插值摄动法及其在力学中的应用

本文研究了最高阶导数乘以小参数，或出现奇点的微分方程的定解问题，用插值摄动法求得了一级近似解，它和通常的奇异摄动法（匹配法、多尺度法）的一级近似解的精度相同。     

非完善板屈曲路径的有限元增量摄动法

本文以Thompson一般稳定性理论为基础,提出非完善结构(有初始几何缺陷)屈曲平衡路径分析的有限元增量摄动法,它克服了增量迭代法及摄动法各自的缺点,利用增量摄动法,还建立了非完善板屈曲平衡路径的数学分析模型,对非完善矩形板在各种边界条件下的屈曲路径实现了数值程序分析,得到了符合实验的结果。     

SH波作用下各向异性介质中裂缝的侧向扩展摄动方法

本文利用摄动法求解在SH波作用下各向异性介质中半无限长裂缝的侧向扩展问题。摄动参数为裂缝的转向角=k。结果表明,强度因子的零阶摄动解具有O[(k)~2]的精度并指出强度因子与裂缝的长度和扩展速度有关。     

保守系统弱非线性振动问题的插值摄动解法

用插值摄动法求得了一类保守系统奇次弱非线性振动问题的一级近似解，精度好，甚至比多尺度法还更好，计算过程简单。     

摄动法分析各向异性介质中Ⅲ型裂缝的侧向扩展

本文内容分为两部分。首先用Green函数方法求解各向异性介质中Ⅱ型裂缝的扩展问题。在此基础上,利用摄动法求解各向异性介质中Ⅱ型裂缝的侧向扩展问题。摄动参数为转向角.结果表明,强度因子的零阶摄动解具有O[~2]的精度,方便了计算。最后进行了数值计算,给出在不同介质中以常速度侧向扩展的裂缝的强度因子随侧向扩展速度和转向角的变化关系。     

基于有限元分析的特征值反问题求解的逆摄动方法

本文研究特征值反问题的求解方法,根据广义特征值反问题理论和有限元法的特点,以转子系统平面梁单元有限元模型结构分析的特征值反问题求解为例,给出一种新的逆摄动方法,给出了本逆摄动法较完整的理论基础,给出了其逆摄动参数的显式计算公式及相应的取值方法,本逆摄动法也可推广到其他单元类型的有限元模型特征值反问题的求解。     

矩阵摄动理论在六轴机车横向运动稳定性分析中的应用

本文提出了一种分析机车横向运动稳定性的方法,即利用复膜态的矩阵摄动法来计算临界速度,该方法避免了反复计算矩阵的特征值从而可节约大量的计算时间,对矩阵摄动法计算精度的研究结果表明,该方法的的精度是足够的。     

线化摄动法结合权残法求解有阻尼的强非线性振动问题

本文用线化摄动法和权残法相结合的方法求解了一类有强阻尼的强非线性振动问题，有较好的精度。     

升阶试函数族在矩形板大挠度问题中的应用

为解决加权残值法求近似解的计算精度问题，将摄动法与加权残值法相结合，首先以板中心挠度为摄动参数进行摄动，将矩形板大挠度非线性偏微分方程组分解为线性偏微分方程组，然后用最小二乘法求解．求解中构造并应用了可以由控制参数，调节的升阶试函数族，计算结果与实验结果基本一致，与以前的研究比较，计算精度明显提高．该方法对于寻求最佳试函数和最佳近似值是一种有效的方法．     

用摄动法建立边界层方程

用摄动法建立边界层方程王培光，王振东（河北大学数学系，保定０７１００２）（天津大学力学系，天津３０００７２）边界层理论是普朗特（１８７５－１９５３年）对流体力学的最主要贡献之一，也是黏性流体力学重要的基础性理论．１９世纪末，流体力学沿着两条看来似无关...     

ON SOLVING HIGH-ORDER SOLUTIONS OF CHIEN’S PERTURBATION METHOD TO STUDY CONVERGENCE BY COMPUTER

In this paper, we have obtained the analytical formula of arbitrary n-th order perturbation solution which perturbation parameter is central deflection for circular thin plate under a concentrated load by means of its integral equation. All unkown constants of every perturbation solution can be determined by computer. Hence higher order perturbation solution is obtained. Based on the solution of higher order perturbation, asymptotical property and suitable interval of Chien’s perturbation method are also discussed.     

T型槽端面密封气膜热弹流润滑动态稳定性

对T型槽端面密封气膜热弹流润滑动态稳定进行了分析. 考虑端面热变形和弹性变形以及辅助密封的阻尼特性，数值分析了不同振动频率下密封气膜动态压力分布和温度分布规律，并利用小扰动方法分析了外界扰动频率对气膜刚度、阻尼和振幅的影响规律. 结果表明:高压和高速条件下，密封端面的弹性变形和热变形产生发散间隙，导致密封气膜厚度显著降低；外界扰动产生附加压力和温度分布，刚度随扰动频率的增加而迅速增加，阻尼随扰动频率的增加而迅速下降；一定扰动频率范围内，轴向振幅与扰动频率成对数线性关系增加，辅助密封阻尼使得密封气膜的振幅显著上升.      

A perturbation solution in the nonlinear theory of circular plates

In this paper, we analyzed some problems of nonlinear circular plates by means of perturbation method. The perturbation parameters chosen here are obtained from solving the equations and are not certain mechanical quantities given precedently. This is an extension of W. Z. Chien’s perturbation method, which uses the central deflection as the perturbation parameter.     

Lie symmetries,symmetrical perturbation and a new adiabatic invariant for disturbed nonholonomic systems

For a nonlinear nonholonomic constrained mechanical system with the action of small forces of perturbation, Lie symmetries, symmetrical perturbation, and a new type of non-Noether adiabatic invariants are presented in general infinitesimal transformation of Lie groups. Based on the invariance of the equations of motion for the system under general infinitesimal transformation of Lie groups, the Lie symmetrical determining equations, constraints restriction equations, additional restriction equations, and exact invariants of the system are given. Then, under the action of small forces of perturbation, the determining equations, constraints restriction equations, and additional restriction equations of the Lie symmetrical perturbation are obtained, and adiabatic invariants of the Lie symmetrical perturbation, the weakly Lie symmetrical perturbation, and the strongly Lie symmetrical perturbation for the disturbed nonholonomic system are obtained, respectively. Furthermore, a set of non-Noether exact invariants and adiabatic invariants are given in the special infinitesimal transformations. Finally, one example is given to illustrate the application of the method and results.     

Determination of the perturbation parameter in large deflection of plates and shallow shells by means of the least square method

In this paper, the least square method of determination of the perturbation parameter is presented when the perturbation technique is used in the solution of large deflection of axisymmetrical plates and shallow shells. The examples of circular plates are calculated and compared with the exact solution and other perturbation solutions. The results show the best agreement with the exact solution among those perturbation solutions.     

Inf-dif-stability of oblique perturbation

Laurent and Rockafellar have studied certain problems of perturbation and of stability in convex minimization problems. Laurent has discussed inf-dif-stability conditions respectively for horizontal perturbation and for vertical perturbation. In this paper, we generalize some results of Laurent^[1] by giving several inf-dif-stability conditions of oblique perturbation.Project supported by the National Natural Science Foundation of China.     

Free-parameter perturbation-method solutions of the nonlinear stability of shallow spherical shells

The free-parameter perturbation method is applied to solve the problems of nonlinear stability of spherical shallow shells under uniform load. As a modified perturbation method, the free-parameter perturbation method enables researchers to obtain all characteristic relations without choosing the certain perturbation parameter. Some examples were discussed to study the variety regulations of deflections and stress of shells in the process of buckling, and the results were compared with those of other researchers.     

圆射流中拟序涡配对的数值模拟

用三维涡丝法结合涡丝的增加与合并技术,对不可压圆射流场,数值模拟了在扰动中加入次谐波后流场拟序涡的配对,配对情况与实验结果一致,通过对不同时刻涡量图的比较与分析,给出了次谐波初始强度对涡配对的影响,初始强度越大,涡配对出现越早,涡配对位置越往上游移动;同时还得到了基波与次谐波初始相位差和涡配对的关系,没有相位差时,次谐波增长最快,相位差增加时,涡配对的速度降低。说明控制次谐波的初始强度和基波与次谐波的相位差,能起到控制圆射流剪切层乃至控制整个射流场的目的。     

Effects of tip perturbation and wing locations on rolling oscillation induced by forebody vortices

The wing rock motion is frequently suffered by a wing-body configuration with low swept wing at high angle of attack. It is found from our experimental study that the tip perturbation and wing longitudinal locations affect significantly the wing rock motion of a wing-body. The natural tip perturbation would make the wing rock motion of a nondeterministic nature and an artificial mini-tip perturbation would make the wing rock motion deterministic. The artificial tip perturbation would, as its circumferential location is varied, generate three different types of motion patterns： （1） limit cycle oscillation, （2） irregular oscillation, （3） equilibrium state with tiny oscillation. The amplitude of rolling oscillation corresponding to the limit cycle oscillatory motion pattern is decreased with the wing location shifting downstream along the body axis.     

The perturbation parameter in the problem of large deflection of clamped circular plates

In the problems of large deflection of clamped circular plates under uniformly distributed loads, various perturbation parameters relating to load, deflection, slope of deflection, membrane force, etc, are studied. For a general perturbation parameter, the variational principle is used for the solution of such a problem. The applicable range of these perturbation parameters are studied in detail. In the case of uniformly loaded plate, perturbation parameter relating to central deflection seems to be the best among all others. The method of determination of perturbation solution by means of variational principle can be used to treat a variety of problems, including the large deflection problems under combine loads. This paper is completed under the guidance of Prof. Chien Wei-zang.