Numerical and analytical study of the propagation of thermoelastic waves in a medium with heat-flux relaxation

The thermoelastic problem of laser exposure of metals and dielectrics is studied taking into account the finite speed of propagation of thermal waves and using a numerical finite-difference algorithm. The resulting numerical solution is compared with the analytical one. The problem is solved in coupled and uncoupled formulations. The solutions of the hyperbolic thermoelastic problem are compared with the solutions of the classical problem. Analytical expressions are obtained for the propagation speeds of the thermoelastic wave components. Times are determined at which the difference between the solutions of the hyperbolic and classical thermoelastic problems can be detected experimentally.     

Thermodynamic restrictions and wave features of a non-linear Maxwell model

A non-linear rate-type constitutive equation, established by Rajagopal, provides a generalization of the Maxwell fluid. This note embodies such a constitutive equation within the scheme of materials with internal variables thus allowing also for solids with both dissipative and thermoelastic mechanisms. The compatibility with the second law of thermodynamics, expressed by the Clausius–Duhem inequality, is examined and the restrictions on the evolution equations are determined. Next the propagation condition of discontinuity waves is derived, for shock waves and acceleration waves, by regarding the body as a definite conductor. Infinitesimal shock waves and acceleration waves show similar effects. The effective acoustic tensor proves to be the sum of a thermoelastic tensor and a tensor arising from the rate-type equation.     

线状脉冲激光激发双层圆柱的波传播

该文建立了一个物理模型来预测均匀、各向同性双层固体圆柱在激光烧蚀或热弹激发下的弹性波传播规律.在建模中忽略了激光源的光学穿透和材料的热扩散.采用空间和时间上的双重傅氏变换对理论模型进行求解,得到其位移场的变换解.通过对铝壳铜芯和铜壳铝芯的数值计算,得到不同内外径比下瞬态位移响应的时域和频域数值波形.用传播路径分析发现结果中存在界面反射波,这可以表明所建立的理沦模型和计算方法是有效的,同时其余波的传播也被分析和解释.     

Thermoelastic generation of ultrasound by line-focused laser irradiation

A two-dimensional theoretical model for the field generated in the thermoelastic regime by line-focused laser illumination of a homogeneous, isotropic, linearly elastic half-space is presented. The model accounts for the effects of thermal diffusion and optical penetration, as well as the finite width and duration of the laser source. The model is obtained by solving the thermoelastic problem in plane strain, rather than by integrating available solutions for the point-source, leading to a lower computational effort. The well-known dipole model follows from appropriate limits. However, it is shown that, by simple elasticity arguments, the strength of the dipole can be related a-priori to the heat input and certain material properties. The strength is found to be smaller than that of the dipoles equivalent to a buried source due to the effect of the free surface. This fact has been overlooked by some previous researchers. Excellent quantitative agreement with experimental observations provides validation for the model. Some representative results are presented to illustrate the generated field and provide insight into the relevance of the different mechanisms taken into account in the model.     

Response of welded thermoelastic solids to the rapid motion of thermomechanical sources parallel to the interface

The analysis of rapidly-moving thermomechanical surface sources is extended to the study of buried thermomechanical sources that move parallel to the interface of two welded dissimilar thermoelastic half-spaces at a constant subcritical speed. The sources are manifest as body force line loads in the coupled equations of thermoelasticity, and a 2-D steady-state situation is treated. Exact integral transform solutions are obtained, and expressions for the displacements and temperature changes are generated by analytical inversion of robust asymptotic versions of the transforms.These expressions show that thermoelastic coupling effects increase with source speed, and that the thermal source is always manifest in combination with a component of the mechanical source, i.e. an effective thermal source term exists. The expressions also exhibit component functions that are in effect hybrids of functions that are seen in purely thermal and isothermal elastic solutions.The critical source speed is defined as the minimum of the two asymptotic thermoelastic Rayleigh speeds in the half-spaces and, when it exists, the asymptotic thermoelastic Stoneley speed. Exact expressions for these speeds are given, and used to present some typical values.     

Wave propagation in thermally conducting linear fibre-reinforced composite materials

The propagation of plane waves in a fibre-reinforced, anisotropic, generalized thermoelastic media is discussed. The governing equations in x–y plane are solved to obtain a cubic equation in phase velocity. Three coupled waves, namely quasi-P, quasi-SV and quasi-thermal waves are shown to exist. The propagation of Rayleigh waves in stress free thermally insulated and transversely isotropic fibre-reinforced thermoelastic solid half-space is also investigated. The frequency equation is obtained for these waves. The velocities of the plane waves are shown graphically with the angle of propagation. The numerical results are also compared to those without thermal disturbances and anisotropy parameters.     

Analysis of plane waves in anisotropic thermoelastic diffusive medium

This paper concentrates on the study of the propagation of harmonic plane waves in a homogeneous anisotropic thermoelastic diffusive medium in the context of different theories of thermoelastic diffusion. It is found that five types of waves propagate in an anisotropic thermoelastic diffusive medium, namely a quasi-elastodiffusive (QED-mode), two quasi-transverse (QSH-mode and QSV-mode), a quasi-mass diffusive (QMD-mode) and a quasi-thermo diffusive (QTD-mode) wave. The governing equations for homogeneous transversely isotropic diffusive medium in different theories of thermoelastic diffusion are taken as a special case. It is noticed that when plane waves propagate in one of the planes of transversely isotropic thermoelastic diffusive solid, purely quasitransverse wave mode(QSH) decouples from rest of the motion and is not affected by the thermal and diffusion vibrations. On the other hand, when plane waves propagate along the axis of solid, two quasi-transverse wave modes (QSH and QSV) decouple from the rest of the motion and are not affected by the thermal and diffusion vibrations. From the obtained results, the different characteristics of waves like phase velocity, attenuation coefficient, specific loss and penetration depth are computed numerically and presented graphically for a single crystal of magnesium. The effects of diffusion and relaxation times on phase velocity, attenuation coefficient, specific loss and penetration depth has been studied. Some particular cases are also discussed.     

Plane Waves and Eigenfrequencies in the Linear Theory of Binary Mixtures of Thermoelastic Solids

In this paper some basic properties of wave numbers of the longitudinal and transverse plane waves are treated. The existence theorems of eigenfrequencies of the interior homogeneous boundary-value problems of steady oscillations of binary mixtures for thermoelastic solids are proved. The connection between plane waves and eigenfrequencies is established. This paper dedicated to my teacher Professor Mikheil Basheleishvili on the occasion of his 80th birthday.     

Reflection and transmission of plane waves at the interface of an elastic half-space and a fractional order thermoelastic half-space

The problem of reflection and transmission due to longitudinal and transverse waves incident obliquely at a plane interface between uniform elastic solid half-space and fractional order thermoelastic solid half-space has been studied. It is found that the amplitude ratios of various reflected and refracted waves are functions of angle of incidence and frequency of incident wave and are influenced by the fractional order thermoelastic properties of media. The expressions of amplitude ratios and energy ratios have been computed numerically for a particular model. The variation of amplitude and energy ratios with angle of incidence is shown graphically. The conservation of energy at the interface is verified.     

Propagation of plane waves in thermoelastic cubic crystal material with two relaxation times

A problem concerned with the reflection and refraction of thermoelastic plane waves at an imperfect interface between two generalized thermally conducting cubic crystal solid half-spaces of different elastic and thermal properties with two relaxation times has been investigated. The generalized thermoelastic theory with two relaxation times developed by Green and Lindsay has been used to study the problem. The expressions for the reflection and refraction coefficients which are the ratios of the amplitudes of reflected and refracted waves to the amplitude of incident waves are obtained for an imperfect boundary and deduced for normal stiffness, transverse stiffness, thermal contact conductance, slip and welded boundaries. Amplitude ratios of different reflected and refracted waves for different boundaries with angle of emergence have been compared graphically for different incident waves. It is observed that the amplitude ratios of reflected and refracted waves are affected by the stiffness and thermal properties of the media.     

基于光纤传感器的固体杨氏模量与泊松比测量方法研究

提出了一种基于光纤传感器的测量固体材料杨氏模量与泊松比的方法,给出了Sagnac光纤干涉仪的环形光纤作为点传感器检测声波及用于声速测量的原理,推导出固体中声波速度与材料的杨氏模量及泊松比的关系式.以光纤Sagnac干涉仪作为传感器贴附于三角铸铁导轨表面,分别测出声表面波与纵波的速度,根据理论推导,得到了铸铁的杨氏模量与泊松比.实验结果与理论数值基本吻合,表明了此测量方法的可行性,为固体材料性能评估提供了一种新的方法.     

Nonlocal coupled thermoelastic wave propagation band structures of nano-scale phononic crystal beams based on GN theory with energy dissipation: An analytical solution

This paper deals with the band structures of thermoelastic waves in nano-scale phononic crystal or metamaterial beams considering nano-size effects. The nonlocal coupled thermoelastic governing equations are derived using the Green–Naghdi theory of the generalized coupled thermoelasticity with energy dissipation and Eringen’s nonlocal theory. The derived governing equations are analytically solved and the field quantities including the temperature and the deflection are obtained in the closed forms. Using the proposed analytical solution, the transfer matrix between two unit-cells are obtained using the thermal and mechanical continuity conditions on the interfaces between the unit-cells and between the two sections of each unit-cell. The band structures of the phononic crystals are obtained using the Bloch–Floquet theorem. The detailed discussions are presented for the band structures of nonlocal thermoelastic waves in nano-scale aluminum/epoxy phononic crystal or metamaterial beams. Also, the effects of the small-scale parameter and the thickness of the epoxy layers on the band structures are studied and discussed by using the derived analytical solution.     

轴对称热载作用厚板的热弹性运动效应分析

对板的上下表面存在一般温度边界条件的情况，解出了板表面受轴对称热辐射作用时，板内轴对称二维瞬态温度场的一般表达式；导出了厚板的热弯曲运动和热平面运动的位移型动力学方程，得出了板的挠度、转角和平面径向位移的无穷积分型公式；提出了一个求解弯曲波传播速度的方法；然后完成了一个代表性算例分析，给出了弯曲波传播规律的直观图象，得出了热加载和热卸载过程中，板内热弯曲波的时空变化特点；找出了剪切变形和旋转惯性对弯曲波传播速度的影响规律；最后，将理论结果与相应的实验结果进行了比较，两者吻合良好。     

On the propagation waves in the theory of thermoelasticity with microtemperatures

The present paper studies the propagation of plane time harmonic waves in an infinite space filled by a thermoelastic material with microtemperatures. It is found that there are seven basic waves traveling with distinct speeds: (a) two transverse elastic waves uncoupled, undamped in time and traveling independently with the speed that is unaffected by the thermal effects; (b) two transverse thermal standing waves decaying exponentially to zero when time tends to infinity and they are unaffected by the elastic deformations; (c) three dilatational waves that are coupled due to the presence of thermal properties of the material. The set of dilatational waves consists of a quasi-elastic longitudinal wave and two quasi-thermal standing waves. The two transverse elastic waves are not subjected to the dispersion, while the other two transverse thermal standing waves and the dilatational waves present the dispersive character. Explicit expressions for all these seven waves are presented. The Rayleigh surface wave propagation problem is addressed and the secular equation is obtained in an explicit form. Numerical computations are performed for a specific model, and the results obtained are depicted graphically.     

Reflection of three-dimensional plane waves at the free surface of a rotating triclinic half-space under the context of generalized thermoelasticity

The reflection of three-dimensional(3D) plane waves in a highly anisotropic(triclinic) medium under the context of generalized thermoelasticity is studied. The thermoelastic nature of the 3D plane waves in an anisotropic medium is investigated in the perspective of the three-phase-lag(TPL), dual-phase-lag(DPL), Green-Naghdi-III(GNIII), Lord-Shulman(LS), and classical coupled(CL) theories. The reflection coefficients and energy ratios for all the reflected waves are obtained in a mathematical form. The rotational effects on the reflection characteristics of the 3D waves are discussed under the context of generalized thermoelasticity. Comparative analyses for the reflection coefficients of the waves among these generalized thermoelastic theories are performed. The energy ratios for each of the reflected waves establish the energy conservation law in the reflection phenomena of the plane waves. The highly anisotropic materials along with the rotation may have a significant role in the phenomenon of the reflection behavior of the 3D waves. Numerical computations are performed for the graphical representation of the study.     

A GENERALIZED THERMOELASTIC DIFFUSION PROBLEM OF THIN PLATE HEATED BY THE ULTRASHORT LASER PULSES 1)

由于超短激光脉冲具有功率密度高、持续时间短、加工精度高等优势, 近年来被广泛应用于超精细加工、光学储存和微电子器件制造等领域. 本文基于L-S型广义热弹扩散理论, 建立了考虑材料记忆依赖效应和空间非局部效应的记忆依赖型非局部广义热弹扩散耦合理论, 它能够准确预测几何尺寸与内部特征尺寸相近结构的热弹扩散瞬态响应. 推导了所建理论的控制方程, 并基于拉普拉斯积分变换获得了控制方程的解. 作为算例, 利用所建理论和求解方法研究了半无限大薄板受非高斯激光脉冲加热和化学冲击联合作用下的热弹扩散瞬态响应问题, 得到了薄板的温度、化学势、位移、应力和浓度等随非局部参数、热时间迟滞因子和扩散时间迟滞因子等参数变化的分布规律. 结果表明: 传热对传质影响显著, 传质对传热影响甚微; 非局部参数对位移、应力影响显著, 对温度、化学势和浓度几乎没有影响. 该理论及求解方法的建立, 旨在实现材料在机械、热、化学势等冲击作用下传热传质瞬态响应的准确预测.     

光纤位移干涉仪在爆轰加载飞片速度测量中的应用

利用光学多普勒效应和外差方法搭建了一台光纤位移干涉仪。装置采用光通信行业中已经发展成熟的器件,主要由带尾纤的半导体激光器、三端口环形器、光纤探头、宽带探测器以及宽带高采样率示波器等构成。整个装置结构简单,价格便宜,采用了信号光和参考光同轴结构,实现了任意反射面的速度测量,克服了偏振模式色散的影响,能够实现长量程测量,量程达到20 mm。利用该装置进行了爆轰加载下飞片速度测量,测量最高速度达到1 300 m/s,工作距离达到20 mm,同时利用VISAR对飞片速度进行了对比测量,结果表明用两种不同方法所测得的速度曲线吻合很好。     

Thermoelastic stability of first strain gradient solids

The problem of thermoelastic stability of a first strain gradient solid under noncons rvative loadings is studied. The Liapunov-Movchan method of elastic stability analysis is reviewed. An energy Liapunov functional is constructed and the sufficiency criteria for the stability of a loaded equilibrium configuration are derived. The effects of motion dependent surface tractions and couples are discussed. The special case of isothermal elastic stability of solids with couple stress is also considered.     

Transient thermoelastic waves in an anisotropic hollow cylinder due to localized heating

This paper presents a theoretical study of transient ultrasonic guided waves generated by concentrated heating of the outer surface of an infinite anisotropic hollow circular cylinder. Generalized thermoelastic theory proposed by Lord and Shulman is adopted to model the dynamic thermoelastic behavior of the cylinder. The concentrated heat source model used is to represent heating due to a pulsed laser beam, which is focused on the outer surface of the cylinder. A semi-analytical finite element (SAFE) method is employed to evaluate guided wave modes in the cylinder. Using integral transform techniques, the modal wave forms are obtained in frequency and wave number domains. Time histories of the propagating modes are then calculated by applying inverse Fourier transformation in the time domain. Numerical results showing the dispersion curves for the group velocities of the propagating modes and transient radial displacements are presented. For this purpose it is assumed that the cylinder is made of transversely isotropic silicon nitride (Si₃N₄). Attention is focused on the propagation characteristics of longitudinal and flexural modes separately.