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.     

对称Toeplitz—plus—Hankel矩阵特征值的快速算法

利用了n阶对称Toeplitz—plus—Hankel矩阵的结构特点和对称性,给出了计算该类矩阵所有特征值的一个快速算法．该算法的计算复杂度为o（n^2 logn）,比文献[1—2]所给的算法来得少．     

复矩阵Hermitian部分的2~n次幂等性

针对J.Gross所研究的复矩阵A的Hermitian部分的幂等性问题,将其扩展到复矩阵A的Hermitian部分的2~n次幂等性,得到了复矩阵A的Hermitian部分是2~n次幂等的充分必要条件;同时也得到了复矩阵A的Hermitian部分是2~n次幂等与A的正规性和特征值之间的关系-由任意2个性质可以推出第3个性质.最后,J.Gross得到的结果成为本文的推论.     

考虑风力发电的电力系统小干扰稳定性分析

建立了适合小干扰稳定分析的风力发电机组的数学模型,用于研究含风电电力系统的小干扰稳定性,推导了考虑同步发电机励磁调节系统动态行为的全系统状态矩阵公式。利用特征值分析法,分析系统的小干扰稳定性。通过算例分析,表明风电场接入系统时,对系统中同步发电机强相关振荡模式的频率影响不大,但当风电出力增加时,相关振荡模式的阻尼增强,有利于系统小干扰稳定性。风电场接入受电端区域时,区域间振荡模式阻尼特性相对差一些,更容易发生振荡。     

不可约M-矩阵最小特征值的算法

利用M-矩阵与非负矩阵的关系,给出了求不可约M-矩阵最小特征值的一个算法,该算法具有计算量小,易在计算机上实现的特点,且可以达到实际需要的精度,并给出了收敛性证明．数值例子表明该算法具有可行性和有效性．     

矩阵的Hadamard积最小特征值的下界估计

对A和B是非奇异M矩阵,利用著名的Gerschgorin圆盘定理,给出了B和A-1的Hadamard积B。A-1的最小特征值τ(BA-1)新的下界估计式,此下界估计式改进了现有的几个结果,并且这个下界估计式只涉及矩阵A和B的元素,易于计算.例证表明,所得下界估计式要比现有的下界估计式更加精确.     

钢筋混凝土框架柱的抗震延性设计

文章重点从强柱弱梁系数、配箍特征值、轴压比几个角度分析,为在抗震设计中实现混凝土框架柱延性提供保证,从而总体上可对结构的抗震能力予以把握。     

基于谱约束的矩阵逼近解的扰动分析

谱约束的矩阵逼近法是结构设计中模型修正的一种重要方法。给出了广义中心对称谱约束解的存在条件和一般解的表达式,对于一个预估矩阵,提供了它的逼近解的表达式,讨论了该逼近解的误差界,并且提供了一个数值方法和数值例子,数值结果表明方法可行且是有效的。     

周期线性传播结构中电磁场的模式匹配

为了对周期性盘荷圆波导中的电磁场进行分析和描述,提出了采用模式匹配技术,并根据波导模式表示出电磁场. 首先在波导中考虑一个专门的盘荷隔板,由入射模引起的反射问题可采用模式匹配技术来解决;然后得到周期性负载波导的矩阵特征值方程;最后由方程的解可得到场结构的传播曲线. 实验结果表明,每种模式都能与边界条件匹配,利用匹配方法分析周期线性结构中的场分布是可靠的.     

Bergman空间上的加权复合算子

文章首先给出了Bergman空间La^2上加权复合算子,通过研究该空间上酉加权复合算子和紧自伴加权复合算子的谱、特征向量以及特征子空间,进一步完善了Bergman空间La^2上加权复合算子的理论。