Evaluation of Fatigue Crack Orientation Using Non-collinear Shear Wave Mixing Method

In this paper, a non-collinear shear wave mixing technique is proposed for evaluation of fatigue crack orientation. Numerical analysis of the nonlinear interaction of two shear waves with crack is performed using two-dimensional finite-element simulations. The simulation results show that the nonlinear interaction of the two shears waves with cracks leads to the generation of transmitted and reflected sum-frequency longitudinal waves (SFLW), moreover the propagation direction of reflected SFLW is correlated with the orientation of crack, which can be used for crack orientation evaluation. Non-collinear wave-mixing experiments were conducted on specimens with fatigue crack. The experimental results show that the directivity of the generated SFLW agrees well with the simulation results, and non-collinear shear wave mixing has potential use in fatigue crack orientation evaluation.     

Nonstationary Rayleigh waves on the thermally-insulated surfaces of some thermoelastic bodies of revolution

Summary The influence of heat conduction and thermal relaxation on the propagation of the surface waves polarized in the sagittal plane along the heat-insulated surfaces of the following thermoelastic bodies of revolution: a cylinder, a sphere, a torus, and a cone is investigated. The modified Maxwell law is used as the law of heat conduction, which allows one to take a finite speed of heat propagation into account. The nonstationary surface waves are interpreted as lines (a straight line or a diverging or converging circumference) on which the temperature and the components of the stress and strain tensors experience a discontinuity. Each of the discontinuity lines propagates with a constant normal velocity across the free from stresses and thermally-insulated surface of the body of revolution along the corresponding lines of curvature and is obtained by coming onto the body's surface of the three strong discontinuity complex wave surfaces which intersect along this line: quasi-thermal, quasi-longitudinal and quasi-transverse volume waves. By applying the theory of discontinuities, the velocities and the intensities of the surface waves have been found. It has been shown that the attenuation of the surface wave intensity is determined by the two factors: the coupling between the related strain and temperature fields and the change in curvature of the surface wave with time if the wave is a curvilinear one.     

The thermo-electromagnetic waves in piezoelectric solids

The Maxwell??s equation and stress equilibrium equation of anisotropic media, coupled to the heat conduction equation, are studied here based on the eigen theory of physical presentation, in which a new thermo-piezoelectric constitutive model is induced. The complete sets of uncoupled thermo-electromagnetic wave equations for piezoelectric solids are deduced. The results show that the equations of electromagnetic waves in anisotropic media subjected to heat become fourth order differential ones, and from them, a new phenomenon of thermo-electromagnetic waves with low propagation speed is obtained. In the final part of this paper, we discuss the propagation behavior of the new thermo-electromagnetic waves in the piezoelectric material of class 6?mm.     

Multiple Scattering of Thermal Waves from a Subsurface Cylindrical Inclusion in Semi-infinite Functionally Graded Materials Using Non-Fourier Model

In this study, a theoretical method is applied to investigate the multiple scattering of thermal waves and temperature field resulting from a subsurface cylindrical inclusion in a semi-infinite functionally graded material (FGM). The adiabatic boundary condition at the semi-infinite surface is considered. The thermal waves are excited at the surface of semi-infinite functionally graded materials by modulated optical beams. The model includes the multiple scattering effects of the cylindrical thermal wave generated by the line heat source. According to the wave equation of heat conduction, a general solution of scattered thermal waves is presented. Numerical calculations illustrate the effect of subsurface inclusion on the temperature and phase change at the sample surface under different physical and geometrical parameters. It is found that the temperature above the conducting cylindrical inclusion decreases because of the existence of the inclusion. The effect of the inclusion on the temperature and phase change at the surface is also related to the non-homogeneous parameter of FGMs, the wave frequency of thermal waves, and the distance between the inclusion and the semi-infinite surface. Finally, the effect of the relaxation time of buried inclusion on the temperature and phase change at the surface is examined.     

Scattering of Thermal Waves and Non-steady Effective Thermal Conductivity of Unidirectional Fibrous Composites with Functionally Graded Interface

In this paper, a thermal wave method is applied to investigate the non-steady effective thermal conductivity of unidirectional fibrous composites with a functionally graded interface, and the analytical solution of the problem is obtained. The Fourier heat conduction law is applied to analyze the propagation of thermal waves in the fibrous composite. The scattering and refraction of thermal waves by a cylindrical fiber with an inhomogeneous interface layer in the matrix are analyzed, and the results of the single scattering problem are applied to the composite medium. The wave fields in different material layers are expressed by using the wave function expansion method, and the expanded mode coefficients are determined by satisfying the boundary conditions of the layers. The theory of Waterman and Truell is employed to obtain the effective propagating wave number and the non-steady effective thermal conductivity of composites. As an example, the effects of a graded interface on the effective thermal conductivity of composites are graphically illustrated and analyzed. Analysis shows that the non-steady effective thermal conductivity under higher frequencies is quite different from the steady thermal conductivity. In the region of intermediate and high frequencies, the effect of the properties of the interface on the effective thermal conductivity is greater. Comparisons with the steady thermal conductivity obtained from other methods are also presented.     

利用波动法研究曲梁结构中的波形转换和能量传递

基于Flugge理论,建立了薄壁均质常曲率曲梁面内运动的6阶微分控制方程,得到了曲梁的频散特性曲线和6种波的轴向位移和径向位移的比值,推导了位移和内力响应的表达式以及物理域和波数域的变换矩阵。利用波的传递和反射矩阵对曲梁和半无限长直梁耦合时的能量传递系数和反射系数进行了求解分析。对于半无限长直梁中给定的拉伸波或弯曲波入射,得到了和频率,曲率半径和伸展角度相关的各种波传递和反射的能量系数表达式。数值结果表明,纵波和弯曲波在经过曲梁结构之后发生了波形转换,并研究了能量传递和反射系数随频率,伸展角度,曲梁曲率半径和截面尺寸比的变化。结果表明,无限长直梁和曲梁耦合系统中,低频时,经过曲梁反射和传递后的弯曲波和纵波会相互转化;高频时弯曲波和纵波都能够没有散射地通过曲梁而进行传播。为改善高频时曲梁中的能量衰减效果,研究了在曲梁结构中插入单个、多个中间支撑或阻振质量块时的能量传递和反射系数。结果表明,阻振质量块能够很好地阻止高频时曲梁中能量的传递,对于周期分布的多个阻振质量块,能量传递系数随频率的变化存在周期结构的阻带特征。这些研究结果为曲梁结构的设计提供定性的理论基础。     

Measurement of the Intrinsic Thermal Conductivity of a Multiwalled Carbon Nanotube and Its Contact Thermal Resistance with the Substrate

The intrinsic thermal conductivity of an individual carbon nanotube and its contact thermal resistance with the heat source/sink can be extracted simultaneously through multiple measurements with different lengths of the tube between the heat source and the heat sink. Experimental results on a 66‐nm‐diameter multiwalled carbon nanotube show that above 100 K, contact thermal resistance can contribute up to 50% of the total measured thermal resistance; therefore, the intrinsic thermal conductivity of the nanotube can be significantly higher than the effective thermal conductivity derived from a single measurement without eliminating the contact thermal resistance. At 300 K, the contact thermal resistance between the tube and the substrate for a unit area is 2.2 × 10^?8 m² K W^?1, which is on the lower end among several published data. Results also indicate that for nanotubes of relatively high thermal conductance, electron‐beam‐induced gold deposition at the tube–substrate contacts may not reduce the contact thermal resistance to a negligible level. These results provide insights into the long‐lasting issue of the contact thermal resistance in nanotube/nanowire thermal conductity measurements and have important implications for further understanding thermal transport through carbon nanotubes and using carbon nanotube arrays as thermal interface materials.     

Effects of an external magnetic field on thermo-acoustical waves in a linear isotropic thermo-elastic dielectric material

Summary Thermo-mechanico-electromagnetic coupled waves propagating in a linear isotropic thermo-elastic dielectric material are theoretically investigated, in case an external magnetic field is applied to the material. Here the constitutive equations derived from the Clausius-Duhem inequality and Vernotte's heat conduction law are adopted. There are three types of coupled waves: the predominantly electromagnetic wave, the predominantly mechanical transverse wave and the predominantly thermo-mechanical longitudinal wave. The first and second waves have no thermal coupling. The third wave has thermal coupling and its propagation velocity and attenuation constant are perturbed by the external magnetic field.     

Elastic wave and energy propagation in angled beams

This investigation comprises an experimental and numerical study of elastic wave propagation in angled beams. Axial impact by two strikers of different lengths was applied to three steel beams, each bent to incorporate a “V” section of different angle in the middle. Finite element simulation using ABAQUS was employed to examine details of the elastic waves generated in the impact tests. The numerical results correlated well with experimental data, and computational simulation was utilized to analyse the propagation of energy associated with the elastic waves. This demonstrated that after several reflections from and transmission across the bends energy is progressively smeared throughout the entire beam and does not concentrate at any particular segment; the bulk of the energy is conveyed via flexural waves. Numerical simulation of wave propagation in a beam with a single angle was also undertaken to study the energy associated with waves reflected from and transmitted across the bend, and how these are affected by the bend angle. The effects of input pulse duration, beam thickness and beam material properties on energy reflection and transmission at a bend are also discussed; this leads to the conclusion that when a longitudinal pulse of a particular frequency impinges on a bend, the ratio between its wavelength and the beam thickness governs the energy reflected from and transmitted across the bend. Moreover, the bend junction geometry (curvature) is found to have a significant influence on the energy reflected and transmitted, especially for obtuse bend angles.     

A Study on Thermal Contact Resistance at the Interface of Two Solids

In this paper, numerical simulations and measurements of the thermal contact conductance (TCC) at the interface between the plane ends of two cylinders in contact are carried out. The random model of surface roughness is developed, and the non-dimensional basic equations are solved based on a grid system with equi-peripheral intervals in the azimuthal direction that can express reasonably the real contact spot distribution. The effects of the contact pressure, the thermal conductivity of the interstitial medium, and the mean absolute slope of the rough surface on the TCC were clarified by using a network method. In the experiments, four pairs of brass cylinders, each of which has similar surface topology, are used for the TCC measurements. The hysteretic nature of TCC versus contact pressure was observed in the first loading cycle. The present numerical results show that the TCC increases linearly with the mean absolute slope of the surfaces even at the same mean roughness. Such a tendency agrees well with the measurements.     

功能梯度材料亚表面缺陷的热波多重散射问题

基于热传导波动模型,采用波函数展开法,研究了半无限功能梯度材料亚表面球形缺陷的热波多重散射.给出了热波散射的一般解.温度波由调制光束在材料表面激发,球形缺陷表面的边界条件为绝热,非均匀参数为指数函数变化.分析了结构几何参数和物理参数对温度分布的影响,并给出了温度变化的数值结果.本研究可为功能梯度材料的分析研究、物理反问题和红外热波成像等提供理论基础和参考数据.     

Electro-magneto-thermo-visco-elastic Plane Waves in Rotating Media with Thermal Relaxation

A study is made of the propagation of plane electro-magneto-thermo-visco-elastic harmonic waves in an unbounded isotropic conducting visco-elastic medium of Kelvin–Voigt type permeated by a primary uniform magnetic field when the entire medium rotates with a uniform angular velocity. The thermal relaxation time of heat conduction, the electric displacement current, the coupling between heat flow density and current density, and that between the temperature gradient and the electric current are included in the analysis. A more general dispersion relation is obtained to determine the effects of rotation, thermal relaxation time, visco-elastic parameters, and the external magnetic field on the phase velocity of the waves. Perturbation techniques are used to study the influence of small magneto-elastic and thermo-elastic couplings on the phase velocity of the waves. Cases of low and high frequencies are also analyzed to determine the effect of rotation, visco-elastic parameters, thermo elastic and magneto-elastic coupling, as well as thermal relaxation time of heat conduction on the waves.     

Reflection and transmission of waves from a plane interface between two microstretch solid half-spaces

In this paper, we have investigated the wave propagation and their reflection and transmission from a plane interface between two different microstretch elastic solid half-spaces in perfect contact. It is shown that there exist five waves in a linear homogeneous isotropic microstretch elastic solid, one of them travel independently, while other waves are two sets of two coupled waves. It is also shown that these waves travel with different velocities, three of which disappear below a critical frequency. Amplitude ratios and energy ratios of various reflected and transmitted waves are presented when a set of coupled longitudinal waves and a set of coupled transverse waves is made incident. It is found that the amplitude ratios of reflected and transmitted waves are functions of angle of incidence, frequency and are affected by the elastic properties of the media. Some special cases have been reduced from the present formulation.     

Generalized RayleighWave Dispersion Analysis in a Pre-stressed Elastic Stratified Half-space with Imperfectly Bonded Interfaces

Within the framework of the piecewise homogeneous body model the influence of the shear-spring type imperfect contact conditions on the dispersion relation of the generalized Rayleigh waves in the system consisting of the initially stressed covering layer and initially stressed half plane is investigated. The second version of the small initial deformation theory of the three-dimensional linearized theory of elastic waves in initially stressed bodies is applied and the elasticity relations of the materials of the constituents are described by the Murnaghan potential. The magnitude of the imperfectness of the contact conditions is estimated through the shear-spring type parameter. Consequently, the influence of the imperfectness of the contact conditions on the generalized Rayleigh wave propagation velocity is studied through the influence of the values of this parameter. Numerical results on the action of the imperfectness of the contact conditions and the influence of the initial stresses in the constituents on the wave dispersion curves are presented and discussed. In particular, it is established that the magnitude of action of the imperfectness of the contact conditions under the influence of the initial stresses on the wave propagation velocity cannot be limited with corresponding ones obtained in the case where the contact between the constituents is complete and in the case where this contact is full slipping one. The possible application of the obtained results on the geophysical and geotechnical engineering is also discussed.     

Effect of Columnar Grain Orientation on Ultrasonic Plane Wave Energy Reflection and Transmission Behaviour in Anisotropic Austenitic Weld Materials

This article describes a comprehensive quantitative analysis on effect of columnar grain orientation on ultrasonic plane wave energy reflection and transmission behaviour in acoustically anisotropic austenitic weld materials. The quantitative results are presented for following general interfaces (a) Isotropic-Anisotropic, (b) Anisotropic-Isotropic, (c) Fluid-Anisotropic, (d) Anisotropic-Fluid, (e) Anisotropic-Anisotropic, (f) Anisotropic-Free surface occur during the ultrasonic non destructive evaluation of austenitic weld materials. Explicit analytical expressions are presented for energy reflection and transmission coefficients at an interface between two arbitrarily oriented transversely isotropic materials. By applying explicit analytical expressions for energy reflection and transmission coefficients, numerical results are presented for several columnar grain orientations of the transverse isotropic austenitic weld material including both real and complex domain of the reflected and transmitted normal component of slowness vectors. Valid domains of incident wave vector angles, angular dependency of energy reflection and transmission coefficients and critical angles for reflected and transmitted waves are discussed. The existence of a reflected (or) transmitted second branch of quasi shear vertical waves and its consequence to the ultrasonic non destructive testing of austenitic weld materials are investigated. The presented comprehensive quantitative evaluation provides an overview on the effect of anisotropic properties on energy reflection and transmission coefficients in columnar grained austenitic weld materials.     

Thermo-acoustical waves in linear thermo-elastic materials

Summary Coupled waves of thermal and mechanical jumps in linear thermo-elastic materials are analysed. General linear anisotropic constitutive equations of thermo-elastic materials are derived from the Clausius-Duhem inequality and Vernotte's heat conduction law is adopted. The waves are defined to have jumps in acceleration and in temperature rate and the four-dimensional thermo-acoustical propagation condition is obtained. The differential equations which govern the variation of the wave amplitudes are obtained. For waves in linear isotropic thermo-elastic materials, there are four principal waves. Two shear waves are purely mechanical and propagate with constant amplitude, while two thermo-longitudinal waves have different propagation velocities: one is larger and other smaller than the purely mechanical longitudinal wave velocity, and their amplitudes decay, in general, exponentially in time.     

Assessment of debonding in sandwich CF/EP composite beams using A0 Lamb wave at low frequency

The aim of this study is to quantitatively assess debonding in sandwich CF/EP composite structures with a honeycomb core using acoustic waves activated and captured by surface-mounted PZT elements. For experimental investigation, debonding was introduced at different locations in sandwich CF/EP composite beams. The fundamental anti-symmetric A₀ Lamb mode was excited at a low frequency. The transmitted and reflected wave signals in both surface panels were captured by PZT elements after interacting with the debonding damage and specimen boundaries. Aided by finite element analysis (FEA), the differences in wave propagation characteristics in sandwich composite beams and composite laminate (e.g. skin panel only) were investigated. The debonding location was assessed using the time-of-flight (ToF) of damage-reflected waves, and the severity of debonding was evaluated using both the magnitude of the reflected wave signal and the delay in the ToF of Lamb wave signals. Good correlation between the experimental and FEA simulation results was observed. The results demonstrate the effectiveness of Lamb waves activated and captured by surface-mounted PZT elements on either surface of sandwich composite structures in assessing debonding.     

直接冷却中氮化铝与无氧铜低温真空接触热导的实验研究

以5W／20K小型G-M制冷机为冷源，对低温下氮化铝（AlN）与无氧铜（OFHC）界面的接触热导进行了实验研究和分析。在45～140K内，氮化铝／无氧铜界面接触热导随温度的升高而增大，同时亦随接触压力的增加而增大。实验中同时得到了氮化铝在低温下的热导率，随温度的升高，氮化铝热导率值逐渐增大。就氮化铝低温热导率及氮化铝／无氧铜接触界面热阻随温度变化规律进行了微结构机理分析。     

低温传热中的热波现象

热波现象是低温传热中的常见现象，对热波理论的研究具有重要的理论与应用价值。本文所涉及的范围包括固体中的热波现象和超流氦中的热波现象，结合近年来在此领域中的研究成果，介绍了其主要公式的推导过程及过热波现象的一些宏现或微观的解释，指出了热波理论的应用前景和在工程中的应用价值。     

超声波在水中衰减的频率效应及其对脉冲回波的影响

超声波在传播中会发生幅值衰减,该衰减不仅与超声波传播的距离有关,还与超声波的频率有关。为了研究高频超声波衰减的频率效应,本文通过脉冲回波法分析脉冲超声波在水中传播反射回波的幅值和频谱变化,研究了超声波在水中传播时幅值衰减与传播距离及其与超声频率之间的关系,通过测量脉冲超声波在水中传播不同距离时的反射回波,并对其进行傅里叶变换,分析了超声波传播衰减的距离效应和频率效应。研究发现:超声波在水中的传播衰减随距离呈指数规律,且不同频率超声波的衰减系数不相同,频率越高,衰减越大,衰减的频率效应可有效解释反射法高频脉冲超声检测中回波脉冲信号的中心频率远低于换能器标称中心频率的现象。