Papers by Keyword: Eigenvalue

Abstract: Free flexural free vibrations of variable section are considered. The vibrations mathematical model represents the boundary value problem consisting of the hyperbolic type and boundary conditions main equation. By means of separation method of variables the task at the beginning comes to homogeneous differential equation of the fourth order for fundamental function with the corresponding boundary conditions. The grid area of an argument change and fundamental function in it are applied. That leads to an algebraic problem of eigenvalues. Multimodal non-negative function which null values match its eigenvalues is designed. The finite differences methods and coordinate descent in combination with the specified function sections graphic visualization at a small amount of descents with an adequate accuracy for eigenvalues practice are given. The known ways to define fundamental functions are applied.

Abstract: The nonlinear second-order differential eigenvalue problem describing eigenvibrations of a bar with elastically attached load is investigated. This problem has an increasing sequence of positive simple eigenvalues with limit point at infinity. The sequence of eigenvalues corresponds to a system of normalized eigenfunctions. The initial nonlinear eigenvalue problem is approximated by the quadrature finite element method on a uniform grid. The existence and accuracy of approximate solutions are studied. Investigations of the present paper can be generalized for the cases of more complicated and important problems on eigenvibrations of beams, plates and shells with elastically attached loads.

Abstract: The characteristic value of gray level co-occurrence matrix to extract can well express the information of texture. Co-occurrence matrix provides the information of image grayscale, interval and change. According to the co-occurrence matrix, it can calculate the corresponding characteristic values of eigenvalue, which can express the texture information of the image. This is thesis designed extraction software a for textile fabric texture feature, and the internal principle is the using of gray level co-occurrence matrix and Matlab programming.

Abstract: This paper studies on the eigenvalue^[1-5] of the a class of upper triangular matrix with linear relation. It discusses the feature of existence and uniqueness of matrix via two given two characteristic pairs(λ,χ),(μ,γ) . Solutions and expressions are provided under satisfied conditions. The possibilities are exanimated by numerical example.

Abstract: The distinctive paper is devoted to problem of identification the dynamic characteristics of mathematical models based on the measured dynamic characteristics of real constructions. It is describes a problem of discrepancy of measured and modeling eigen pairs. It is shown that the problem is systemic. The creation and verification processes of mathematical (finite element) models used in the design constructions need some work and adjustments. For a reliable analysis of the construction ways are suggested to overcome the identified gaps using adaptive procedures.

Abstract: A rod composed of two different prismatic rods built-up with rectilinear orthotropic materials is studied. Composite parts of the prismatic rods are connected entirely by their common surface. The anisotropy axis is perpendicular to the cross-section plane. The problem has been solved in Cartesian coordinate system. The functions of stresses are presented by the sums of solutions corresponding to positive eigenvalues of homogeneous boundary problems and partial solutions of inhomogeneous boundary problems. From condition of existence of the non-trivial solution of the homogeneous boundary problem an equation in respect to eigenvalues is derived of which roots are real and different. If there are roots in (0; 1) interval, then the stresses tend to infinity at the vertex of the cross-section of the composite rod have a feature with the order equal to where - is the smallest root in the interval (0, 1).

Abstract: In this paper, we present an efficient algorithm for computing the logarithms of k-circulant matrices. And then we prove that nonsingular k-circulant matrices always has infinitely many k-circulant logarithms.

Abstract: Low frequency oscillation caused by system interconnection has been the main factor to threat the secure operation of power grid. It’s significant to research on the problem of low frequency oscillation. This paper summarizes the generation mechanism and analysis methods of low frequency oscillation. Each analysis method has both advantages and disadvantages.

Abstract: Based on the weighted inverse topological change method and by introducing a new concept of mass submembers, a dynamical system can be transformed into a static one. Using the properties of the weighted D value, i.e. the weighted D value decreases monotonously with parameter λ increasing; a new method called the weighted D value iteration method is presented for computing the eigenpairs (eigenvalues and eigenvectors). Using this method a series of eigenpairs of a finite element structure can be obtained. It has a merit of simpler algorithm and less computation efforts. Not as the power method, its stability and convergence rate does not depend on the distribution of eigenvalues, and convergent quickly. An example is given to demonstrate the valid of this method.

Abstract: This paper presents a perturbation based method for small-signal stability analysis in microgrid based on the uncertainty of microgrid parameters. The small-signal state-space model is built including the dynamic characteristics of the controllers, the power measurement and the system circuit and load dynamics model. The system eigenvalues of operating point at a steady-state in microgrid are obtained by the model. Based on perturbation theory, the corresponding low-frequency eigenvaluea and damping ratio of the microgrid system are calculated when the microgrid parameters changing in the range. Then the relationship between small-signal frequency stability and parameters changes can be determined. The validity of the proposed method and the importance of the stablility analysis of the microgrid small-signal are proved by the simulation results.