轴对称相变热传导变分原理及其应用

给出了轴对称相变热传导问题的偏微分方程及三类边界条件,构造了其相应的泛函,证明了一阶变分为零与原问题的等价性。采用等效热容法处理相变潜热。最后,对一个工程中典型的轴对称相变热传导问题-电渣重熔中的金属凝固过程-进行了相界面的模拟计算,计算结果与实验值吻合。     

基于边界积分法的气泡动态特性综述

近年来,边界积分法(boundary integral method,BIM)被普遍应用于气泡动力学模拟,本文综述了边界积分法及其相关技术在气泡动力学特性模拟中的应用与发展.首先,讨论了气泡的重要性及边界积分法的应用;其次,讨论了气泡动态特性的数值模拟,从射流冲击前的单连通域到射流冲击后的环状气泡即双连通域的发展过程,其中包括轴对称模型和三维模型;再次,讨论了气泡运动数值模拟过程中的两种关键技术;最后,综述了近边界气泡的研究进展,并在上述基础上提出了一些尚需进一步解决的问题.      

扁薄球壳非对称大变形问题

本文用修正选代法研究了扁球壳非对称大变形问题，求得了在线性液体载荷作用下的扁球壳变形的二次近似解析解并绘出了摄动点的挠度与载荷的特征曲线族．应用本文方法还可对其他板壳的非轴对称大变形问题进行讨论．本文通过算例对平板及不同初挠度的扁球壳大挠度变形进行了讨论．     

热及电场诱导石英光纤的电光系数

利用多载流子模型及单轴对称和光激励机理,从理论上计算了经热及电场诱导后的石英光纤的电光系数γ与D型光纤的距离d、诱导时间t和外加电压V的关系。结果表明,尽量缩短d并在适当时间内诱导,能有效提高电光系数;电光系数与外加电压近似平方根关系：γ33与γ13的比值非常接近3。理论结果与实验报道相当一致。     

轴对称粗糙圆杆的扭转变形

本文旨在研究轴对称表面粗糙圆杆的扭转变形。通过微元法,推导了轴对称表面粗糙圆杆的控制微分方程。结合摄动法和离散傅里叶变换,获得了粗糙圆杆的扭转角摄动解。对比典型粗糙圆杆的材料力学解析解或有限元解,验证了本文摄动解的有效性。通过系统计算,探究了粗糙面的统计参数对于扭转角的影响规律并建立了经验公式。本文的研究成果拓展了材料力学中扭转问题解的范围,并为数学物理方法提供了具体的力学实践。     

考虑接触效应的具脱层轴对称层合圆板的非线性动力响应

基于von Karman板理论,利用三分区模型,建立了在面内压力和横向荷载联合作用下具脱层的轴对称正交层合圆板的非线性运动微分方程,其中,考虑了横向剪切效应和脱层接触效应.在此基础上,利用正交配点法进行了求解,并着重讨论了脱层之间的接触效应对结构非线性动力响应的影响.     

上覆单相弹性层的饱和地基上弹性圆板轴对称竖向振动分析

基于弹性层和饱和土半空间轴对称弹性波动方程，运用Hankel积分变换方法，得到它们在变换空间内的解．进而由层间完全接触条件及圆板底面的混合边值条件，构造一组描述上覆单相弹性层的饱和地基上弹性圆板轴对称竖向振动的对偶积分方程．将该对偶积分方程化为易于数值计算的第二类Fredholm积分方程，求得地基表面动力柔度系数随无量纲频率的变化曲线及弹性圆板的相对位移幅值．     

Non-Axisymmetric Oscillation of Acoustically Levitated Water Drops at Specific Frequencies

A category of non-axisymmetric oscillations of acoustically levitated water drops was observed. These oscillations can be qualitatively described by superposing a sectorial oscillating term upon the initial oblate shape resulting from the effect of acoustic radiation pressure. The oscillation frequencies are around 25 Hz for the 2-lobed mode and exactly 50 Hz for the 3- and 4-1obed modes. These oscillations were excited by the disturbance from the power supply. For the same water drop, higher mode oscillations were observed with more oblate initial shape, indicating that the eigenfrequencies of these non-axisymmetric oscillations decrease with increasing initial distortion. The maximum velocity and acceleration within the oscillating drop can attain 0.3 m·s^-1 and 98.7 m·s^-2 respectively, resulting in strong fluid convection and enhanced heat and mass transfer.     

Experimental investigation about the effect of non-axisymmetric wake impact on a low speed axial compressor

Non-axisymmetric wake impact experiments were carried out after the best exciting frequency for a low speed axial compressor had been found by axisymmetric wake impact experiments. When the number and circumferential distribution of inlet guide vanes （IGV） are logical, the wakes of non-axisymmetric IGVs can exert beneficial unsteady exciting effect on their downstream rotor flow fields and improve the compressor＇s performance. In the present paper, four non-axisymmetric wake impact plans were found working better than the axisymmetric wake impact plan. Compared with the base plan, the best non-axisymmetric plan increased the compressor＇s peak efficiency, and the total pressure rise by 1.1 and 2%, and enhanced the stall margin by 4.4%. The main reason why non-axisymmetric plans worked better than the axisymmetric plan was explained as the change of the unsteady exciting signal arising from IGV wakes. Besides the high-frequency components, the nonaxisymmetric plan generated a beneficial low-frequency square-wave exciting signal and other secondary frequency components. Compared with the axisymmetric plan, multifrequency exciting wakes arising from the non-axisymmetric plans are easier to get coupling relation with complex vortices such as clearance vortices, passage vortices and shedding vortices.     

压电材料轴对称有限元分析

给出了横观各向同性压电材料轴对称问题有限元法列式,叙述了压电材料有限元法分析中的一些特殊处理步骤,包括无量纲化和特征值问题计算中对电势自由度的凝聚。对压电材料轴对称问题的一些经典静力问题进行有限元计算,同时对压电圆板的轴对称自由振动进行了计算,和解析结果作了比较,二者符合良好。