Based on mass - spring model , a method of automatic mode - selecting method is presented to solve the difficulties of selecting corresponding modes close to the excitation frequency , in adaptive perturbation for mistuned bladed disks 摘要针对自适应摄动法在失谐叶盘受迫振动分析中，选择接近激振力频率的相应模态数目难于控制的问题，基于质量弹簧模型，提出一种自动选择模态的方法。
However , it is difficult to choose proper perturbation parameter in the process of applying this method . even in present day , there have not a dependable norm to confirm certain parameter and researcher often search it through engineering experience 但选择摄动参数却是正则摄动法求解过程中的一个比较困难的问题，现在对于这一问题仍然没有一个一般的原则，而主要是利用经验对该问题进行处理。
Anechoic coatings " efficiency is getted from its front and back many layer ' s transfer loss compared . first , absorptive characteristic of homogeneous material is analyzed thoroughly . then wkb perturbation means are used to calculate absorption coefficient of the impedance transition structure in this paper 本论文首先对均匀材料的吸声特性做了深入的分析，并详细讨论了wkb微扰摄动法，利用wkb方法计算阻抗过渡结构的吸声系数。
The global bifurcation analysis of the nonlinear nonplanar cantilever is given by a global perturbation method developed by kovacic and wiggins . it is found that the nonlinear nonplanar cantilever can undergo the hopf bifurcation , heteroclinic bifurcations and silnikov - type homoclinic orbit to saddle focus , which means that the nonlinear nonplanar cantilever can give rise to the chaotic motion in the sense of smale horseshoes 利用kovacic和wiggins的全局摄动法对非线性非平面运动悬臂梁进行了全局动力学分析，发现系统存在hopf分叉和异宿分叉，并证明系统有silnikov型鞍焦点型同宿轨道，可以产生smale马蹄意义下的混沌。
Secondly , the effectiveness and limitation of the classical perturbation , such as the method of multiple scales and the poincare - lindstedt method , are discussed in detail through a duffing oscillator with delayed velocity feedback . it is shown that the two perturbation methods are effective only in solving the approximate solution of the first two orders . an ambiguity or paradox will be encountered when they are used to seeking for the third or higher order approximation of solution 其次，以一具有时滞速度反馈的duffing系统为例，研究了经典摄动法如多尺度法， poincar - lindstedt法等在求解时滞微分方程级数解时的适用性和局限性问题，指出利用这些方法只能有效求得系统的前两阶近似解，而在求系统的三次以上近似解时会出现矛盾或二义性。
The structural dynamic sa in project is of great importance for the study on dynamic design , optimization design , control theory and dynamic modification etc . and direct method , difference method and perturbation method for dynamic sa are adopted regular , though following shortages are obvious : only local impact of the factors on the model can be obtained ; model dependence ; the interval is usually the same for all of the variables and is not related to our degree of knowledge of the variables ; shortage of precision and so on 工程结构的动态特性灵敏度分析对工程结构的动态设计、优化设计、控制理论和动态修改等方面的研究有着十分重要的意义。目前，结构动态特性灵敏度的分析法一般采用局部法，如直接法、差分法和摄动法。但是这些方法只能求参数域某点的灵敏度，不仅受模型、计算精度的限制，而且二阶以上的灵敏度求解比较困难。
Abstract : in this paper , the authors study the initial value problems of a class of weakly nonlinear differential equation . the first and the second order approximate solutions are obtained . their accuracies are high and the more the approximate order is high , the more the accuracy is high . if the regular perturbation method is used to solve the same problems , then , when the independent variable is big , so is the error of the solution 文摘:用插值摄动法1研究一类弱非线性常微分方程的初值问题，得到了一级及二级近似解.解的精度很高，并逐级提高.如果用正则摄动法求解此类问题，则当自变量较大时，误差很大
Based on the normal form obtained above , a global perturbation method is utilized to give the analysis for the global bifurcations and chaotic dynamics of the rotor - ambs system . the global bifurcations analysis indicates that there exist the heteroclinic bifurcations and the silnikov - type homoclinic orbit in the averaged equations 利用全局摄动法研究了电磁轴承-转子系统的全局分叉和混沌动力学，利用数值模拟方法分别对平均方程和原方程进行了分析，得到了的描述系统混沌运动的相图和波形图，从而验证了理论结果的正确性。
Compare with some presently used methods for solving interval equations and interval analysis of structures , the presented methods have high efficiency of calculation , low computational burden and high accuracy . ( b ) secondly , the proposed methods for solving interval fem were extended to the solving of fuzzy structures 与目前国际上已提出的其它区间方程组求解和结构的区间分析方法(如规划方法、直接组合解法和区间摄动法等)相比，本文所提出的方法计算效率高，计算量小。
To ensure all segments under construction to approach corresponding construction segmental reasonable states in both configuration and mechanics states and good behavior of structure after completion , escaping from all kinds of accidents in whole process of construction with high efficiency , safety , excellent quality of engineering achieved , the grey prediction model ngm ( 1 , 1 ) was proposed to fit prediction of any raw grey series by studying grey causes and whitening results based on the normalized mapping rules ; random perturbation method of genetic algorithms was proposed to raise efficiency of forward rolling optimization ; simultaneous analysis of strength and stability was carried out to ensure safety of strength and stability 摘要为了保证实际施工中结构各节段在构形和受力状态两方面逼近施工节段合理状态，避免事故发生，确保工程高效、安全、优质，基于归一化映射规则，研究灰因和白果，提出了适应任意灰序列的灰预测模型ngm ( 1 , 1 ) ；研究遗传算法的随机摄动法，提高向前滚动优化效率；研究强度、稳定性的同步分析技术，保证施工过程强度、稳定性安全。
