Microstructure characterization of short-chain branching polyethylene with differential scanning calorimetry and successive selfnucleation/annealing thermal fractionation

A series of the copolymers of ethylene with 1-hexene(M1–M9) synthesized by metallocene catalyst Et[Ind]2ZrCl2/MAO was studied by differential scanning calorimetry and successive self-nucleation and annealing(SSA) thermal fractionation. The distribution of methylene sequence length(MSL) in the different copolymers was determined using the SSA method. The comonomer contents of samples M4 and M5 are 2.04 mol% and 2.78 mol%, respectively. Both M4 and M5 have low comonomer content and their MSL distribution profiles exhibit a monotonous increase trend with their MSL. The longest MSL of M5 is 167, and its corresponding molar percent is 43.95%, which is higher than that of M4. Moreover, the melting temperature(Tm) of M5 is also higher than that of M4. The comonomer contents of samples M7, M8, and M9 are 8.73 mol%, 14.18 mol% and 15.05 mol%, respectively. M7, M8, and M9 have high comonomer contents, and their MSL distribution profiles display unimodality. M7 has a lower peak value of 33 and a narrow MSL distribution, resulting in a Tm lower than that of M8 and M9. The MSL and its distribution are also key points that influence the melting behavior of copolymers. Sometimes, MSL and its distribution of copolymers have a greater impact on it than the total comonomer contents, which is different from traditional views.     

Electrospinning of nylon-6,6 solutions into nanofibers: Rheology and morphology relationships

The relationship between the rheological properties of nylon-6,6 solutions and the morphology of their electrospun nanofibers was established. The viscosity of nylon-6,6 in formic acid(90%) was measured in the concentration range of 5 wt%-25 wt% using a programmable viscometer. Electrospinning of nylon-6,6 solutions was carried out under controlled parameters. The chemical structure, morphology and thermal properties of the obtained nanofibers were investigated using Fourier transform infrared spectroscopy(FTIR), scanning electron microscopy(SEM) and differential scanning calorimetry(DSC), respectively. Entanglement concentration(ce) was found to be 15 wt% and a power law relationship between specific viscosity and solution concentration was observed with exponents of 2.0 and 3.3 for semi-dilute unentangled(c ce) and semi-dilute entangled(c ce) regimes, respectively. The diameter and uniformity of the nanofibers were found to be dependent on the viscosity. Moreover, the average diameter of electrospun nanofibers was found to be dependent on zero shear rate viscosity and normalized concentration(c/ce) in a power law relationship with exponents of 0.298 and 0.816, respectively. For nylon-6,6 solutions, the entanglement concentration(ce = 15 wt%) provides the threshold viscosity required for the formation of a stable polymeric jet during electrospinning and producing uniform beadless fibers. For concentrations less than ce, beaded fibers with some irregularities are formed. DSC analysis showed an increase in crystallinity of all electrospun samples compared to original polymer. Furthermore, Based on FTIR spectroscopy, α phase is dominant in electrospun nanofibers and minor amount of β and γ phases is also available.     

Synthesis,characterization, thermal stability and antibacterial activity of coumarin based methacrylate copolymers

Monomer of 7-methacryloyloxy-4-methylcoumarin(MAOMC) was synthesized and characterized by FTIR, 1H-NMR and 13C-NMR spectroscopy. Copolymers of MAOMC with butoxyethylmethacrylate(BOEMA) at different feed compositions were prepared by free radical solution polymerization at(70 ± 1) °C in ethylmethylketone(EMK) using benzyl peroxide(BPO) as an initiator. The copolymers were characterized by FTIR and 1H-NMR spectroscopy. Thermogravimetric analysis(TGA) and differential scanning calorimetry(DSC) of the copolymers showed moderate thermal stability and higher Tg values. Gel permeation chromatography(GPC) was used to find out the molecular weights of the different copolymers. Antibacterial activities of the copolymers were also investigated against the selected pathogenic bacteria's. The antibacterial activity of the copolymer increases as the MAOMC content increases in the copolymer. This shows that coumarin moiety plays a very important role in the antibacterial activity.     

基于线性算子的广义逆矩阵的几何表示北大核心

广义逆矩阵是矩阵理论的重要内容.由于广义逆矩阵的定义众多,计算较为繁杂,使得初学者很难理解和掌握其本质.基于线性方程组求解问题的等价表示,从线性算子的角度展示多种广义逆矩阵定义的背景及其几何直观意义.通过对一个特殊算例的分析与求解,实现了对多种广义逆矩阵的几何解释及其在线性方程组求解中的作用,淡化了广义逆矩阵计算的繁杂,加深初学者对广义逆矩阵的理解与掌握.     

分布振子复合板的模态阻尼及多点激励下阻尼减振相关性

分布阻尼振子可拓宽结构减振频带,因此可将振子分布于板中以形成复合板（简称“分布振子复合板”）,进而实现较宽的减振频带．对于多点支撑处受到宽频非一致激励（例如在不同激励点处的激励频率、幅值与相位有差异）的分布振子复合板,目前还缺乏有效简便的优化控制指标．在作者之前的研究中,针对含分布振子的梁推导了基于模态应变能的模态阻尼计算理论,讨论了模态阻尼与单点激励下梁的减振效果的相关性,并应用于宽频减振设计优化．本文进一步将模态阻尼计算理论推广到分布振子复合板,并将研究从梁的单点激励扩展到板的多点非一致激励下的阻尼减振相关性．首先,在利用模态应变能法推导得到分布振子复合板的模态阻尼计算公式后,从理论上讨论了不同边界条件与模态阶次对计算结果的影响,以及计算理论的适用性．而后,进一步通过有限元参数分析了边界条件、频率比、模态阶次与质量比的影响．最后,通过算例分析了无振子板或分布振子复合板在四个激励点具有多种幅值与相位组合情况下的稳态响应．结果表明,推导的模态阻尼计算公式可正确预测不同边界条件下的模态阻尼,且理论预测的模态阻尼与基板的稳态平均加速度减小率、稳态峰值应变能减小率均有较高的相关性．     

不同细料含量土石混合料塑性行为离散元模拟

土石混合料是指由大粒径的块石和作为填充成分的细粒土组成的二元混合料, 其塑性行为与细料含量密切相关. 目前对细粒含量如何影响土石混合料塑性行为及其细观机制的研究尚不充分, 为此本文开展了不同细料含量土石混合料的二维离散元数值模拟, 基于二阶功失稳准则与细观力学理论, 探究了细料含量对石料骨架土石混合料失稳特性与非关联流动特性的影响, 并揭示了细料含量影响土石混合料塑性力学行为的细观机制. 研究结果表明, 细颗粒可通过限制集合体塑性变形从而起到促进集合体整体稳定的作用; 细颗粒控制颗粒集合体塑性变形的方向(即塑性势面法方向), 随着细料含量增大, 土石混合料的塑性势面法方向和屈服面法方向之间的夹角减小, 非关联流动性减弱, 材料分岔失稳区域变窄; 尽管加入到石颗粒中的部分细颗粒与石颗粒共同承担骨架作用, 但是细颗粒的加入不影响颗粒集合体的力学状态, 不改变材料屈服面法方向. 相关研究结果可为建立考虑细料含量的土石混合料弹塑性本构模型提供理论依据.      

交通载荷作用下跨海桥梁-电缆组合结构随机振动分析

电缆沿桥跨海铺设是海缆铺设的一种新的形式, 针对由汽车和列车交通载荷诱发的沿跨海桥梁敷设电缆的振动问题, 建立了桥梁-电缆的整体组合结构分析模型, 将汽车和列车的作用载荷简化为移动的随机集中载荷序列, 发展虚拟激励法(pseudo-excitation method, PEM)用于分析移动随机载荷作用下电缆位移和应力响应的标准差及演变功率谱 (power spectral density, PSD), 并研究了汽车和列车运行速度对电缆动力响应标准差的影响. PEM将移动随机载荷问题转化为特定频率简谐移动载荷作用下的动力响应分析, 能够计算得到与Monte Carlo (MC) 方法非常吻合的电缆动力响应标准差, 但所需的时域响应分析次数远少于MC方法. 数值结果表明, 随着汽车和列车运行速度的提升, 电缆位移和应力标准差呈现增大的趋势; 在汽车和列车交通载荷作用下, 铝护套的位移标准差和功率谱的值比缆芯要大, 这可能会使得电缆的疲劳破坏首先发生在铝护套层, 本文工作对电缆沿桥跨海铺设实际工程具有一定的借鉴意义.      

优化迭代步长的两种改进增量谐波平衡法

增量谐波平衡法(IHB法)是一个半解析半数值的方法, 其最大优点是适合于强非线性系统振动的高精度求解. 然而, IHB法与其他数值方法一样, 也存在如何选择初值的问题, 如初值选择不当, 会存在不收敛的情况. 针对这一问题, 本文提出了两种基于优化算法的IHB法: 一是结合回溯线搜索优化算法(BLS)的改进IHB法(GIHB1), 用来调节IHB法的迭代步长, 使得步长逐渐减小满足收敛条件; 二是引入狗腿算法的思想并结合BLS算法的改进IHB法(GIHB2), 在牛顿-拉弗森(Newton-Raphson)迭代中引入负梯度方向, 并在狗腿算法中引入2个参数来调节BSL搜索方式用于调节迭代的方式, 使迭代方向沿着较快的下降方向, 从而减少迭代的步数, 提升收敛的速度. 最后, 给出的两个算例表明两种改进IHB法在解决初值问题上的有效性.      

Hermite梯度重构核近似配点法及其在功能梯度材料板的静力分析中的应用

由于直接配点法在求解边值问题时边界上的求解精度较低,本文提出了Hermite梯度重构核近似配点法（HGCM）来改进边界求解精度。重构核近似是无网格法中一种常用的近似函数,但是其在求解高阶导数时格式复杂且非常耗时。HGCM采用梯度重构核近似构建形函数的任意高阶导数,提高了计算效率;通过Hermite配点法构建离散方程,提高了边界求解精度。这种方法在求解对应变系数四阶偏微分方程的功能梯度材料板的静力问题时精度高,计算效率高,并可进一步推广应用于高阶偏微分方程描述的边值问题。     

基于神经网络的核电厂设备易损性分析

核电结构的易损性分析是核电厂地震安全评估中至关重要的一环, 但是由于核电结构的复杂性以及考虑土?结相互作用SSI时较大的计算规模, 使得计算核电厂设备易损性曲线十分耗时. 为发展高效的核电厂设备易损性分析方法, 本文采用核电结构土?结相互作用分析的分区计算方法, 并利用有限的SSI分析结果建立神经元模型ANN代替有限元模型, 分别基于对数正态假定的回归法和蒙特卡洛法进行了设备易损性分析. ANN数值模拟包括了以下内容: (1)基于半偏相关系数选择最相关的地震动参数作为ANN输入, 并通过交叉检验建立神经元模型; (2)量化研究ANN数值模拟的预测不确定性, 其中包含了由于简化地震动输入引起的随机不确定性和训练样本缺失引起的认知不确定性; (3)基于ANN模型预测结果分别采用蒙特卡洛法和基于对数正态假定的回归法进行设备的易损性分析. 本文探讨了不同的地震强度指标以及土层材料的不确定性对易损性曲线的影响, 同时验证了回归法中对数正态模型假定的基本合理性, 为核电厂设备易损性分析提供了一种可能方向.