椭圆边界上的自然积分算子及各向异性外问题的耦合算法

1.引 言为求解微分方程的外边值问题常需要引进人工边界（见[1-4]）,对人工边界外部区域作自然边界归化得到的自然积分方程即Dirichlet-Neumann映射,正是人工边界上的准确的边界条件（见[2-6]）,这是一类非局部边界条件.自然积分算子即Dirichlet-Neumann算子,     

考虑Soret和Dufour效应的方腔内双扩散自然对流格子Boltzmann模拟

采用格子Boltzmann方法,考虑Soret和Dufour效应,对内置高浓度发热圆的方腔内部双扩散自然对流现象进行数值模拟.高浓度发热圆位于方腔中心,四周壁面均为低温低浓度.在该模型中,用三个独立的LBGK方程分别模拟速度场、温度场和浓度场,并通过Boussinesq近似将它们耦合起来.分析Soret数和Dufour数对方腔内部双扩散自然对流的影响,得到流线图、等温线图、等浓度线图、发热圆表面平均Nusselt数和平均Sherwood数.结果表明：Soret和Dufour效应对方腔内双扩散自然对流影响明显,不能忽略.     

自然闪电条件下敷地线缆耦合试验

研制了一套能够同时测量线缆皮线和芯线感应电流的试验系统,研究自然闪电条件下敷地线缆的耦合问题。结果表明:不同位置处的线缆皮线感应电流波形基本一致,但幅值存在一定差异,说明感应电流空间分布不均匀; 所测线缆芯线和皮线感应电流的时域波形和频谱比较相似,能量集中在1 kHz~1 MHz之间; 正负地闪芯线感应电压波形均为单一脉冲型,波形持续时间10~49 μs; 正地闪线缆感应电压的幅值范围及幅值平均值都大于负地闪相应结果,说明正地闪产生的线缆耦合作用大于负地闪; 不同雷电过程的线缆感应电压幅值与磁感应强度有较小的相关性,而同一雷电过程则基本成线性关系; 正地闪线缆感应电压波形持续时间、半峰值宽度、10%~90%上升时间的范围及均值都比负地闪的要大。     

自然对流换热的高精度非结构网格有限体积法

用非结构网格有限体积法求解自然对流换热时,传统的对流项离散格式难以兼顾数值精度与计算效率,我们发展了一种耦合高精度格式的延迟修正方法,用于对流项的离散.高Re数下方腔驱动流数值计算验证了该方法具有较高的计算精度和较好的稳定性.Boussinesq流体的自然对流换热数值模拟,表明该方法能有效克服高Ra数时数值计算发散,可准确捕捉自然对流换热问题中不同偏心率下的等温线和流线分布特征.     

氨分子逐级键解离能降低的解释

采用理论计算方法解释了氨逐级解离能降低的现象。计算结果表明,随着N与H原子结合数目的减少,键解离能降低、键长增长;随着N与H原子结合数目的增多,N的2s电子跃迁到N的2p轨道上的几率增大,减小了屏蔽作用;更多电子从H的1s轨道迁移到N的2p轨道,增大了N和H之间的静电作用;单电子或孤对电子与N-H键夹角的增大减小了排斥作用。这3个因素造成NH3的逐级键解离能有降低的趋势。     

VIBRATION ANALYSIS OF A BEAM WITH EMBEDDED SHAPE MEMORY ALLOY WIRES

In this study, analytical relations for evaluating the exact solution of natural fre- quency and mode shape of beams with embedded shape memory alloy （SMA） wires are presented. Beams are modeled according to Euler-Bernoulli, Timoshenko and third order beam （Reddy） the- ories. A relation is obtained for determining the effect of axial load generated by the recovery action of pre-strained SMA wires. By defining some dimensionless quantities~ the effect of different me- chanical properties on the frequencies and mode shapes of the system are carefully examined. The effect of axial load generated by SMA wires with buckling load and frequency jump is accurately studied.     

DYNAMIC CHARACTERISTICS OF LAG VIBRATION OF A WIND TURBINE BLADE

Lagwise dynamic characteristics of a wind turbine blade subjected to unsteady aero- dynamic loads are studied in this paper. The partial differential equations governing the coupled longitudinal-transverse vibration of the blade with large bending deflection are obtained by ap- plying Hamilton＇s principle. The modal problem of the coupled vibration is handled by using the method of numerical integration of Green＇s function. Influences of the rotating speed, the pitch angle, the setting angle, and the aerodynamic loads on natural frequencies are discussed. Results show that： （I） Lagwise natural frequencies ascend with the increase of rotating speed; effects of the rotating speed on low-frequencies are dramatic while these effects on high-frequencies become less. （2） Influences of the pitch angle on natural frequencies are little; in the range of the normal rotating speed, the first frequency ascends with the increase of the absolute value of the pitch angle, while it is contrary to the second and third frequencies. （3） Effects of the setting angle on natural frequencies depend on the rotating speed; influences are not significant at low speed, while they are dramatic on the first frequency at high speed. （4） Effects of the aerodynamic loads on natural frequencies are very little; frequencies derived from the model considering aerodynamic loads are smaller than those from the model neglecting aerodynamic loads; relative errors of the results corresponding to two models ascend with the increase of the absolute value of the setting angle.     

应变梯度理论自然邻近混合伽辽金法

应变梯度理论考虑了位移二阶梯度对应变能密度函数的贡献,在本构关系中引入了与材料微结构特征尺寸相关的参数,可以唯象地解释尺度效应现象。基于约束变分原理,把位移与位移一阶梯度作为独立场变量,使用拉格朗日乘子法引入二者的协调关系,放松对试探函数连续性与完备性的要求,建立了二维及三维问题的应变梯度理论自然邻近混合伽辽金法。通过算例对方法的计算性能进行了考查,结果表明,该方法具有良好的数值精度,能够模拟材料力学性能的尺度效应。     

Theoretical Studies on the Dihydrogen Bonding Between Shortchain Hydrocarbon and Magnesium Hydride

The C--H…H dihydrogen-bonded complexes of methane, ethylene, acetylene, and their derivatives with magnesium hydride were systematically investigated at MP2/aug-cc-PVTZ level. The results confirm that the strength of dihydrogen bonding increases in the following order of proton donors： C（sp3）-H〈C（sp2）-H〈C（sp）-H and chlorine substituents enhance the C-H…H interaction. In the majority of the complexes with a cyclic structure, the Mg-H proton-accepting bond is more sensitive to the surroundings than C-H proton-donating bond. The nature of the electrostatic interaction in these C-H…H dihydrogen bonds was also unveiled by means of the atoms in mo- lecules（AIM） analysis. The natural bond orbital（NBO） analysis suggests that the charge transfer in the cyclic com- plexes is characteristic of dual-channel. The direction of the net charge transfer in the cyclic complexes is contrary to that previously found in dihydrogen bonded systems.     

流过半无限竖直可渗透壁面时的磁流体动力学自由对流

研究不可压缩粘性导电流体,流过半无限竖直可渗透平板时,将其偏微分形式的流动和传热的基本控制方程,应用适当的相似变换,简化为非线性的常微分方程组．对两种抽吸参数:大的和小的抽吸参数,采用摄动法得到变换后方程的近似解．数值结果表明,随着磁场参数和抽吸参数的增大,任意点的速度场在减小;磁场参数的影响,引起热边界层厚度的增大;速度和温度场随着热汇参数的增大而减小．