Surface wave propagation in wood: prospective method for the determination of wood off-diagonal terms of stiffness matrix

Overall elastic properties of wood can be studied by ultrasonic methods. Orthotropic symmetry is assumed (nine constants). This article describes two methods developed for the determination of three off-diagonal terms of the stiffness matrix. The first method deals with bulk waves (BAW), and the second with surface wave (SAW) measurements. The BAW method requires repeated off-axis measurements and an optimization criterion for selecting the C_ij-terms. The SAW method gives the value of the C_ij-term corresponding to a specific plane of symmetry, from only one on-axis measurement. The six diagonal terms of the stiffness matrix can be obtained easily from on-axis bulk wave measurements. From the nine terms of the matrix, the compliance terms (S_ij) and corresponding technical terms are calculated. Technical constants determined from ultrasonic measurements are in agreement with those obtained by classical statistical methods. The experiments were performed on beech and spruce. The SAW technique is expected to be of more interest for further investigations of wood mechanical properties.     

Elastic constants of a plate from impact-echo resonance and Rayleigh wave velocity

A new method is proposed for calculating the dynamic elastic constants of an isotropic plate from measurements of the impact-echo resonance and Rayleigh wave velocity. Poisson's ratio is shown to be a single-valued function of the ratio between thickness frequency and Rayleigh wave velocity. This dependence is derived theoretically from the condition of resonance at the minimum frequency of the first-order symmetric Lamb mode. A finite element model is developed to determine how this frequency varies with Poisson's ratio. The results obtained by modal analysis and the power-spectral density technique are in good agreement with those calculated as the solution of the S1 Lamb mode equation. The method is verified by impact-echo tests on concrete and methacrylate plates. A laser interferometer is used to detect the vibration. Thickness frequencies are accurately identified by applying the multicross-spectral density to the signals detected at several points close to the impact point. In a separate experiment, Rayleigh waves are generated by the mediator technique. The wave velocities are determined from the arrival times of the surface wave at several points. Finally, the main sources of uncertainty are evaluated.     

Second-order and third-order elastic constants of B95 aluminum alloy and B95/nanodiamond composite

All independent second-order and third-order elastic constants in B95 aluminum alloy and B95/nanodiamond composite have been determined. To determine the second-order elastic constants, the densities and velocities of longitudinal and shear bulk acoustic waves in the materials under study have been measured. To quantitatively characterize the nonlinear elastic properties, the third-order elastic constants (TOECs) of B95 alloy and B95/nanodiamond composite have been determined. The Thurston-Brugger method has been used to experimentally determine the TOECs. For this purpose, the relative changes in the bulk wave velocity have been experimentally measured depending on the uniaxial compression applied to the samples under study and all independent TOECs have been calculated. The elastic wave velocities have been measured by the ultrasonic pulse method at a frequency of 10 MHz. The results obtained have been discussed.     

Elastic constants determination by direct measurement of the beat wavelength between A0 and S0 Lamb modes with pulsed TV holography

A whole-field optical technique of high sensitivity, namely pulsed TV holography with phase evaluation by the Spatial Fourier Transform Method, is applied to the acquisition of instantaneous displacement fields of ultrasonic Lamb waves in aluminium plates a few millimetres thick. Two Lamb modes, the A0 and S0 ones, are simultaneously generated in the plate, producing a clear beating. Several values of the beat wavelength, corresponding to different excitation frequencies, are obtained by direct measurement of the distance between nodes in the wave field. The obtained values are fitted to the theoretical Rayleigh–Lamb frequency spectrum in order to determine the elastic constants of the plate material. We conclude that it is necessary to know the value of another parameter to univocally solve the problem, and so the bulk longitudinal wave velocity is measured by the pulse-echo method. Then the Poisson's ratio is obtained and, from these two parameters, the Young's modulus can also be determined.     

Leaky wave detection at air-solid interfaces by laser interferometry

A recently developed optical heterodyne interferometer is proved to be sensitive to detect ultrasonic waves leaking out from metals (and from non-metals as well) several centimeters away from the metal surface in air. This measurement is based on the detection of the optical index variation in air due to the leaky wave. Experiments were carried out using both ultrasonic leaky Rayleigh and leaky Lamb waves in the low-megahertz region. Optical measurements of these leaky wave velocities in semi-infinite materials and plates, which are related to elastic constants of the materials, showed a good correlation to the predicted values. Optical measurements of the amplitude of the leaky waves were used to obtain attenuation coefficients, which correlate to the structural integrity of the materials. Surface and near-surface defects were also detected. This optical method can be used for metals with low-reflectivity surfaces. Thus, it can be used for non-polished surfaces and can be extended for non-contact, non-destructive evaluation applications.     

Determination of the elastic constants of a composite plate using wavelet transforms and neural networks

An inverse method based on a combination of the wavelet transform and artificial neural networks is presented. The method is used to recover the elastic constants of a fiber-reinforced composite plate from experimental measurements of ultrasonic Lamb waves generated and detected with lasers. In this method, the elastic constants are not recovered from the dispersion curves but rather directly from the measured waveforms. Transient waveforms obtained by numerical simulations for different elastic constants are used as input to train the neural network. The wavelet transform is used to extract the eigenvectors from the Lamb wave signals to simplify the structure of the neutral network. The eigenvectors are then introduced into a multilayer internally recurrent neural network with a back-propagation algorithm. Finally, experimental waveforms recoded on a titanium-graphite composite plate are used as input to recover the elastic constants of the material.     

Time-domain analysis of second-harmonic generation of primary Lamb wave propagation in an elastic plate

Within the second-order perturbation approximation,this paper investigates the physical process of generation of the time-domain second harmonic by a primary Lamb wave waveform in an elastic plate.The present work is performed based on the preconditions that the phase velocity matching is satisfied and that the transfer of energy from the primary Lamb wave to the double frequency Lamb wave is not zero.It investigates the influences of the difference between the group velocities of the primary Lamb wave and the double frequency Lamb wave,the propagation distance and the duration of the primary Lamb wave waveform on the envelope shape of the time-domain second harmonic.It finds that the maximum magnitude of the envelope of the second-harmonic waveform can grow within some propagation distance even if the condition of group velocity matching is not satisfied.Our analyses also indicate that the maximum magnitude of the envelope of the second-harmonic waveform is kept constant beyond a specific propagation distance.Furthermore,it concludes that the integration amplitude of the time-domain second-harmonic waveform always grows with propagation distance within the second-order perturbation.The present research yields new physical insight not previously available into the effect of generation of the time-domain second harmonic by propagation of a primary Lamb wave waveform.     

基于群速度失配的超声兰姆波二次谐波的时域测量方法

考虑到发射和接收换能器对超声兰姆波时域二次谐波信号所带来的不可避免的影响,提出一种基于基频与二倍频兰姆波群速度失配的超声兰姆波二次谐波的时域测量方法。当基频与二倍频超声兰姆波的相速度匹配而群速度失配时,在超声兰姆波传播过程中所发生的二次谐波信号,在时域上可与源于斜劈换能器的二次谐波信号相分离。采用仅源自于基频兰姆波的时域二次谐波的积分振幅,定量描述兰姆波二次谐波的发生效率。以铝板中传播的兰姆波为例,给出了时域二次谐波的具体测量过程。本文提出的测量方法放宽了超声兰姆波二次谐波的测量条件,且扣除了换能器对二次谐波信号所带来的影响,所测得的二次谐波信号完全来自于基频兰姆波时域信号的二次谐波发生效应。      

Parameter measurement of the cylindrically curved thin layer using low-frequency circumferential Lamb waves

The characteristic parameters of a cylindrically curved thin layer include its elastic constants, thickness and curved radius. A layer is considered thin if the echoes from the front and back surfaces of the layer cannot be separated in the time domain, and/or that the wave arrivals corresponding to longitudinal and shear wave part cannot be identified in the time or space domain. This paper describes a low-frequency circumferential Lamb wave method to characterize those parameters of a cylindrically curved thin layer. The technique is based on the measurement of circumferential Lamb wave phase velocity and the unknown parameter is estimated through minimizing the mean square error obtained by comparing theoretical and experimental phase velocities. The sensitivity and accuracy of the proposed technique to different parameters are analyzed. Using the present technique, a cylindrically curved thin layer with thickness down to ten percent of the longitudinal wavelength can be successfully measured with an average relative error less than two-percent in our experiment.     

Development of an advanced multimode automatic ultrasonic texture measurement system for laboratory and production line application

We present work on the development of an ultrasonic texture measurement system for sheet metals using non-contact transducers, suitable for use both in the laboratory and on the production line. Variation of the velocity of the zero-order symmetric (S0) Lamb wave is used to determine the crystallographic texture of polycrystalline metal sheets ranging in thickness from 0.1 to 3 mm. This system features improvements on previous state-of-the-art ultrasonic technology in that it probes velocity over a continuous range of angles using only two electromagnetic acoustic transducers (EMATs). This is demonstrated to offer a significant improvement in accuracy and allows the detection and investigation of asymmetric anisotropies in the sheets. Another advantage of the system is its potential for combining several different measurements using a single pair of transducers. The capability is demonstrated for through-thickness shear wave measurements as well as the zero-order symmetric Lamb wave measurements which are the primary means of determining the texture. The change between generating Lamb and through-thickness bulk waves can be made entirely by changing the electrical circuit connected to the EMATs without modifying the transducer assembly in any way. Measurement of all of the above waves can provide information on the sheet thickness and other physical properties of the sheet in addition to texture. Certain texture parameters can be calculated from both Lamb and shear wave velocities, allowing self-calibration of the system.     

The influence of backward wave transmission on quantitative ultrasonic evaluation using Lamb wave propagation

In view of the various novel quantitative ultrasonic evaluation techniques developed using Lamb wave propagation, the influence of an important related phenomenon, backward transmission, is investigated in this paper. Using the discrete layer theory and a multiple integral transform method, the surface displacement and velocity responses of isotropic plates and cross-ply laminated composite plates due to the Lamb waves excited by parabolic- and piston-type transmitting transducers are evaluated. Analytical expressions for the surface displacement and velocity frequency response functions are developed. Based on this a large volume of calculations is carried out. Through examining the characteristics of the surface displacement and velocity frequency response functions and, especially, the different propagation modes' contributions to them, the influence of the backward wave transmission related to quantitative ultrasonic nondestructive evaluation applications is discussed and some important conclusions are drawn.     

基于赛利斯模型和分数阶微分的兰姆波信号消噪

为降低噪声对超声兰姆波检测信号的影响,提高信噪比和增加特征提取的精度,提出了一种赛利斯模型下分数阶微分方法用于超声兰姆波信号去噪.该方法对含噪声的兰姆波信号幅值谱进行各阶分数微分,用赛利斯分布作为待处幅值谱的模型,提出了幅值谱分数阶微分最大值和过零点与微分阶数的拟合三次关系式,建立了幅值谱特征参数的计算式来提取特征参数和重建原始信号的幅值谱,并结合相位谱重构去噪后的兰姆波信号.仿真结果表明,该方法可以有效地提高兰姆波信号甚至微弱兰姆波信号的信噪比,同时降低均方误差和平滑度.实验结果显示,与小波去噪和集合经验模态去噪方法相比,该方法在没有信号先验知识的情况下,可以更有效地去除兰姆波信号的噪声,同时更好地保留主信号的细节特征.因此,本文提出的方法可以有效地去除兰姆波检测信号中混入的噪声.     

A semi-automatic processing technique for elastic-wave laboratory data

This paper addresses the problem of determining the onset of transient signals such as seismograms, acoustic emissions or ultrasonic signals. Usual manual techniques of onset-time picking are time consuming when numerous measurements are available. This may occur when dealing with (i) anisotropic rocks requiring many elastic wave velocities measurements in the laboratory, (ii) 4-D seismic field data or (iii) laboratory acoustic emissions data. We present a semi-automatic processing technique devoted to the study of case (i). It is based on ultrasonic signal analysis by wavelet transform and an onset-time picking procedure combining Akaike Information Criterion and cross-correlation method. The first step consists in extracting, from the whole experimentally recorded signal, the frequency component corresponding to the perturbation induced by a typical ultrasonic transducer in the laboratory. The second step is dedicated to the onset-time picking of the phase arrival in the extracted signal. The use of this processing technique based on mathematical arguments reduces human subjectivity. Main outcomes are: (i) increase of signal-to-noise ratio; (ii) measurement of elastic wave velocities at prescribed central frequency; (iii) drastic increase of efficiency in wave data processing; and (iv) increase in reliability (repeatability) of wave data acquisition.     

The measurement of residual stress in textured steel using an ultrasonic velocity combinations technique

A new ultrasonic technique for the determination of residual stresses in steel, intended to correct for the effects of variable texture and microstructure, is proposed. The method is based upon the use of the compressional wave time delay in addition to the time delays of two orthogonally polarized shear waves used in the shear wave birefringence technique. This method is justified theoretically using expressions for the ultrasonic velocities in an aggregate of orthorhombic symmetry composed of cubic crystallites.Measurements of the three time delays for propagation in the through thickness direction have been made on a large number of steel plates selected at random. The measurements are found to fall on two lines, and reveal that two types of texture are present in rolled steel plates. In the presence of a stress, the measured points deviate from the lines and this effect is quantified theoretically using elastic constants obtained by applying a uniaxial compressive stress to one of the samples.The usefulness of the technique to determine a residual stress distribution is demonstrated by measurements near the tip of a crack in a compact tension specimen.     

Ultrasonic characterization of Cu-Al-Ni single crystals lattice stability in the vicinity of the phase transition

Measurements of elastic constants of the austenite phase when approaching the phase transformation either upon cooling or stressing is of the crucial interest for the shape memory alloy field. Acoustic properties (wave velocity and also attenuation changes) of the Cu-Al-Ni single crystal were investigated in situ during stress-induced martensitic transformation at constant (room) temperature. The parent austenite cubic lattice of the Cu-Al-Ni exhibits very high elastic anisotropy (anisotropy factor A approximately 12). The measurements were made using nine combinations of (i) applied uniaxial compression in a given crystal direction, (ii) the wave propagation and (iii) polarization vectors. The chosen configurations are sufficient for evaluation of all independent third order elastic constants (TOEC). The longitudinal modes were also measured by the immersion technique, using the transducer pair in a water tank installed on the testing machine. The device works as "a ultrasonic extensometer" measuring a transverse strain of the specimen. The dependencies of both natural and initial wave velocities on the applied stress may be evaluated. Three elastic constants of the stress-induced martensite were determined. The elastic properties were found to vary with the increasing stress above the Ms transformation temperature, which is interpreted as a precursor for the martensitic transformation. The onset of the transformation was additionally identified from the acoustic emission measurement.     

The group velocity variation of Lamb wave in fiber reinforced composite plate

Experimentally measured Lamb wave group velocities in composite materials with anisotropic characteristics are not the same as the theoretical group velocities which is calculated with the Lamb wave dispersion equation. This discrepancy arises from the fact that the angle between the group velocity direction and the phase velocity direction in anisotropic materials exists. Wave propagation in a composite material with anisotropic characteristics should be considered with respect to magnitude correction in addition to direction correction. In this study, S0 mode phase velocity dispersion curves are depicted with the variation of degree with respect to the fiber direction using a Lamb wave dispersion relation in the unidirectional, bidirectional, and quasi-isotropic composite plates. Slowness surface is sketched by the reciprocal value of the phase velocity curves. The magnitude and direction of the group velocity could be calculated from the slowness surface. The recalculated group velocities with consideration of the magnitude and direction from the slowness surface are compared with experimentally measured group velocities. The proposed method shows good agreements with theoretical and experimental results.     

Ultrasonic, hardness and x-ray densitometric analysis of wood

Ultrasonic, hardness and x-ray densitometric methods were used to predict the wood quality of Douglas fir sapwood from pruned and control trees. Measurements were performed on logs and on increment cores.

On logs, hardness was tested by a pilodyn instrument. Longitudinal waves (80 kHz) were used to measure the velocity in the radial anisotropic direction of the wood. Surface waves of the same frequency were employed to measure the velocity on the circumference of the log in the longitudinal anisotropic direction of the wood.

On increment cores, 1 MHz waves, longitudinal and transverse, were used to measure the velocity of ultrasonic pulses along three anisotropic axes of the wood, using the through-transmission technique.

The predictive power of the pilodyn test and of the surface wave velocity method for logs was judged in relation to several independent variables on cores given by the densitometric method and by ultrasonic velocities and elastic constants of the wood.     

Light scattering from surface acoustic phonons in metals and semiconductors

Several examples of Brillouin scattering from thermally excited surface acoustic phonons in metals and opaque semiconductors are presented. The measured surface velocities are consistently lower by 1–5% than the values calculated from the bulk elastic constants. The spectra also show the continuum of Lamb excitations having some surface-type character with velocities ranging between the bulk transverse velocity and the bulk longitudinal velocity.     

Laboratory and modeling study on modulated wave properties

Development of Benjamin?Feir instability is investigated under laboratory conditions and by analytical modeling. Nonlinear properties of the wave train with discrete spectrum are also investigated. The mechanically generated waves are composed of several discrete waves, while the newly generated harmonics are still combined into discrete spectra with the same frequency step. The technique proposed in this study allows us to study accurately the nonlinear variations in main properties of each harmonic with fixed frequency, such as amplitude, phase speed, and wavenumber along the wave tank together with velocities of wave packet crests, especially for the large transient waves. The phase speeds of short waves increase near large transient waves, and the velocities of longer waves are close to the values determined by the linear theory of waves. The relative long wave accompanied by short waves can dramatically change the local kurtosis and skewness of the wave field. They may play an important role for the generation of large transient wave and provide an opportunity for triggering of the freak waves.     

Assessment of fatigue damage in solid plates through the ultrasonic Lamb wave approach

Changes(degradations) in the mechanical properties of solid plates induced by cyclic fatigue loading will influence the features of ultrasonic Lamb wave propagation,such as dispersion and attenuation.This paper has qualitatively analyzed the feasibility of using the amplitude-frequency characteristics and the stress wave factors(SWFs) of ultrasonic Lamb wave propagation to assess fatigue damage in solid plates.Liquid wedge transducers located on the surface of solid plates tested are used to generate and detect the Lamb wave signals.Based on the Ritec-SNAP ultrasonic measurement system,the experimental setup for assessing the degree of fatigue damage in solid plates using ultrasonic Lamb wave approach has been established.For several rolled aluminum sheets subjected to tension-tension cyclic loading,the experimental examinations have been performed for the relationships between the amplitude-frequency characteristics of ultrasonic Lamb wave propagation and the numbers of loading cycles(denoted by N),as well as the correlations between the Lamb wave SWFs and N.The experimental results show that the Lamb wave SWFs decrease monotonously and sensitively with the increment of cycles of fatigue loading.Based on the correlations between the Lamb wave SWFs and N,it is further verified that ultrasonic Lamb wave propagation combined with the Lamb wave SWFs can be used to effectively assess early fatigue damage in solid plates.