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把特征向量的各阶导数表示成所有模态的线性组合,并利用左模态与右模态间的双正交性,首先导出了任意非亏损矩阵的重特征值的一阶导数所满足的特征值问题,然后根据此特征值问题无、看重根的情况,再导出了异导重特征值和等导重特征值对应的可微特征向量、特征值和特征向量各阶导数的一般计算公式。算例显示了方法的正确性。 相似文献
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基于陀螺模态综合法,从总装阵的块式结构出发,构造性地证明了具有n片桨叶的旋翼型结构陀螺特征值问题存在一系列的(n-3)重特征根,得到了对应的(n-3)个完备的振型.结论进而推广到有阻尼的旋翼型结构.继续研究证明过程表明:结论适用于更广泛的一类具有重复子结构的结构系统,结果表明这类结构几何上的重复性或对称性导致的重根不会引入退化性.不同类型的算例验证了所得到的解析结果.本文还试图说明动力子结构法的定性性质保持特性是值得继续探讨的课题 相似文献
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Alexander P. Seyranian 《基于设计的结构力学与机械力学》2013,41(2):261-284
ABSTRACT This paper is devoted to sensitivity analysis of eigenvalues of nonsym-metric operators that depend on parameters. Special attention is given to the case of multiple eigenvalues. Due to the nondifferentiability (in the common sense) of multiple roots, directional derivatives of eigenvalues and eigenvectors in parametric space are obtained. Sensitivity analysis is based on the perturbation method of eigenvalues and eigenvectors. The generalized eigenvalue problem and vibrational systems are also investigated. Strong and weak interaction of eigenvalues are distinguished and interactions in two- and three-dimensional space are treated geometrically. It is shown that the strong interaction of eigenvalues is a typical catastrophe. Simple examples that illustrate the main ideas are presented. The results obtained are important for qualitative and quantitative study of mechanical systems subjected to static and dynamic instability phenomena. 相似文献
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利用奇异值分解方法来讨论系统广义模态的可控可观性的量度问题,得到了亏损系统广义模态可控可观性的量度指标,同时用实例说明了本文方法是有效的。 相似文献
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任意非亏损系统特征灵敏度分析的直接摄动法 总被引:1,自引:0,他引:1
本文发展了一种任意非亏损系统特征灵敏度分析的二阶段摄动法,将未摄动的问题的解作为零阶近似,把摄动影响作为摄动后问题的高阶修正,经过严格的数学推导,得到了支配高阶修正量的完全方程组。本方法无损知道摄问题的全部特征向量,仅需知被摄模态的特征对。本方法可处理被摄问题具有重特征值,甚至具有等导重特征值这一高度退化极难处理的情况。算例显示了本方法的正确性。 相似文献
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This paper presents methods for computing a second-order sensitivity matrix and the Hessian matrix of eigenvalues and eigenvectors of multiple parameter structures. Second-order perturbations of eigenvalues and eigenvectors are transformed into multiple parameter forms,and the second-order perturbation sensitivity matrices of eigenvalues and eigenvectors are developed.With these formulations,the efficient methods based on the second-order Taylor expansion and second-order perturbation are obtained to estimate changes of eigenvalues and eigenvectors when the design parameters are changed. The presented method avoids direct differential operation,and thus reduces difficulty for computing the second-order sensitivity matrices of eigenpairs.A numerical example is given to demonstrate application and accuracy of the proposed method. 相似文献
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齐朝晖 《应用数学和力学(英文版)》2002,23(2):187-193
IntroductionManymechanicalsystemscanbeviewedaslinearHamiltoniansystems.Whenwestudytheeffectsofsystemparametersonthebehaviorofthesystems,thesystemcanberegardedasthesystemdependingonparameters.Veryimportantsystemparameters ,suchascriticalload ,criticalang… 相似文献
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《International Journal of Solids and Structures》2003,40(23):6457-6472
This paper presents numerical methods of counting the number of eigenvalues for non-proportionally damped system in some interested regions on the complex plane. Most of the eigenvalue analysis methods for proportionally damped systems use the well-known Sturm sequence property to check the missed eigenvalues when only a set of the lowest modes is used. However, in the case of the non-proportionally damped systems such as the soil–structure interaction system, the structural control system and composite structures, no counterpart of the Sturm sequence property for undamped systems has been established yet. In this study, a numerical method based on argument principle is explained with emphasis on the discretization of the contour and a new method based on Gleyse’s theorem is proposed. To verify the applicability of the methods, two numerical examples are considered. 相似文献
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A new matrix perturbation analysis method is presented for efficient approximatesolution of the complex modal quadratic generalized eigenvalue problem of viscouslydamped linear vibration systems.First,the damping matrix is decomposed into the sum of aproportional-and a nonproportional-damping parts,and the solutions of the real modaleigenproblem with the proportional dampings are determined,which are a set of initialapproximate solutions of the complex modal eigenproblem.Second,by taking thenonproportional-damping part as a small modification to the proportional one and using thematrix perturbation analysis method,a set of approximate solutions of the complex modaleigenvalue problem can be obtained analytically.The result is quite simple.The new methodis applicable to the systems with viscous dampings-which do not deviate far away from theproportional-damping case.It is particularly important that the solution technique be alsoeffective to the systems with heavy,but not over,dampings.The solution formul 相似文献
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《Comptes Rendus Mecanique》2017,345(12):844-867
In this paper, we characterize random eigenspaces with a non-intrusive method based on the decoupling of random eigenvalues from their corresponding random eigenvectors. This method allows us to estimate the first statistical moments of the random eigenvalues of the system with a reduced number of deterministic finite element computations. The originality of this work is to adapt the method used to estimate each random eigenvalue depending on a global accuracy requirement. This allows us to ensure a minimal computational cost. The stochastic model of the structure is thus reduced by exploiting specific properties of random eigenvectors associated with the random eigenfrequencies being sought. An indicator with no additional computation cost is proposed to identify when the method needs to be enhanced. Finally, a simple three-beam frame and an industrial structure illustrate the proposed approach. 相似文献
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An acceleration for the eigensystem realization algorithm with partial singular values decomposition
The real-time identification of dynamic parameters is important for the control system of spacecraft. The eigensystem realization
algorithm (ERA) is currently the typical method for such application. In order to identify the dynamic parameter of spacecraft
rapidly and accurately, an accelerated ERA with a partial singular values decomposition (PSVD) algorithm is presented. In
the PSVD, the Hankel matrix is reduced to dual diagonal form first, and then transformed into a tridiagonal matrix. The eigenvalues
are computed by the bisection method in terms of the Sturm property, and the corresponding eigenvectors are obtained by the
inverse iteration method. Finally, the eigenvalues and the eigenvectors are transformed into the singular values and the singular
value vectors of the original matrix. An example for space station is presented to demonstrate the efficacy and accuracy of
the proposed algorithm. 相似文献
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《Mechanics Research Communications》1987,14(2):115-122
Eigenvalue bounds for damped linear mechanical systems are presented based on a ‘modified equation of state’. The system exhibits nonmodal damping, by which we mean that classical normal modes do not obtain. The special case of an underdamped system is discussed, leading to bounds on a generalized damping ratio. The bounds are expressed in terms of the extreme eigenvalues of the constituent matrices. Geometrically, they define rectangular regions in the complex plane which contain the system eigenvalues. 相似文献
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广义特征值问题中重特征值的特征向量导数 总被引:8,自引:0,他引:8
本文把重特征值的特征向量导数的计算方法,推广到非亏损矩阵的广义特征值问题,并给出了特征值导数也有重根时特征向量导数的计算式。本方法的优点是只需已知所考虑的重特征值的特征向量,因而计算量小,对于大型复杂结构更为适用。 相似文献
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广义特征值问题中重特征值的特征向量导数 总被引:3,自引:0,他引:3
本文把重特征值的特征向量导数的计算方法,推广到非亏损矩阵的广义特征值问题,并给出了特征值导数也有重根时特征向量导数的计算式。本方法的优点是只需已知所考虑的重特征值的特征向量,因而计算量小,对于大型复杂结构更为适用。 相似文献
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对于线性系统,根据其质量、刚度或阻尼等矩阵的性质了解特征值,是十分有意义的问题.对于有阻尼陀螺系统,本文首先通过模态正交性推导了有关矩阵的若干关系式.然后分析了复特征值的两类表达式的适用性,着重讨论了通过一元二次方程研究特征值性质的现行处理方法存在的困难.提出一种确定特征值的补充方法,指出可能存在虚数特征值的系统的性质.算例表明结论正确 相似文献