长骨裂纹宽度和角度对低阶超声导波的影响

超声导波检测长骨骨折和监测骨折愈合已成为一种极具前景的课题,但高频厚积下导波多模式混叠带来的模式识别和分离问题一直是一个难点。为避免上述问题,在低频下仅激励两个低阶兰姆波SO和AO模式,采用二维时域有限差分(2DFDTD)法定量分析裂纹宽度和骨折角度对SO和AO幅度的影响。结果表明,SO与AO模式的幅度均随裂纹宽度的增加而下降;AO的幅度随骨折角度增大而上升,SO幅度随骨折角度增大先下降后上升,转折点约为45°。SO与AO的幅度比值在不同骨折角度下均能较好地表征裂纹宽度的变化,可为横断型和斜切型长骨骨折状况的超声评价及骨折愈合监测提供依据。      

超声导波评价长骨骨折的仿体实验研究

定量超声评价长骨骨折已成为近年来的研究热点之一,超声导波模式转换理论可被应用于长骨骨折状况的评价。采用三维时域有限差分法分析骨折长骨中导波模式转换的基本规律,提取模式转换定量评价参数;进而结合亚克力管仿体实验,分析不同裂纹程度下导波模式的转换情况。仿真与仿体实验表明,导波模式能量参数与裂纹程度具有很好的相关性,可用于评价长骨骨折状况。     

Coded excitation of ultrasonic guided waves in long bone fracture assessment

Ultrasonic guided wave (GW) assessment of long bone fracture have conventionally been based on pulse excitation. However, the high attenuation during propagation diminishes the amplitude of received GWs and results in low signal-to-noise ratio (SNR). The Barker code (BC) excitation and the optimal binary code (OBC) excitation were utilized in this study to overcome this limitation. Both simulations and in vitro experiments were performed on the fractured cortical bone plate model, and measured signals from both the BC and OBC excitations were decoded using the finite impulse response least squares inverse filter (FIR-LSIF) and then compared with sine pulse (SP) excited signals. The results suggest the efficiency of coded excitation for amplitude and SNR improvement. Furthermore, time–frequency representation (TFR) analysis was applied to experimental signals; with increasing fracture depth, energy transformation between predominate GW modes A1 and S2 was confirmed. These results show the potential of using BC and OBC excitations to evaluate the depth of long bone fracture.     

基于周向SH0导波的管道轴向缺陷定量表征*

随着管道服役时间的增加,其损伤逐渐累积,最终导致泄漏或爆炸事故。引入导波在线监测管道损伤是确保其安全运行的重要保障。周向零阶水平剪切(CSH0)波具有不易频散、对管道轴向缺陷敏感等优秀特性,非常适用于管道轴向缺陷的定量表征。该文 基于周向SH0导波在管道的传播特性,通过有限元模拟和试验对管道周向SH0模态导波与轴向缺陷的定量关系展开研究。结果表明：管道曲率半径越大,周向SH0模态的传播特性越接近板中SH0模态的传播特性;导波信号的反射系数和透射系数对轴向缺陷的长度和深度均呈现单调变化。依此建立了缺陷定量表征的关系云图,可用于评估缺陷尺寸。     

Reflection and transmission coefficients for guided waves reflected by defects in viscoelastic material plates

The paper presents a Fourier transform-based signal processing procedure for quantifying the reflection and transmission coefficients and mode conversion of guided waves diffracted by defects in plates made of viscoelastic materials. The case of the S(0) Lamb wave mode incident on a notch in a Perspex plate is considered. The procedure is applied to numerical data produced by a finite element code that simulates the propagation of attenuated guided modes and their diffraction by the notch, including mode conversion. Its validity and precision are checked by the way of the energy balance computation and by comparison with results obtained using an orthogonality relation-based processing method.     

Comment on "Three-dimensional finite element modeling of guided ultrasound wave propagation in intact and healing long bones," [J. Acoust. Soc. Am. 121(6), 3907-3921 (2007)

Protopappas et al. performed finite element (FE) studies on the propagation of guided ultrasound waves in intact and healing long bones, and found that the dispersion of guided modes was significantly influenced by the irregularity and anisotropy of the bone. A time-frequency (t-f) method was applied to the obtained signals and several wave modes were identified. However, this technique was unable to quantify their observations and provide monitoring capabilities. One possible reason of this shortcoming may come from the inherent disadvantage of the t-f method. The objective of this comment is to demonstrate that it is necessary to combine other techniques with FE simulations for the extraction of significant quantitative ultrasonic features. Individual guided modes in an isotropic pipe have been theoretically examined using the normal mode expansion (NME) method, and many modes that are missed by the t-f analysis have been identified. It is concluded that in order to extract quantitative ultrasonic features, FE simulations should be supplemented by other techniques such as the NME.     

Transmission analysis of ultrasonic Lamb mode conversion in a plate with partial-thickness notch

Mode conversions of Lamb waves can occur upon encountering damage or defect such as a notch, leading to newly-converted modes apart from wave reflection and transmission. In this paper, the transmission of the fundamental Lamb modes symmetrical S0 and anti-symmetrical A0 with anti-symmetrical notches were investigated in steel plates within the relatively short propagation distance. The group velocity and modal energy of the converted modes were analyzed using simulations and experiments. Two-dimensional finite difference time domain (2D-FDTD) method was employed to calculate the scattering field and extract numerical trends for simulation study and experimental confirmation. Both simulations and experiments revealed that the apparent group velocities of the converted modes in the transmitted signals subject to the notch positions. To describe the mode conversion degree and evaluate the notch severity, wave packets of the originally-transmitted modes and newly-converted modes were separated and corresponding mode energy percentages were analyzed at different notch severities. Frequency-sweeping measurements illustrated that the modal energy percentages varied monotonically over the notch-depth increase with a statistically consistency (R = 1.00, P < 0.0004).     

Effect of bone cortical thickness on velocity measurements using ultrasonic axial transmission: a 2D simulation study

In recent years, quantitative ultrasound (QUS) has played an increasing role in the assessment of bone status. The axial transmission technique allows to investigate skeletal sites such as the cortical layer of long bones (radius, tibia), inadequate to through-transmission techniques. Nevertheless, the type of propagation involved along bone specimens has not been clearly elucidated. Axial transmission is investigated here by means of two-dimensional simulations at 1 MHz. We focus our interest on the apparent speed of sound (SOS) of the first arriving signal (FAS). Its dependence on the thickness of the plate is discussed and compared to previous work. Different time criteria are used to derive the apparent SOS of the FAS as a function of source-receiver distance. Frequency-wave number analysis is performed in order to understand the type of propagation involved. For thick plates (thickness>lambdabone, longitudinal wavelength in bone), and for a limited range of source-receiver distances, the FAS corresponds to the lateral wave. Its velocity equals the longitudinal bulk velocity of the bone. For plate thickness less than lambdabone, some plate modes contribute to the FAS, and the apparent SOS decreases with the thickness in a way that depends on both the time criterion and on the source-receiver distance. The FAS corresponds neither to the lateral wave nor to a single plate mode. For very thin plates (thickness< lambdabone/4), the apparent SOS tends towards the velocity of the lowest order symmetrical vibration mode (S0 Lamb mode).     

长骨中振动声激发超声导波的方法

为了实现一定频段内任意低频下在长骨中激励导波信号,本文提出一种采用聚焦高频(5 MHz)超声换能器在长骨皮质骨中激发低频(150 kHz)超声导波的振动声方法.首先介绍了板状超声导波理论和双声束共聚焦法与单声束调幅法激发振动声的基本原理;进而采用三维有限元仿真方法分析振动声激发低频超声导波的基本现象,然后结合牛胫骨板离体实验,验证振动声激发低频超声导波的可行性.结果均表明,双声束共焦与单声束振动超声均可在骨板中激发低频超声导波.相关研究方法有助于提高空间域长骨中超声导波测量精度,以及在一定频段内实现任意频率激励等,对发展低频超声导波在体测量长骨皮质骨的新技术具有一定的指导意义.     

Feasibility of bone assessment with leaky Lamb waves in bone phantoms and a bovine tibia

In this study, the effect of cortical thickness variation on the propagation of leaky Lamb waves is investigated by using an axial transmission technique commonly used to characterize long bones. Three Lucite plates with thicknesses of 1, 3, and 5 mm as bone phantoms and one bovine tibia with a cortical thickness of 2 mm were used at various low frequencies. Experimental measurements in bone phantoms show that the peak frequency and amplitude of excited Lamb modes strongly depend on the thickness of the Lucite plate. In the bovine tibia, the S0 and A0 Lamb modes are consistently observed in the frequency-thickness region from 0.2 to 1.0 MHz mm, and can be effectively launched at a frequency of 200 kHz, suggesting 200 kHz to be the optimal signal frequency for in vivo clinical applications. It can be also seen that both modes are affected by the frequency-thickness product, but the effect is greater for the A0 mode. Hence, the A0 Lamb mode seems more sensitive to cortical thickness change due to aging and osteoporosis. This study suggests that the use of leaky Lamb waves is feasible for ultrasonic bone assessment.     

Three-dimensional finite element modeling of guided ultrasound wave propagation in intact and healing long bones

The use of guided waves has recently drawn significant interest in the ultrasonic characterization of bone aiming at supplementing the information provided by traditional velocity measurements. This work presents a three-dimensional finite element study of guided wave propagation in intact and healing bones. A model of the fracture callus was constructed and the healing course was simulated as a three-stage process. The dispersion of guided modes generated by a broadband 1-MHz excitation was represented in the time-frequency domain. Wave propagation in the intact bone model was first investigated and comparisons were then made with a simplified geometry using analytical dispersion curves of the tube modes. Then, the effect of callus consolidation on the propagation characteristics was examined. It was shown that the dispersion of guided waves was significantly influenced by the irregularity and anisotropy of the bone. Also, guided waves were sensitive to material and geometrical changes that take place during healing. Conversely, when the first-arriving signal at the receiver corresponded to a nondispersive lateral wave, its propagation velocity was almost unaffected by the elastic symmetry and geometry of the bone and also could not characterize the callus tissue throughout its thickness. In conclusion, guided waves can enhance the capabilities of ultrasonic evaluation.     

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.     

非线性兰姆波在阶梯板中传播的有限元仿真

在非线性兰姆波检测中,累积二次谐波是重要的检测信号.该文利用有限元法仿真了非线性兰姆波在阶梯板中的产生和传播过程,通过二维离散傅里叶变换分析了兰姆波的传播模态和各个模态通过波导横截面的能流大小,给出了各个模态在阶梯板中的反射、透射系数,总结了其随阶梯板厚度的变化规律.研究发现,随着台阶增高,散射效应使得兰姆波更难入射波...     

Interaction of low-frequency axisymmetric ultrasonic guided waves with bends in pipes of arbitrary bend angle and general bend radius

The use of ultrasonic guided waves for the inspection of pipes with elbow and U-type bends has received much attention in recent years, but studies for more general bend angles which may also occur commonly, for example in cross-country pipes, are limited. Here, we address this topic considering a general bend angle φ, a more general mean bend radius R in terms of the wavelength of the mode studied and pipe thickness b. We use 3D Finite Element (FE) simulation to understand the propagation of fundamental axisymmetric L(0, 2) mode across bends of different angles φ. The effect of the ratio of the mean bend radius to the wavelength of the mode studied, on the transmission and reflection of incident wave is also considered. The studies show that as the bend angle is reduced, a progressively larger extent of mode-conversion affects the transmission and velocity characteristics of the L(0, 2) mode. However the overall message on the potential of guided waves for inspection and monitoring of bent pipes remains positive, as bends seem to impact mode transmission only to the extent of 20% even at low bend angles. The conclusions seem to be valid for different typical pipe thicknesses b and bend radii. The modeling approach is validated by experiments and discussed in light of physics of guided waves.     

对称单负介质包层平面波导的模式特征

系统研究了负μ材料(MNG)作为包层的对称三层平板波导的传输特性. 研究发现,这种波导既支持快波的传播,又支持TE₀,TE₁模式的慢波传输. 其模式特性不同于左手介质波导和传统介质波导,导模存在的模折射率范围要比它们的大. MNG波导的TE₀快波模缺失,且TE_m模(m>1)的传播常数大于TM_m模的传播常数. TE_m模具有双模特征,且与波导的结构参数密切相关,导致波导中的净能流出现负值. 关键词： 单负介质 平板波导 快波与慢波 传播常数     

Guided modes in asymmetric metal-cladding left-handed material waveguides

We investigate guided modes in the asymmetric waveguide structure with a left-handed material (LHM) layer surrounded by air and metal. A graphical method is proposed to determine the guided modes. New properties of the oscillating and surface guided modes, such as absence of the fundamental mode, coexistence of the oscillating and surface guided modes, fast attenuation of the surface guided modes, and mode degeneracy, are analyzed in detail. We also investigate dispersive characteristics of the metal-LHM- air optical waveguide. The propagation constant increases with decreasing slab thickness for the first-order oscillating mode, which is different from that in traditional metal-cladding waveguides.     

Energy concentration at the center of large aspect ratio rectangular waveguides at high frequencies

Waveguides in non-destructive evaluation (NDE) applications are commonly of a regular geometry (e.g., circular and ring cross section) for which analytical solutions exist. In this paper, wave propagation in infinitely long strips of large rectangular aspect ratio is discussed. Due to the finite width of strips, a large number of modes exist within the structure. This complicates the analysis and usually discourages the use of strip waveguides in NDE sensors. However, it is shown that among the many modes of a strip, there are some with very desirable properties. This is highlighted by the example of two guided wave modes of a large aspect ratio rectangular strip whose dispersion characteristics approach those of the fundamental modes of an infinitely wide plate at high frequencies. The energy of these modes concentrates in the central region of the strip and decays toward the edges so that the strip waveguide can easily be mechanically attached to other components without influencing the wave propagation. Dispersion curves and mode shapes were derived by using a semianalytical finite element technique and are presented over a range of frequencies. It is shown that selective excitation of both modes is possible in practice and the experimental setup is described.     

Variational analysis of Er:Ti:LiNbO3 waveguide lasers based on Gaussian/two-half Gaussian mode field distribution

Starting with two dimensional, scalar wave equation, a variational equation was established for the fundamental TE and TM modes guided in Ti:LiNbO₃ waveguides on the basis of assuming a symmetric Gaussian mode field function in the width direction and two-half Gaussian trial functions in the depth direction. The controllable waveguide fabrication parameters, including channel width, diffusion temperature, initial Ti-strip thickness and diffusion time, dependent of fundamental mode size, effective pump area, coupling efficiency between pump and laser modes, and the coupling loss between a Ti:LiNbO₃ waveguide and a fiber were numerically calculated for Z-cut Er:Ti:LiNbO₃ channel waveguide lasers at three possible emission wavelengths 1532,1563 and 1576 nm and two possible pump wavelengths 1480 and 980 nm. The calculated results were compared with those of Gaussian/Hermite–Gaussian mode field distribution in detail.     

On ultrasound waves guided by bones with coupled soft tissues: A mechanism study and in vitro calibration

The influence of soft tissues coupled with cortical bones on precision of quantitative ultrasound (QUS) has been an issue in the clinical bone assessment in conjunction with the use of ultrasound. In this study, the effect arising from soft tissues on propagation characteristics of guided ultrasound waves in bones was investigated using tubular Sawbones phantoms covered with a layer of mimicked soft tissue of different thicknesses and elastic moduli, and an in vitro porcine femur in terms of the axial transmission measurement. Results revealed that presence of soft tissues can exert significant influence on the propagation of ultrasound waves in bones, leading to reduced propagation velocities and attenuated wave magnitudes compared with the counterparts in a free bone in the absence of soft tissues. However such an effect is not phenomenally dependent on the variations in thickness and elastic modulus of the coupled soft tissues, making it possible to compensate for the coupling effect regardless of the difference in properties of the soft tissues. Based on an in vitro calibration, this study proposed quantitative compensation for the effect of soft tissues on ultrasound waves in bones, facilitating development of high-precision QUS.     

Characteristics analysis of hybrid plasmonic waveguide for low-loss lightwave guiding

It has been experimentally demonstrated that a low-loss guided hybrid mode is supported if a metal strip is embedded in a low index polymer layer surrounded by two high index slabs. In this paper, further numerical analyses on the guided hybrid modes are reported to fully elucidate the characteristics of the hybrid plasmonic waveguide. For a one-dimensional slab structure with a metal film of infinite width, simulation results exhibit that low-loss guided hybrid modes are associated with surface plasmon modes and dual dielectric slab modes. The optical properties of the guided modes are improved by increasing the field intensity which is confined into lossless dielectric layers by decreasing the metal film thickness and increasing the refractive index and thickness of the high-index slabs. The finite element method is used to investigate the lateral mode confinement of the optical guided modes by the corresponding metal strip. By reducing the metal film width, the guided modes are confined in the plane transverse to the direction of propagation and the characteristics are significantly improved. The hybrid plasmonic waveguide can be exploited for long-range propagation-based application such as optical interconnection.