平方非线性振动方程的渐近解及其数值验证

改进的Lindstedt-Poincar啨(L-P)法在传统的L-P法的基础上,对频率的展开式作了改进;卷积分法则提供了一个求近似解的迭代格式.本文首先用这两种方法求得平方非线性振动方程的二阶渐近解,并用Picard逐步逼近法证明由卷积分法得到的渐近解在有限的时间上是一致收敛的.其次,一种数值阶验证技术证实求得的二阶渐近解对小参数都是一致有效的.最后,对这两种渐近解进行误差的数值比较,结果表明它们对大参数无效,并简明分析其失效的原因.因此,这两种方法在平方非线性振动方程中的应用受到小参数的限制.     

两自由度非线性系统1:3内共振的渐近摄动分析

提出了一种改进的渐近摄动法,并用该方法研究了同时含平方项和立方项的两自由度非线性系统在1:3内共振情况下的非线性动力学行为.分别在平均方程和原方程的基础上得到了幅频响应曲线和分叉图,对比表明两种结果基本吻合.改进后的渐近摄动法比原有渐近摄动法更容易应用于1:3内共振情况.     

隐蔽式钢结构损伤检测机器人振动阻尼比计算

隐蔽式钢结构损伤检测机器人效能部件产生的阻尼是时变阻尼,计算结果会随着载荷的变化而变化,单一振动阻尼比的计算无法真实反馈阻尼信息,对此构造振动阻尼综合计算方法.基于当前损伤检测机器人的固有结构和应变结构数值,进行包络取值计算,提取在各类型效能器下的最终振动阻尼数值,以此为基础针对机器人应变性数值,通过计算各时刻点的应变性能完成时变计算取值,根据上述两种取值的最终结果,改进以往单一综合值计算方法,定义应变效能和总效能,实现最终振动阻尼比的计算.仿真数据表明,与传统的单一均值求取法对比,设计的综合计算方法计算结果偏离度更低,可以有效提高最终计算准确度.     

某车辆地板总成振动分析与改进

运用整车振动测量、实验模态分析及线性动力学计算等方法对车辆地板总成的振动特性进行分析研究,确认柴油机的二阶往复惯性力是系统的激励源,地板总成的固有频谱与振源频率在某些转速范围内有交集,引起车辆地板总成的异常振动。经实验模态分析的验证,建立了车辆地板的计算模型。在此基础上改进了地板总成的结构,使其固有频谱避开了振源频谱,改善了振动特性。该实验和计算方法对解决类似的工程问题具有参考价值。     

载流梁在磁场中的横向固有振动分析

在考虑结构变形对电磁场的影响基础上，假设载流梁的变形为小变形，把变形后载流梁中的电流方向改变看成是电流矢量的刚性旋转．建立了载流梁在磁场中的横向固有振动控制方程．方程表明载流梁在磁场中的横向固有振动是一个典型的非线性问题．采用摄动法求得了其近似解，得到了载流梁在磁场中的横向固有振动频率及位移解析表达式．并通过实例计算讨论分析了导线与载流梁间距、载流梁的电流与导线电流的方向及大小、载流梁梁长及其半径等因素对载流梁横向固有振动的影响，得到了一些有价值的结论．     

瞬态加热环境下变厚度板温度场及热模态分析

瞬态加热会严重影响结构的固有振动特性. 以变厚度板为研究对象,进行热载状态下结构的瞬态温度场和振动特性分析. 计算结果表明,在加热过程中,结构温度发生显著变化并引起热应力,进一步影响到结构的固有振动特性.     

细长弹箭固有振动特性分析有限元传递矩阵法

使用有限元传递矩阵法分析了某大长径比弹箭的固有振动特性，成功求得了其固有振动频率和振型函数，计算结果得到试验验证．该方法兼备有限元法建模方便、应用范围广和传递矩阵法应用灵活、矩阵阶次低、计算速度快的优点，易于分析复杂变截面结构弹箭的振动特性，并且可直接利用商业有限元软件得到该方法仿真所必需的质量矩阵和刚度矩阵．     

基于改进EMD的爆炸微差延期时间尺度识别及应用

经验模式分解(EMD)具有高度的自适应性,但是存在较大的端点效应.为此提出利用支持向量机-镜像延拓法对其端点效应进行处理,实际效果良好.提出了爆炸微差延时的改进EMD时间尺度识别法,并以某工程中微差爆炸监测到的爆炸振动信号为例,通过改进的EMD时间尺度法对监测得到的爆炸振动信号进行分解,从而获得多个固有模态函数(IMF)分类;然后通过Hilbert变换提取这些IMF中占主成分的IMF分量的包络幅值,进而达到识别实际微差延时的目的.该方法为爆炸延期参数设计提供了分析手段.     

非线性地基上正交异性矩形板的非线性热振动

研究了非线性地基上正交异性矩形板的非线性固有热振动.采用常规的L-P法分析非线性地基上正交异性矩形板的非线性热振动难以得到高精度的近似解,为此,先对该强非线性振动系统进行参数变换,将该强非线性振动系统转化为弱非线性振动系统.然后采用改进的L-P法进行求解,得到了强非线性振动系统的高精度近似解.此外,讨论了温度、地基特征参数、长宽比等因素对非线性地基上正交异性矩形板非线性热振动固有频率的影响,得到了非线性地基上正交异性矩形板热振动频率随温度下降、地基特征参数变大、长宽比变大而增大的结论.     

基于FEM的叶栅动态特性仿真研究

计算机仿真在航空航天领域得到了广泛的应用.有限单元法是大型复杂结构或多自由度体系分析的有力工具.对大型承载飞机普遍使用的发动机转子叶栅,使用有限单元法(FEM)进行建模,然后对叶栅的结构及旋转状态下的动态特性进行分析.同时在不同转速下计算模态和振动频率,对等效压力分布、等效应力分布和整体形变进行仿真,并绘制了叶栅共振曲线的坎贝尔图,显示了固有振动频率和振动响应条件下共振激励作用.利用有限单元法的建模方法进行仿真,结果表明,使用上述方优化设计,使叶栅转动特性安全有效.     

The asymptotic optimization of pre-edited ANN classifier

The generalization problem of an artificial neural network (ANN) classifier with unlimited size of training sample, namely asymptotic optimization in probability, is discussed in this paper. As an improved ANN network model, the pre-edited ANN classifier shows better practical performance than the standard one. However, it has not been widely applied due to the absence of the related theoretical support. To further promote its application in practice, the asymptotic optimization of the pre-edited ANN classifier is studied in this paper. To help study ANN asymptotic optimization in probability, we gives a review of the previous research works on asymptotic optimization in probability of non-parametric classifier, and grouped the main methods into four classes: two-step method, one-step method, generalization method and hypothesis method. In this paper, we adopt generalization/hypothesis mixed method to prove that pre-edited ANN is asymptotically optimal in probability. Furthermore, a simulation is presented to provide an experimental support for our theoretical work.     

Calculation of the sound field in an inhomogeneous layered hydro-acoustic waveguide with a stepped bottom

For the model of the waveguide which is a multilayered medium with a cylindrical seamount, the asymptotic behavior of the unknowns in the corresponding infinite system is studied. The obtained asymptotic behavior of the unknowns allows us to use the method of improved reduction for finding the coefficients of the normal modes. The convergence of the algorithm is illustrated by the example of some geophysical waveguides.     

Asymptotic stability analysis of nonlinear real-time networked control systems

The paper deals with the problem of the asymptotic stability for general continuous nonlinear networked control systems （NCSs）. Based on Lyapunov stability theorem combined with improved Razumikhin technique, the sufficient conditions of asymptotic stability for the system are derived. With the proposed method, the estimate of maximum allowable delay bound （MADB） for linear networked control system is also given. Compared to the other methods, the proposed method gives a much less conservative MADB and more general results. Numerical examples and some simulations are worked out to demonstrate the effectiveness and performance of the proposed method.     

非线性机械系统PID控制渐近稳定性分析

应用Lyapunov直接稳定性理论和LaSalle不变性原理, 证明了不确定非线性机械系统常用线性PID控制的半全局渐近稳定性. 同时证明了为提高系统的响应速度而发展的一种非线性PI加D (NPI-D)控制系统的全局渐近稳定性. 两自由度机器人系统的数值仿真结果验证了NPI-D控制的良好性能.     

Richardson Extrapolation of Iterated Discrete Galerkin Method for Eigenvalue Problem of a Two Dimensional Compact Integral Operator

We consider approximation of eigenelements of a two-dimensional compact integral operator with a smooth kernel by discrete Galerkin and iterated discrete Galerkin methods. By choosing numerical quadrature appropriately, we obtain superconvergence rates for eigenvalues and iterated eigenvectors, and for gap between the spectral subspaces. We propose an asymptotic error expansions of the iterated discrete Galerkin method and asymptotic error expansion of approximate eigenvalues. We then apply Richardson extrapolation to obtain improved error bounds for the eigenvalues. Numerical examples are presented to illustrate theoretical estimate.     

“Booster method” for singularly perturbed robin problems i

An improved numerical method is presented for singularly perturbed Robin problems in this paper. In this method (“Booster method”), an asymptotic approximation is incorporated into a finite difference scheme to improve the numerical solution. Error estimates are proposed for the present method. In order to show the efficiency numerical examples are presented.     

Combination of the boundary integral equation method and the extrapolation method

Many numerical methods including the boundary integral equation method start with division of the domain of calculation into intervals. The accuracy of their results can be improved considerably by extrapolation. To be able to apply the extrapolation method it is necessary to know the asymptotic expansion of the error.In this paper the principle of the extrapolation method and subjects important for its application are described. Above all it is shown how to determine the asymptotic expansions numerically by trial and error. In the first sections the matter is explained in a general manner to encourage users of various numerical methods—among them users of the finite element method—to try to extrapolate their results. Then the investigations are exemplified in detail by the boundary integral equation method. The accuracy of approximate solutions of integral equations for plane elastostatic problems with prescribed boundary tractions and displacements is improved by extrapolation. Particular attention is paid to boundary tractions and displacements with discontinuous derivatives.To induce also practically orientated readers without specialized mathematical knowledge to think about applying the extrapolation method the basic topics are represented in an extensive manner and illustrated by simple examples. (For a survey of this paper see end of Section 1.)     

“booster method” for singularly perturbed robin problems-II

Singularly perturbed Robin problems are considered in this paper. In order to get an improved numerical solution to these problems, a computational method (“Booster Method”) is suggested. In this method, an asymptotic approximation is incorporated into a finite difference scheme to improve the numerical solution. Error estimates are proposed when implemented in known difference schemes. Numerical examples are presented to illustrate the present method.     

CNN的全局渐近稳定性分析与改进

研究一类通用细胞神经网络的稳定性问题.采用Lipschitiz连续性条件证明了系统平衡点的存在性,利用Lyapunov函数稳定性分析方法结合不等式分析,给出系统平衡点唯一和全局渐近稳定的充分条件,该条件推广并改进了已有结论,具有更好的通用性,经实验仿真是可行的.     

Investigation of asymptotic stability of equilibria by localization of the invariant compact sets

The method of localization of invariant compact sets was proposed to study for asymptotic stability the equilibrium points of an autonomous system of differential equations. This approach relies on the necessary and sufficient conditions for asymptotic stability formulated in terms of positive invariant sets and invariant compact sets, and enables one to study the equilibrium points for asymptotic stability in the cases where it is impossible to use the first approximation or the method of Lyapunov functions. The possibilities of the method were illustrated by examples.