半无限长压电杆的瞬态热冲击问题

采用具有一个热松弛时间的L－S广义热弹性理论，研究了一维半无限长压电杆在一端受到热冲击时的边值问题。借助拉普拉斯正，反变换技术，在所考虑时间非常短的情况下，对问题进行了求解，得到了压电杆上的位移，压力及温度分布的近似解析解，发现应力及温度分布中分别存在两个阶跃点，并给出了算例。     

无限长圆柱体中广义电磁热弹耦合问题研究

基于L-S广义热弹性理论,研究了处于磁场中无限长理想圆柱导体在边界受热冲击作用时的电磁热弹耦合问题.建立了广义电磁热弹耦合的有限元方程,为避免积分变换方法求解带来的精度丟失.采用将有限元方程直接在时间域求解的方法,得到了圆柱体中的温度、位移、应力、感应磁场和感应电场的分布规律,反映了热的波动性及电磁热弹的耦合效应.结果表明,将有限元方程直接在时间域求解,可以获得各物理量的准确分布.得到温度在热波波前处的阶跃,准确地反应热波的波动效应.     

激光脉冲加热的二维广义热弹性问题研究

基于L-S广义热弹性理论,研究了半无限大板局部受到激光脉冲加热时的广义热弹性问题.为避免常规积分变换方法求解带来的精度丢失,采用有限元法直接在时间域进行求解,得到了激光脉冲加热时板中的温度、位移及应力的变化规律.结果表明,直接求解方法可以准确描述热在介质中以有限的速度传播,同时发现,激光脉冲加热过后,结构的最高温度随着时间的推移逐渐降低,且最高温度的位置总在热波波前附近,此处的应力也明显高于其他区域.     

圆柱外表面受热冲击问题的广义热弹性分析

基于 L-S 广义热弹性理论, 针对实心圆柱体在外表面受均匀热冲击作用下的一维广义热弹性问题进行研究分析. 利用热冲击的瞬时特征, 借助于 Laplace 正、反变换技术及柱函数的渐近性质, 推导了热冲击作用周期内温度场、位移场和应力场的渐近表达式. 通过计算, 得到了热冲击条件下各物理场的分布规律以及延迟效应和耦合效应对热弹性响应的影响规律. 结果表明: 当考虑延迟效应和耦合效应时, 热扰动将以两组速度不同的波的形式向前传播, 延迟效应和耦合效应对各物理场的建立时间, 阶跃间隔和阶跃峰值均产生影响, 且延迟效应和耦合效应均在一定程度上削弱了热冲击的作用效果.      

热冲击下温度相关物性对热弹性响应的渐进分析

计及材料物性与温度的相关性,基于Green-Naghdi能量无耗散广义热弹性理论(G-N II理论),对热冲击下具有变物性特征材料的热弹性响应进行了求解分析.借助Laplace正、反变换技术以及Krichhoff变换,在热物性参数随真实温度呈线性规律的前提下,推导了半无限大体受热冲击作用时热弹性响应的解析表达式,通过求解分析,得到了热冲击下热波、热弹性波的传播规律,位移场、温度场以及应力场的分布情况,以及物性随温度相关性对热弹性响应的影响效果.结果表明:当考虑材料物性随温度的变化时,热波、热弹性波的传播以及各物理场的分布均受到不同程度的影响,且物性随温度相关性对热弹性响应的作用效果将受到材料热-力耦合特性的影响.     

热冲击下物性与温度相关性对热弹性响应的渐进分析

计及材料物性与温度的相关性,基于Green-Naghdi能量无耗散广义热弹性理论(G-N II理论),对热冲击下具有变物性特征材料的热弹性响应进行了求解分析。借助Laplace正、反变换技术以及Krichhoff变换,在热物性参数随真实温度呈线性规律的前提下,推导了半无限大体受热冲击作用时热弹性响应的解析表达式,通过求解分析,得到了热冲击下热波、热弹性波的传播规律,位移场、温度场以及应力场的分布情况,以及物性随温度相关性对热弹性响应的影响效果。结果表明：当考虑材料物性随温度的变化时,热波、热弹性波的传播以及各物理场的分布均受到不同程度的影响,且物性随温度相关性对热弹性响应的作用效果将受到材料热-力耦合特性的影响。     

物性与温度相关材料广义热弹性模型及渐近分析

计及材料物性与温度的相关性,基于Clausius不等式和L-S广义热弹性理论,通过对自由能公式的高阶展开,构建了具有变物性特征的广义耦合热弹性动力学模型。推导了各向同性材料表面受热冲击问题的线性化控制方程组,利用热冲击的瞬时特征,借助于Laplace正、逆变换技术及其极限性质,给出了变物性条件下一维热冲击问题的温度场、位移场和应力场的渐近表达式。通过算例,得到了热冲击作用下各物理场的分布规律以及材料物性与温度相关性对于热弹性响应的影响规律。结果表明：材料物性与温度相关性对于各物理场的阶跃位置、阶跃间隔以及阶跃峰值均产生影响,但值得注意的是,相比于位移场和应力场的显著影响,其对温度场的影响效果并不明显。     

短脉冲激光加热分数阶导热及其热应力研究

短脉冲激光加热引起材料内部复杂的传热过程及热变形,现有的以Fourier定律或Cattaneo-Vernotte松弛方程结合弹性理论为框架建立起来热应力理论在刻画其热物理过程存在严重缺陷. 本文基于分数阶微积分理论, 以半空间为研究对象, 建立了分数阶Cattaneo热传导方程和相应的热应力方程, 给出了问题的初始条件和边界条件, 采用拉普拉斯变换方法, 给出了非高斯时间分布激光热源辐射下温度场和热应力场的解析解, 研究了短脉冲激光加热的温度场及热应力场的热物理行为. 数值计算中, 首先对理论解进行数值验证, 然后取分数阶变量$p=0.5$研究温度场和热应力场的变化特点及激光参数对温度和热应力的影响,最后数值计算分数阶参数对温度和热应力场的影响. 计算结果表明, 分数阶Cattaneo传热方程和热应力方程描述的温度和热应力任然具有波动特性,与经典的Fourier传热模型和标准的Cattaneo传热模型相比, 分数阶阶次越大, 热波波速越小, 热波波动性越明显; 反之, 则热波波速越大, 热扩散性越强.激光加热和冷却的速度越快, 温度上升和下降的速度越快, 压应力和拉应力交替变化越快, 温度变化幅值越小, 热应力幅值影响不明显.      

铁木辛柯梁中的卸载弯曲波及二次断裂

半无限长梁承受恒定弯矩作用后, 如果自由端的初始弯矩突然释放, 将在梁中激发出一列卸载弯曲应力波. 采用铁木辛柯梁和瑞利梁来研究突然卸载所激发出的弯曲波的传播特征. 利用拉普拉斯变换方法进行分析, 首先推导出铁木辛柯梁和瑞利梁中的卸载弯曲波的像函数解析解, 采用数值反变换方法给出了时域上波传播的响应解, 并研究了梁中各点的横向位移、弯矩和剪力随时间的变化规律. 计算结果表明: 与简化的欧拉梁不同, 旋转惯性的引入使铁木辛柯梁和瑞利梁中的弯曲波传播具有强烈的局部化效应, 特别是梁中各点经历的弯矩变化, 和其距离自由端的位置相关, 不同时刻的弯矩峰值大小不同;瑞利梁中离自由端不同距离各点的峰值弯矩先增大后降低, 最后达到一个渐近值;铁木辛柯梁中各点的峰值弯矩总体上随着时间单调增大到同一个渐近值, 该渐近值与欧拉梁中的峰值弯矩值相同, 均为1.43.切应力效应的引入进一步降低了铁木辛柯梁中卸载弯曲波的波速, 同时也使得铁木辛柯梁中弯矩峰值的最大值小于瑞利梁中的最大值. 对于脆性细长梁的纯弯曲断裂, 铁木辛柯梁可以较好地预测二次断裂的发生位置, 相应的碎片尺寸约为7倍梁横截面厚度.      

无黏流体与固体界面的漏瑞利波

漏瑞利波存在于半无限无黏性流体和半无限固体媒质的界面处. 首先推导流固无限各向同性介质界面处漏瑞利波的特征方程和位移及应力的解析计算公式. 然后结合典型结构通过数值计算研究了漏瑞利波特性以及位移和应力在流体和固体中的分布规律. 数值计算结果表明漏瑞利波的相速度和衰减随流固密度比的增大而增大, 在流固界面上法向位移连续而切向位移不连续. 流固密度比对固体媒质中沿垂直于漏瑞利波的传播方向的位移、正应力和剪应力有比较大的影响,而对沿漏瑞利波的传播方向的正应力几乎没影响. 为利用漏瑞利波的无损检测与评价提供了理论基础.      

Thermoelastic solutions for thermal distributions moving over thin slim rod under memory-dependent three-phase lag magneto-thermoelasticity

Abstract

Enlightened by the Caputo fractional derivative, the present study deals with a novel mathematical model of generalized thermoelasticity to investigate the transient phenomena due to the influence of magnetic field and moving heat source in a rod in the context of three-phase lag (TPL) theory of thermoelasticity. Both ends of the rod are fixed and heat insulated. Employing Laplace transform as a tool, the problem has been transformed into the space-domain and solved analytically. Finally, solutions in the real-time domain are obtained by applying the inverse Laplace transform. Numerical calculation for stress, displacement, and temperature within the rod is carried out and displayed graphically. The effect of moving heat source speed on temperature, stress, and temperature is studied. It is found from the distributions that the temperature, thermally induced displacement and stress of the rod are found to decrease at large source speed. For the better understanding of the effect of moving heat source on all the distributions, three animations are added.     

Generalized thermoelastic infinite transversely isotropic body with a cylindrical cavity due to moving heat source and harmonically varying heat

In this paper, the induced temperature, displacement, and stress fields in an infinite transversely isotropic unbounded medium with cylindrical cavity due to a moving heat source and harmonically varying heat are investigated. This problem is solved in the context of the linear theory of generalized thermoelasticity with dual phase lag model. The governing equations are expressed in Laplace transform domain. Based on Fourier series expansion technique the inversion of Laplace transform is done numerically. The numerical estimates of the displacement, temperature and stress are obtained and presented graphically. The theories of coupled thermoelasticity, generalized thermoelasticity with one relaxation time, and thermoelasticity without energy dissipation can extracted as special cases. Some comparisons have been shown in figures to present the effect of the heat source, dual phase lags parameters and the angular frequency of thermal vibration on all the studied fields.     

Generalized solutions of transient thermal shock problem with bounded boundaries

In this work, the generalized thermoelastic solutions with bounded boundaries for the transient shock problem are proposed by an asymptotic method. The governing equations are taken in the context of the generalized thermoelasticity with one relaxation time (L–S theory). The general solutions for any set of boundary conditions are obtained in the physical domain by the Laplace transform techniques. The corresponding asymptotic solutions for a thin plate with finite thickness, subjected to different sudden temperature rises in its two boundaries, are obtained by means of the limit theorem of Laplace transform. In the context of these asymptotic solutions, two specific problems with different boundary conditions have been conducted. The distributions of displacement, temperature and stresses, as well as the propagations, intersections and reflections of two elastic waves, named as thermoelastic wave and thermal wave separately, are obtained and plotted. These results are agreed with the results obtained in the existing literatures.     

Relaxation Effects of a Saturated Porous Media Using the Two-Dimensional Generalized Thermoelastic Theory

A model of the equations of a generalized thermoelasticity (GT) with relaxation times for a saturated porous medium is given in this article. The formulation can be applied to the GT theories: Lord–Shulman theory, Green–Lindsay theory, and Coupled theory for the porous medium. A two-dimensional thermoelastic problem that is subjected to a time-dependent thermal/mechanical source is investigated with the model of the generalized porous thermoelasticity. By using the Laplace transform and the Fourier transform technique, solutions for the displacement, temperature, pore pressure, and stresses are obtained with a semi-analytical approach in the transform domain. Numerical results are also performed for portraying the nature of variations of the field variables. In addition, comparisons are presented with the corresponding four theories.     

Transient thermopiezoelectric response of a one-dimensional functionally graded piezoelectric medium to a moving heat source

The thermopiezoelectricity problem of a one-dimensional (1-D), finite length, functionally graded medium excited by a moving heat source is investigated in this paper. The Lord and Shulman theory of generalized coupled thermoelasticity is employed to account for both the finite speed of thermal waves and coupling of temperature field with displacement and electric fields. Except thermal relaxation time and specific heat, which are taken to be constant for simplicity, all other properties are assumed to vary exponentially along the length through an arbitrary non-homogeneity index. Laplace transform has been used to eliminate the time effect, and three coupled fields, namely, displacement, temperature, and electric fields are obtained analytically in the Laplace domain. The solutions are then inverted to time domain using a numerical Laplace inversion method. Numerical examples are displayed to illustrate the effects of non-homogeneity index, length and thermal relaxation time on the results. When the medium is homogeneous, the results of the current paper are reduced to exactly the same results available in the literature.     

考虑非局部效应和记忆依赖微分的广义热弹问题

现有的广义热弹理论主要适用于求解时间尺度极短但空间尺度仍属宏观尺度的广义热弹问题的动态响应,而当所研究的弹性体的特征几何尺寸也属微尺度时,弹性体的力学响应将呈现出强烈的尺寸相关性,现有的广义热弹理论不再适用. 本文基于通过非局部效应和记记依赖微分修正的广义热弹性理论,研究了两端固定、受移动热源作用的有限长热弹杆的动态响应. 建立了问题的控制方程,给出了问题的初始条件及边界条件,运用拉普拉斯变换及其数值反变换,对方程进行了求解. 数值计算中,首先考察了时间延迟因子对模型所预测各物理量分布的影响;然后对比了模型中的时间延迟因子在两种不同类别核函数下(通过归一化条件修正和未修正形式)对各物理量分布的影响效应;最后考察了考虑新的可以描述尺寸效应的非局部因子对无量纲温度、位移及应力的影响,并用图形进行了示例. 结果表明, 时间延迟因子增大,各物理量的峰值变大,传播距离变小,且时间延迟因子在归一化条件修正过的核函数下影响更加显著;非局部参数几乎不影响无量纲温度的分布,轻微影响无量纲位移的分布,但对无量纲应力的峰值的影响显著.      

Effect of rotation in magneto-thermoelastic transversely isotropic hollow cylinder with three-phase-lag model

This article deals with the various heat source responses in a transversely isotropic hollow cylinder under the purview of three-phase-lag (TPL) generalized thermoelasticity theory. In presence of magnetic field and due to the rotating behavior of the cylinder, the governing equations are redefined for generalized thermoelasticity with thermal time delay. In order to obtain the stress, displacement and temperature field, the field functions are expressed in terms of modified Bessel functions in Laplace transformed domain. When the outer radius of hollow cylinder tends to infinity, the corresponding results are discussed. Finally an appropriate Laplace transform inversion technique is adopted.