Starting solutions for oscillating motions of a generalized Burgers’ fluid in cylindrical domains

Exact solutions for the motions of a generalized Burgers’ fluid due to longitudinal and torsional oscillations of a circular cylinder are obtained using Hankel transform and Laplace transform. These solutions are expressed as sum of steady-state and transient solutions. They describe the motion of the fluid for some time after its initiation. After that time, when the transients disappear, the motion is described by the steady-state solution which is periodic in time and independent of the initial conditions. Finally, by means of graphical illustrations, the velocity field is determined for sine and cosine combined oscillations of the boundary.     

随机Burgers方程的有限体积方法

本文应用有限体积方法研究带有不确定性输入参数的Burgers方程,其特点是在时间离散上采用二阶有限差分,在控制体上对非线性对流项采用不同的定义方式.在边界条件和粘性系数存在随机扰动的情况下,通过数值模拟验证了算法的收敛性和稳定性,并进一步测试了通过加密空间网格点的方法来抑制边界和粘性系数扰动对计算结果的影响.     

岩石非定常Burgers蠕变模型及其参数识别

针对岩石蠕变的非线性特征,提出了一种非线性黏壶元件,并分别替换Burgers模型中的两个线性黏壶元件,从而建立了一种非定常参数Burgers模型。推导了非定常Burgers模型的一维蠕变方程,分析模型参数λ₁与λ₂取值范围对蠕变方程的影响,从理论上确定了非定常模型能够描述蠕变的3个阶段。在此基础上,将非定常Burgers模型的蠕变方程推广至三维应力状态下,并基于Levenberg-Marquardt算法对向家坝岩石的三轴压缩蠕变试验曲线进行拟合及参数识别。通过对比定常与非定常Burgers模型的拟合曲线与相关系数,可以发现非定常Burgers模型拟合效果更好,且能够准确描述包括加速蠕变在内的岩石三阶段蠕变特性,验证了所构建非线性模型的适用性与合理性。     

广义Burgers方程的非经典相似约化

讨论了具任意系数的广义Burgers方程的相似约化，这种约化是基于Bluman和Cole所提出的非经典对称群方法。给出了这些约化所对应的常微分方程相应的一些新的精确特解，从而进一步拓展了利用非经典对称群研究变系数非线性偏微分方程的研究领域。     

二维Burgers方程的RKDG有限元解法?

本文应用RKDG有限元方法求解具有周期边界条件的二维非粘性Burgers方程,并给出稳定性分析和误差估计。基于一致网格剖分,采用Q1矩形元和广义斜率限制器进行数值模拟。在相同网格剖分下与三角元相比,矩形元剖分的自由度较少,计算复杂度低,易于实现。     

Burgers＇方程的特征混合有限元数值模拟

本文对Burgers’方程采用特征混合有限元方法进行数值模拟，证明了特征混合元格式的稳定性。作为数值例子，我们计算了正弦波传播和冲击波传播，通过与混合元和有限元方法的比较，说明了该方法在粘性系数逐渐减小时对锋线前沿处理的有效性。     

Burgers′方程的特征混合有限元数值模拟

本文对Burgers′方程采用特征混合有限元方法进行数值模拟,证明了特征混合元格式的稳定性.作为数值例子,我们计算了正弦波传播和冲击波传播,通过与混合元和有限元方法的比较,说明了该方法在粘性系数逐渐减小时对锋线前沿处理的有效性.     

考虑失效的非线性Burgers’海冰模型及其数值应用

该文以发表的海冰蠕变实验为基础,建立考虑损伤失效的非线性Burgers’海冰模型。此模型在Jordaan模型基础上考虑韧脆转变应变率影响,使原有模型应用范围扩展至较高应变率。在模型中引入经验损伤失效准则,以准确反映不同应变率、围压等工况下海冰损伤失效过程。应用FORTRAN语言,通过隐式积分中心法对此模型进行数值求解,并将其嵌入到有限元软件LS-DYNA中。对实验室尺度的柱状冰蠕变实验、真实尺度冰块-刚性板碰撞场景进行数值模拟,分析蠕变实验的轴向应变-时间曲线,讨论冰块碰撞得到的压力-面积曲线及碰撞力时历曲线。这些数值模拟结果与实验及真实碰撞结果吻合较好,验证此模型的正确性及其对工程实际进行模拟的可行性。     

非线性Burgers方程求解的自适应Euler-Lagrange无单元Galerkin方法

建立了求解非线性Burgers方程的自适应Euler-Lagrange无单元Galerkin(adaptiveEuler-Lagrange element-free Galerkin,AELEFG)方法.该方法将Euler形式的非线性Burgers方程转化成Lagrange形式的纯扩散方程,使用节点自适应无单元Galerkin(element-free Galerkin,EFG)方法求解该扩散方程,并沿特征路径反向追踪对对流项进行处理.数值结果表明,运用AELEFG方法求解非线性Burgers方程具有较高的精度及稳定性.     

基于Burgers模型对缓冲材料EPE压缩蠕变行为的分析

目的 为解决缓冲材料发泡聚乙烯因蠕变引起保护失效的问题,基于Burgers模型,分析载荷、应力保持时间对EPE压缩蠕变行为的影响。方法 根据不同应力下的不同保持时长压缩蠕变试验结果,拟合EPE不同应力下的压缩蠕变试验数据,分析不同应力、应力保持时间下的EPE蠕变过程中蠕变总量、弹性应变、黏弹性应变和黏性应变的变化规律。结果 Burgers四元件力学模型对EPE不同应力下的压缩蠕变实验数据拟合度为0.992 4～0.998 9。在同一应力保持时间下,随着应力从3.3 kPa增加到5.3 kPa,弹性模量E₁、弹性模量E₂、黏度系数η₂、黏度系数η1都逐渐减小,蠕变总量、黏性应变呈非线性显著增加,弹性应变、粘弹性应变呈线性微量增加;在同一应力下,随着应力保持时间从20 d增加到120 d,弹性应变一直保持不变,占蠕变总量的比例降低,粘弹性应变先微量增加后保持不变,占蠕变总量的比例降低,黏性应变增加,占蠕变总量的比例增加。结论 Burgers模型可较准确地模拟EPE不稳定蠕变阶段和稳定蠕变阶段的压缩蠕变行为;应力的增加导致EP...     

一类广义Kdv—Burgers型方程的谱方法及其误差估计

本文讨论了一类带三阶粘性项的广义Ｋｄｖ－Ｂｕｒｇｅｒｓ型方程的周期边值问题。用谱方法（连续的和离散的）结合Ｂｅｍｓｔｅｉｎ估计建立了所论问题的逼近解，证明了古典光滑解的存在性和唯一性，建立了近似解的收敛性和谱方法格式的误差估计。     

一类广义Kdv－Burgers型方程的谱方法及其误差估计

本文讨论了一类带三阶粘性项的广义Ｋｄｖ－Ｂｕｒｇｅｒｓ型方程的周期边值问题。用谱方法（连续的和离散的）结合Ｂｅｍｓｔｅｉｎ估计建立了所论问题的逼近解，证明了古典光滑解的存在性和唯一性，建立了近似解的收敛性和谱方法格式的误差估计。     

一维Burgers方程的FD-SD法的后验误差估计及空间网格调节技术

讨论了一维Burgers方程的差分-流线扩散法的后验误差估计，并依此来实现空间网格局部的合理调整，所给的数值算例也验证了此方法的正确性和可行性。     

考虑围压对粗粒土蠕变特性影响的Burgers模型参数修正方法研究

传统的Burgers模型假设只有偏应力引起蠕变,而没有考虑围压对蠕变特性的影响,因此其主要用于描述岩石的蠕变特性。但不同于岩石,堆石料等粗粒土是由颗粒集合而成的摩擦型材料,其蠕变特性与围压密切相关。为了考虑围压对粗粒土蠕变特性的影响,该文首先推导了Burgers模型的三轴蠕变理论解,并根据各参数物理意义,提出一套简便实用的参数反演方法,用于获取同一围压不同偏应力下粗粒土的Burgers模型参数;进而总结并分析不同粗粒土的三轴蠕变实验结果,发现幂函数能较好地描述Burgers模型各参数随围压变化的规律;在此基础上,提出考虑围压对粗粒土蠕变特性影响的Burgers模型参数修正方法,并通过三组粗粒土的蠕变实验结果验证了所提方法的有效性。     

Loss of coherency and interphase α/β angular deviation from the Burgers orientation relationship in a Ti–6Al–4V alloy compressed at 800 °C

The mutual relationship between phases in two-phase titanium alloys, α_HCP and β_BCC, is such that: {0001}_α||{110}_β; $ \left\langle {11\bar{2}0} \right\rangle_{\user1{\alpha }} ||\left\langle {111} \right\rangle_{\user1{\beta }} $ , which in literature are known as Burgers orientation relationships. The coherency of the two phases is controlled by this crystallographic mutual relationship. Loss of coherency between phases during deformation can originate from a non-parallelism between the two boundary crystallographic planes. This study focuses on α_HCP/β_BCC interface coherency evolution in a lamellar Ti–6Al–4V alloy subjected to hot compression at 800 °C. The strain rate was 10^?3 s^?1 and deformation was carried out to average true strains of ε = 0.29, 0.69, and 1.20. Loss of coherency was found at strains ε ≥ 0.50. For these strains, the lamellar α + β microstructure also evolved to a spheroidized morphology. The loss of interface coherency was thus associated with the acceleration of the lamellar microstructure dynamic spheroidization.     

Crystal Structure of Monohydrate of γ-Modification of Rubidium Uranoniobate

The compound γ-RbNbUO₆·H₂O was prepared for the first time as single crystals, which were studied by X-ray diffraction. Crystal data: rhombic system, space group Pcab, a = 7.614(2), b = 11.219(2), c = 16.510(3) Å, Z = 8. The crystal structure is built from uranium-containing layers of the composition [NbUO₆] _2∝ ^δ? , infinite in two directions. The water molecules and rubidium atoms distributed over two randomly occupied positions are accommodated between the layers.     

Investigation of the Dynamics of Evaporation of Condensed Bodies on the Basis of the Law of Spectral‐Radiation Intensity of Particles

The fundamentals of radiation theory and the mechanism of evaporation of condensed bodies are presented. The distribution functions of particles of a body by energies and by the intensity of their transition from one energy level to another in the process of evaporation have been obtained based on the law of spectralradiation intensity of the body particles. The temperature dependence of the resulting vapor flow on the outer surface of a massive condensed body and a thin layer in equilibrium and nonequilibrium states, which, in the limit, transforms to the known Hertz–Knudsen formula, has been found.     

应力水平和纤维角度对CGF/PP复合材料蠕变行为的影响及其Burgers模型参数的数值预测

采用DMA的Creep模式分别测试了短时间内（15 min）聚丙烯（PP）在不同应力水平和温度下的单向拉伸蠕变行为,长时间内（10 h）连续玻璃纤维增强聚丙烯（CGF/PP）复合材料单层板在不同应力水平和不同纤维角度上的拉伸蠕变行为。利用Burgers黏弹性模型拟合了蠕变测试数据,构建了相关参数与应力水平和纤维角度的依赖性。结果表明:PP和CGF/PP单层板的蠕变柔量均随应力增大而显著增加,稳态蠕变速率也随之增加,蠕变模量保留率明显下降,PP基体的黏弹性主要决定了CGF/PP单层板在低应力水平下的蠕变行为; 30%应力水平下,偏轴拉伸的纤维角度在0°~90°范围内存在拉-剪耦合效应,在45°时最为显著,此时稳态蠕变速率和蠕变变形量最大;利用四元件Burgers黏弹性模型拟合各条件下蠕变曲线得到的数值模型与实验数据具有较好的相关性,相关系数达到0.99,从得到的数值模型可知相关模型参数存在明显的应力和角度依赖关系;利用模型参数的数值拟合公式分别预测10 MPa应力下0°纤维方向的蠕变曲线及45°纤维方向上30%应力水平的偏轴蠕变曲线均与实验曲线一致,表明本文得到的数值模型的可靠性。      

Magnetothermal Analysis of Nanocrystallization of Amorphous and Relaxations of Nanocrystalline Materials

For a few years it has been realized that nanocrystalline phases can be formed during crystallization of amorphous alloys annealed isothermally below the crystallization temperature of usual heating experiments. Data of this transformation monitored by the measurement of magnetic susceptibility are presented. A method using a magnetic balance with electronic stabilisation and combined computer facilities is applied. Constant heating and cooling rates as well as isothermal heat treatments are used. Magnetic measurements are able to detect the onset of the transformation of amorphous Ni-P alloys much earlier than was possible with differential scanning calorimetry. The transformation kinetics can be analyzed by means of the Avrami plot based on the Johnson-Mehl-Avrami equation.The kinetics of solid state reactions in the nanostructured material can be investigated similarly. Formation of a Ni-phase in a nanostructured Hf-Ni alloy could be detected in a very early stage, where calorimetric methods are not sensitive. Segregation phenomena could be detected from the experiments even after long time. The sensitivity of the applied method is not dependent on the heating rate as the sensitivity of scanning calorimetry is