, physical explanations are provided for the aforementioned observations by establishing a correlation between helical surface waves generated by oblique insonification of an immersed infinite solid elastic cylinder and the longitudinal and flexural guided modes that can propagate along the cylinder. In particular, it is shown that the backscattering enhancement observed at ka?0.1 is due to the excitation of the first longitudinal guided mode travelling at the bar velocity along the cylinder. It is also demonstrated that the dipole resonance mode observed at incidence angles larger than the Rayleigh coupling angle is associated with the first flexural guided mode of the cylinder. The correlation established between the scattering and propagation problems can be used in both numerical and experimental studies of interaction of mechanical waves with cylinders.     

Guided waves in a plate with linearly varying thickness: experimental and numerical results

The aim of this work is to give experimental and numerical results on the behaviour of guided waves that propagate downslope in a free elastic plate with slowly linearly varying thickness. We show experimentally the propagation of adiabatic modes, which are guided waves that adapt to the varying thickness of the plate. As the thickness is decreasing, a given guided wave will reach its thickness cut-off. When this happens, we show that two phenomena occur: the reflection of this wave and its propagation backward in the plate, its conversion into a different guided wave which goes on propagating downslope in the plate. The numerical study is done with the software Ansys, based on the finite element method. The results obtained confirm the experimental ones.     

Thickness-shear modes and magnetoelastic waves in a longitudinally magnetized ferromagnetic plate

Magnetoelastic (ME) waves and thickness-shear modes in the ferromagnetic plate are studied. Coupled vibrations of magnetization and shear elastic deformations excited simultaneously by a variable magnetic field propagate in two mutually perpendicular directions: parallel and normal to a surface. For parameters characteristic of isotropic ferromagnet with the sample magnetization and Zeeman field parallel to the surface, resonant frequencies of shear modes are computed and their dispersion law is examined. It is shown that the dependence of dimensional resonances frequencies on wave number k_z of ME wave propagating along saturating field direction occurs. The possibility of excitation of ME waves with different k_z explains multimode character of thickness ME resonances.     

Two-dimensional wave propagation in a rotating elastic solid with voids

Two-dimensional wave propagation is studied in an isothermal linear isotropic elastic material with voids rotating with constant angular velocity based on a theory of elastic material with voids developed by Ie?an (1986) in the thermoelastic context. It is found that there exist three coupled plane waves propagating with distinct phase speeds. The presence of voids and the rotation of the medium are responsible for this coupling. In the absence of voids, the classical longitudinal and transverse waves are found to be coupled through the rotation of the medium. At very large frequency or when the angular rotation is very small relative to the wave frequency the waves are decoupled and propagate with distinct phase speeds. These are (i) a longitudinal wave, (ii) a transverse wave and (iii) a longitudinal wave corresponding to the change in void volume fraction. The first two correspond to the waves of classical elasticity, while the third is new and arises from the presence of the voids. The results are illustrated graphically.     

Ordinary and extraordinary cyclotron waves in metals

Dispersion equations for the ordinary and extraordinary cyclotron waves propagating perpendicular to the magnetic field in metals in the critical region where the wavelength is comparable to the electron Larmor radius are derived as an infinite but rapidly converging power series expansion in δ( = Ω/Ω-M). Numerical studies for the cyclotron wave propagation near the first seven resonances are carried out. The non-local behaviour of those waves in the critical region 01 ⩽ kR ⩽ 3-0 is studied. For the ordinary waves the first few resonances show significant dispersion than those near higher resonances which are dispersion-free. Only one extraordinary wave propagates near the fundamental cyclotron frequency. For the higher resonances, two modes propagate near each of the resonant frequencies, of which one mode remains constant for all values ofkR whereas the second mode shows significant dispersion. But beyond the fifth resonance both the modes are dispersion free.     

The measurement of A0 and S0 lamb wave attenuation to determine the normal and shear stiffnesses of a compressively loaded interface

Guided waves in an elastic plate surrounded by air propagate with very low attenuation. This paper describes the effect on this propagation of compressively loading an elastomer with high internal damping against one surface of the elastic plate. The propagation of both A0 and S0 Lamb modes is considered. The principal effect is shown to be increased attenuation of the guided waves. This attenuation is caused by leakage of energy from the plate into the elastomer, where it is dissipated due to high viscoelastic damping. It is shown that the increase in attenuation is strongly dependent on the compressive load applied across the solid-solid interface. This interface is represented as a spring layer in a continuum model of the system. Both normal and shear stiffnesses of the interface are quantified from the attenuation of A0 and S0 Lamb waves measured at each step of the compressive loading. The normal stiffness is also measured independently by normal incidence, bulk longitudinal wave ultrasound. The resulting predictions of wave propagation behavior, such as attenuation, obtained by the model are in excellent agreement with those measured experimentally.     

Comparison between the dispersion curves calculated in complex frequency and the minima of the reflection coefficients for an embedded layer

Analytical solutions of Lamb functions for symmetric and antisymmetric elastodynamic modes propagating within a solid layer embedded in an infinite medium are presented. Alternative theoretical analyses of such modes are performed, first in terms of the usual approach of harmonic heterogeneous plane waves (real frequency and complex slowness) and then in terms of transient homogeneous plane waves (complex frequency and real slowness). An example structure of a 0.1-mm-thick "alpha case" (an oxygen-rich phase of titanium that is relatively stiff) plate embedded in titanium is used for the study. A large difference between the usual dispersion curves calculated in real frequency and complex slowness and those calculated in complex frequency and real slowness is shown. Thus the choice between a spatial and a temporal parameter to describe the imaginary part of the guided waves is shown to be significant. The minima and the zeros of the longitudinal and shear plane-wave reflection coefficients are calculated and are compared with the dispersion curves. It is found that they do not match with the dispersion curves for complex slowness, but they do agree quite well with the dispersion curves for complex frequency. This implies that the complex frequency approach is better suited for the comparison of the modal properties with near-field reflection measurements.     

无限流体中孔隙介质圆柱周向导波的传播特性

为研究无限大流体约束的孔隙圆柱中周向导波的传播规律,分析孔隙参数对导波传播特性的影响,建立了无限流体中孔隙介质圆柱的理论模型,利用孔隙介质弹性波动理论,建立了周向导波频散方程,通过数值模拟计算得到无限流体中孔隙介质圆柱的频散曲线,探讨了圆柱半径和孔隙参数对导波传播特性的影响,并对导波的衰减特性进行了分析;通过数值计算,得到了周向导波的时域波形,讨论了孔隙参数对波形的影响.结果表明,孔隙介质圆柱半径的改变影响圆柱尺度,孔隙度的改变影响孔隙介质中体声波的波速,都对周向导波频散曲线产生一定的影响,所得到的频散曲线特征及衰减曲线与时域波形吻合.研究结果对开展无限流体中孔隙介质圆柱的超声无损评价提供了一定的理论参考.     

Normal modes of a poroelastic plate and their relation to the reflection and transmission coefficients

A poroelastic plate that obeys the Biot theory is considered. Compact new forms of its reflection and transmission coefficients, similar to those of the resonance scattering theory for an elastic plate, are derived. A numerical comparison of the reflection coefficient modulus with the plate normal modes, at low frequency, shows that a study of the reflection or transmission coefficient does not provide the same kind of information on the poroelastic plate than an investigation of guided leaky waves propagation.     

Coherent waves in a multiply scattering poro-elastic medium obeying Biot's theory

Twersky's theory is generalized to multiple scattering by a uniform random distribution of cylinders in a poro-elastic medium. The high-frequency regime only, where no dispersion effects occur in the absence of scatterers, is investigated in the frame of Biot's theory. The scatterers lie within a slab of the host medium, and an incident wave gives rise to a fast longitudinal coherent wave, a slow longitudinal one, as well as a shear one in the slab. The dispersion equations of those three coherent waves are derived. The shear coherent wave propagates independently of the other two, while the longitudinal coherent waves obey a coupled dispersion equation involving conversion terms. Numerically speaking, coupling effects are significant only when forward scattering by a single cylinder of the fast wave into the slow one (or the slow wave into the fast) is larger than forward scattering with no conversion.     

Coherent waves in a multiply scattering poro-elastic medium obeying Biot's theory

Twersky's theory is generalized to multiple scattering by a uniform random distribution of cylinders in a poro-elastic medium. The high-frequency regime only, where no dispersion effects occur in the absence of scatterers, is investigated in the frame of Biot's theory. The scatterers lie within a slab of the host medium, and an incident wave gives rise to a fast longitudinal coherent wave, a slow longitudinal one, as well as a shear one in the slab. The dispersion equations of those three coherent waves are derived. The shear coherent wave propagates independently of the other two, while the longitudinal coherent waves obey a coupled dispersion equation involving conversion terms. Numerically speaking, coupling effects are significant only when forward scattering by a single cylinder of the fast wave into the slow one (or the slow wave into the fast) is larger than forward scattering with no conversion.     

Vibrational properties of thin films adsorbed on crystals with strong spatial dispersion

The effect of strong spatial dispersion of the substrate crystal onto the dynamics of thin epitaxially adsorbed films is described in a simple model through the following quantities: i) phonon reflection coefficients ii) depth-dependent local densities of states (LDOS) and iii) finite-lifetime surface states called leaky waves. The correspondence of these three types of characteristics accessible in different experimental methods is established. The bulk band of the substrate crystal consists of two distinct frequency ranges separated by an edge singularity: above the singularity the substrate supports two different waves for a given frequency, whereas only one wave can exist for each frequency in the low-frequency range. The resonances in the low-frequency range are found to correspond to maxima in the LDOS, to maxima in the amplitude of a near field arising in phonon reflection and to leaky waves involving a single leakage wave packet. The antiresonances in the same frequency range are characterised by minima in LDOS and in the near field, whereas the corresponding leaky waves involve two leakage wave packets. The only leaky waves found in the high-frequency range involve two leakage wave packets and are related to resonances. The antiresonances then are characterised by an anomalous increase in the extraordinary reflected wave. The edge singularity manifests itself in an additional quasi resonance, whose features depend on the coupling between the substrate and the thin film.     

Three-Dimensional Scattering of an Incident Plane Shear Horizontal Guided Wave by a Partly through-Thickness Hole in a Plate

We investigate the three-dimensional(3D) scattering problem of an incident plane shear horizontal wave by a partly through-thickness hole in an isotropic plate,in which the Lamb wave modes are also included due to the mode conversions by the scattering obstacle in the 3D problem.An analytical model is presented such that the wave fields are expanded in all of propagating and evanescent SH modes and Lamb modes,and the scattered far-fields of three fundamental guided wave modes are analyzed numerically for different sizes of the holes and frequencies.The numerical results are verified by comparing with those obtained by using the approximate Poisson/Mindlin plate model for small hole radius and low frequency.It is also found that the scattering patterns are different from those of the SO wave incidence.Our work is useful for quantitative evaluation of the plate-like structure by ultrasonic guided waves.     

Ultrasonic waves propagation in absorbing thin plates application to paper characterization

Guided wave theory is applied to a thin orthotropic and absorbing plate for low frequency propagation of ultrasonic waves. The aim of this paper is to give some physical interpretations of the non-destructive characterization of paper materials, which are cellulosic fibrous networks. It is shown that the propagation problem reduces to two normal modes of propagation in the plane of the plate. Each of them depends on four complex and independent stiffnesses that are combinations of elementary complex stiffnesses of the media. The imaginary part of these stiffnesses corresponds to a possible mechanism of energy dissipation during the wave propagation for this kind of material. The reverse problem, which gives four complex values, is then numerically solved using a small attenuation assumption. The specially designed experimental set-up has led to the first measurements of tracing paper damping factors. The phase velocity measurements of the plate waves agree with the results already found by several paper researchers. As a particular and new result, the shear wave velocities are found to present a quasi-isotropic repartition in the plane of the paper sheet. It was found that the absorbing phenomenon can occur for each propagation mode in such a material. The attenuation values are small, except for one of them that corresponds to a coupling term in the propagation model. The anisotropy of their repartition is also shown in the case of quasi-longitudinal waves.     

Spin precession waves in superfluid 3He-B

Spin precession waves of homogeneously precessing domains (HPD) in superfluid 3He-B have been studied at 11 bars and temperatures down to 0.45T(c). The waves were excited by an alternating longitudinal magnetic field with an axial symmetry, applied as a small perturbation ranging from 1 nT up to a few micro T. When the spin precession wave is excited, two nuclear magnetic resonances simultaneously coexist: first, the high frequency resonance used for excitation of the HPD, and, second, the low-frequency resonance of the HPD wave mode. We report the first experimental evidence of the nonlinear behavior of low-frequency precession spin wave modes of the continuously maintained HPD.     

Stability of higher-order bragg interactions in active periodic media

The stability of waves in unbounded, longitudinally periodic media is studied for index and gain coupling. Time-independent periodic media are found to support both stable and absolutely unstable waves. The wave characteristics depend upon average gain or loss, coupling type, and Bragg order. The extended coupled waves (ECW) equations provide explicit values of threshold, frequency, and temporal growth rate for instabilities at all Bragg resonances through the dispersion relation. The first and second Bragg resonances are studied in detail since they are the archetypes for all odd and even resonances. Applications to multiharmonic periodicities and complex couplings are briefly discussed with particular not taken of possible reductions of the stability thresholds and removal of threshold degeneracies. Comparisons are made to the longitudinally bounded case of distributed feedback (DFB) lasers.