Effect of the centrifugal forces on the finite element eigenvalue solution of a rotating blade: a comparative study

In this study, the effect of the centrifugal forces on the eigenvalue solution obtained using two different nonlinear finite element formulations is examined. Both formulations can correctly describe arbitrary rigid body displacements and can be used in the large deformation analysis. The first formulation is based on the geometrically exact beam theory, which assumes that the cross section does not deform in its own plane and remains plane after deformation. The second formulation, the absolute nodal coordinate formulation (ANCF), relaxes this assumption and introduces modes that couple the deformation of the cross section and the axial and bending deformations. In the absolute nodal coordinate formulation, four different models are developed; a beam model based on a general continuum mechanics approach, a beam model based on an elastic line approach, a beam model based on an elastic line approach combined with the Hellinger–Reissner principle, and a plate model based on a general continuum mechanics approach. The use of the general continuum mechanics approach leads to a model that includes the ANCF coupled deformation modes. Because of these modes, the continuum mechanics model differs from the models based on the elastic line approach. In both the geometrically exact beam and the absolute nodal coordinate formulations, the centrifugal forces are formulated in terms of the element nodal coordinates. The effect of the centrifugal forces on the flap and lag modes of the rotating beam is examined, and the results obtained using the two formulations are compared for different values of the beam angular velocity. The numerical comparative study presented in this investigation shows that when the effect of some ANCF coupled deformation modes is neglected, the eigenvalue solutions obtained using the geometrically exact beam and the absolute nodal coordinate formulations are in a good agreement. The results also show that as the effect of the centrifugal forces, which tend to increase the beam stiffness, increases, the effect of the ANCF coupled deformation modes on the computed eigenvalues becomes less significant. It is shown in this paper that when the effect of the Poisson ration is neglected, the eigenvalue solution obtained using the absolute nodal coordinate formulation based on a general continuum mechanics approach is in a good agreement with the solution obtained using the geometrically exact beam model.     

时滞线性系统(t)=Ax(t) Bx(t-τ)稳定性的新判据

提出了 x(t) =Ax(t) Bx(t- τ)时滞无关稳定的一个充分条件 ,并进而研究了系统在不满足时滞无关稳定条件下 ,不稳定特征根的区域范围 ,给出了一个与时滞相关稳定的新的充分条件 .文末 ,给出了本文结论的示例 ,并与已有结果进行了比较 ,表明了该方法的有效性和可行性 .     

Maximization of eigenvalues using topology optimization

Topology optimization is used to optimize the eigenvalues of plates. The results are intended especially for MicroElectroMechanical Systems (MEMS) but can be seen as more general. The problem is not formulated as a case of reinforcement of an existing structure, so there is a problem related to localized modes in low density areas. The topology optimization problem is formulated using the SIMP method. Special attention is paid to a numerical method for removing localized eigenmodes in low density areas. The method is applied to numerical examples of maximizing the first eigenfrequency. One example is a practical MEMS application; a probe used in an Atomic Force Microscope (AFM). For the AFM probe the optimization is complicated by a constraint on the stiffness and constraints on higher order eigenvalues. Received June 10, 1999     

箭头矩阵在最小最大特征值条件下的完成问题

引入并讨论了对称箭头矩阵完成问题:在事先给定的对称箭头矩阵中嵌入一行一列使之成为新的对称箭头矩阵,并且具有指定最小最大特征值.利用箭头矩阵特征多项式之间的递归关系,给出并证明了这个问题存在惟一解的充要条件,以及解的一般公式与计算方法.同时还给出了存在非负解及均匀箭柄解的充要条件.利用该问题解决了逆特征值问题:求一个对称箭头矩阵,使它的各阶顺序主子阵具有给定的最小最大特征值.并给出该逆特征值问题解的计算方法.数值计算表明,该算法更有效.     

Hybrid shape parameter strategy for the RBF approximation of vibrating systems

Shape parameters play an important role in radial basis function (RBF) approximations. Therefore, the choice of them is an active field in numerical analysis research. In this paper, first we review the available strategies in the literature for selecting shape parameters. Then, we introduce an alternative approach called hybrid strategy for scaling the RBFs. This strategy is constructed based on the advantages of the older ones and discards their disadvantages. The efficiency of the new strategy is demonstrated by comparing the effects of different strategies on approximating the eigenvalues of ordinary and partial differential equations with different boundary conditions.     

New hybrid Monte Carlo methods and computing the dominant generalized eigenvalue

In this paper, the computation of dominant generalized eigenvalue problem using the new Monte Carlo method are presented. We also compare the numerical results and the CPU-time of two different methods for evaluating dominant generalized eigenvalue. The first method is the QR method. The second method is the extended Monte Carlo method which is called the resolvent Monte Carlo algorithm. Finally, using these methods the numerical results for the general symmetric dense/sparse matrices are performed.     

A symmetric positive definite preconditioner for saddle-point problems

For the classical saddle-point problem, we present precisely two intervals containing the positive and the negative eigenvalues of the preconditioned matrix, respectively, when the inexact version of the symmetric positive definite preconditioner introduced in Section 2.1 of Gill et al. [Preconditioners for indefinite systems arising in optimization, SIAM J. Matrix Anal. Appl. 13 (1992), pp. 292–311] is employed. The model of Stokes problem is used to test the effectiveness of the presented bounds as well as the quality of the symmetric positive definite preconditioner.     

一种能够规避窄带干扰的新型宽带短波探测序列生成算法

针对宽带短波探测系统不足以对抗大功率窄带干扰的问题,分析了窄带干扰能量聚集的低秩性质,运用特征分解算法分离干扰以用于序列频谱成形,结合变换域通信系统基本原理得出了一种能够规避干扰的探测序列构造方法,且据此设计出改进的探测系统方案。仿真结果表明,新的生成序列可以有效规避窄带干扰,具有良好的误码性能,较传统探测序列具有更强的抗干扰能力。     

MATLAB计算分子振动本征值和本征函数

分子动力学和分子光谱等的研究中,常常需要计算分子的振动本征值和振动本征函数。采用传统计算语言编程实现,往往繁琐而困难。MATLAB语言以矩阵为基本元素,自带的库函数可以高效便捷地解决计算其中涉及的许多数学问题。本文采用MATLAB语言计算了Morse势和双井(double well)势的振动本征值和振动本征函数。结果表明,MATLAB语言用于分子振动本征值和本征函数的计算,是一种简洁、高效的运算工具。所编制的程序具有普适性,只需对势能函数进行简单修改即可用于真实双原子分子的振动计算。     

求解矩阵特征值的改进PSO算法

为了改进粒子群算法在求解矩阵特征值时只能根据矩阵特征值范围逐一求解特征值的现状。提出了一种改进的粒子群算法。改进的粒子群算法采用寻找到一个特征值后,适当改变适应值函数的策略,使搜索区域远离已寻找到的特征值,继续寻找其他的特征值,如此反复,直到寻找到所有的特征值为止。利用四个不同类型的矩阵求解特征值进行仿真,实验结果也验证了算法的实用性和有效性。