• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.21 no.5
• /
• pp.707-718
• /
• 1997

This paper presents an efficient numerical method for the computation of eigenpair derivatives for a real symmetric eigenvalue problem with distinct and multiple eigenvalues. The method has a very simple algorithm and gives an exact solution. Furthermore, it saves computer sotrage and CPU time. The algorithm preserves not only the symmetricity but also the band width of the matrices, allowing efficient computer storage and solution techniques. Results from the proposed method for calculating the eigenpair derivatives are compared with those from Rudisill and Chu's method and Nelson's method which is known efficient one in the case of distinct natural frequencies. As an example to demonstrate the efficiency of the proposed method in the case of distinct eigenvalues, a cantilever plate is considered. The design parameter of the cantilever plate is its thickness. For the eigenvalue problem with multiple natural frequencies, the adjacent eigenvectors are used in the algebraic equation as side conditions, lying adjacent to the multiplicity of multiple natural frequency distinct eigenvalues, which appear when design parameter varies. A cantilever beam is used to demonstrate the efficiency of the proposed method in the case of multiple natural frequencies. Results form the proposed method for calculating the eigenpair derivatives are compared with those from Dailey's method(an amendation of Ojalvo's work) which finds the exact eigenvector derivatives. The design parameter of the cantilever beam is its height. Data is presented showing the amount of CPU time used to compute the first ten eigenpair derivatives by each method. It is important to note that the numerical stability of the proposed method is proved.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
• /
• v.13 no.10
• /
• pp.989-997
• /
• 2002

This paper presents a new technique that enhances the performance of the smart antenna system especially in signal environments of wide angular spread by adopting a weight vector obtained from two eigenvectors of theautocovariance matrix of the received data. While the conventional beamformingtechnique employs only one eigenvector corresponding to the largest eigenvalue, the proposed algorithm uses two eigenvectors corresponding to the largest and second largest eigenvalue in such a way that it can be robust enough to the signal environments of wide angular spread. An efficient adaptive procedure is shown to verify that the optimal weight vector consisting of the two eigenvectors is obtained with a reasonable complexity(3.5$N_2$+ 12N) and accuracy. it is also shown in this paper that the numerical results obtained from the proposed adaptive procedure well agree with those obtained from a commercial tool computing the eigen-function of MATLABTM.

• Journal of Information Processing Systems
• /
• v.18 no.3
• /
• pp.293-301
• /
• 2022

Direction of arrival (DOA) estimation of space signals is a basic problem in array signal processing. DOA estimation based on the multiple signal classification (MUSIC) algorithm can theoretically overcome the Rayleigh limit and achieve super resolution. However, owing to its inadequate real-time performance and accuracy in practical engineering applications, its applications are limited. To address this problem, in this study, a DOA estimation algorithm with high parallelism and precision based on an analysis of the characteristics of complex matrix eigenvalue decomposition and the coordinate rotation digital computer (CORDIC) algorithm is proposed. For parallel and single precision, floating-point numbers are used to construct an orthogonal identity matrix. Thus, the efficiency and accuracy of the algorithm are guaranteed. Furthermore, the accuracy and computation of the fixed-point algorithm, double-precision floating-point algorithm, and proposed algorithm are compared. Without increasing complexity, the proposed algorithm can achieve remarkably higher accuracy and efficiency than the fixed-point algorithm and double-precision floating-point calculations, respectively.

• Steel and Composite Structures
• /
• v.20 no.5
• /
• pp.1087-1102
• /
• 2016

The paper proposes to characterize the free vibration behaviour of non-uniform cylindrical shells using spline approximation under first order shear deformation theory. The system of coupled differential equations in terms of displacement and rotational functions are obtained. These functions are approximated by cubic splines. A generalized eigenvalue problem is obtained and solved numerically for an eigenfrequency parameter and an associated eigenvector which are spline coefficients. Four and two layered cylindrical shells consisting of two different lamination materials and plies comprising of same as well as different materials under two different boundary conditions are analyzed. The effect of length parameter, circumferential node number, material properties, ply orientation, number of lay ups, and coefficients of thickness variations on the frequency parameter is investigated.

• Structural Engineering and Mechanics
• /
• v.58 no.6
• /
• pp.1001-1020
• /
• 2016

The study is to investigate the free vibration of antisymmetric angle-ply conical shells having non-uniform sinusoidal thickness variation. The arbitrarily varying thickness is considered in the axial direction of the shell. The vibrational behavior of shear deformable conical shells is analyzed for three different support conditions. The coupled differential equations in terms displacement and rotational functions are obtained. These displacement and rotational functions are invariantly approximated using cubic spline. A generalized eigenvalue problem is obtained and solved numerically for an eigenfrequency parameter and an associated eigenvector of spline coefficients. The vibration characteristic of the shells is examined for cone angle, aspect ratio, sinusoidal thickness variation, layer number, stacking sequence, and boundary conditions.

• Structural Engineering and Mechanics
• /
• v.45 no.2
• /
• pp.259-275
• /
• 2013

Free vibration of symmetric angle-ply layered conical shell frusta of variable thickness is analyzed under shear deformation theory with different boundary conditions by applying collocation with spline approximation. Linear and exponential variation in thickness of layers are assumed in axial direction. Displacements and rotational functions are approximated by Bickley-type splines of order three and obtained a generalized eigenvalue problem. This problem is solved numerically for an eigenfrequency parameter and an associated eigenvector of spline coefficients. The vibration of three and five-layered conical shells, made up of two different type of materials are considered. Parametric studies are made for analysing the frequencies of the shell with respect to the coefficients of thickness variations, length-to-radius ratio, length-to-thickness ratio and ply angles with different combination of the materials. The results are compared with the available data and new results are presented in terms of tables and graphs.

• Journal of Mechanical Science and Technology
• /
• v.14 no.3
• /
• pp.306-313
• /
• 2000

The homogenization method and the density function method are common approaches to evaluate the equivalent material properties for design cells composed of matter and void. In this research, using a new topology optimization method based on the homogenized material with a penalty factor and the chessboard prevention strategy, we obtain the optimal layout of a structure for the natural frequency of a designated mode. The volume fraction of nodes of each finite element is chosen as the design variable and a total material usage constraint is imposed. In this paper, the subspace method is used to evaluate the eigenvalue and its corresponding eigenvector of the structure for the designated mode and the recursive quadratic programming algorithm, PLBA algorithm, is used to solve the topology optimization problem.

• Proceedings of the KIEE Conference
• /
• 1995.07b
• /
• pp.729-732
• /
• 1995

This paper presents a Generalized Iteration (GI) which includes power method, inverse power method, shifted inverse power method, and Rayleigh quotient iteration (RQI), and modified RQI (MRQI). Furthermore, we propose a GI-based algorithm to find arbitrary eigenpairs for Hermitian matrices. The proposed algorithm appears to be much faster and more accurate than the valuable generalized MRQI of Hu (GMRQI-Hu). The idea of GI is also employed to speed up the GMRQI-Hu and we propose a modified version of Hu's GMRQI (GMRQI-Hu-mod) which is improved in the convergence rate. Some numerical simulation results are presented to confirm our contributions

• Geomechanics and Engineering
• /
• v.35 no.5
• /
• pp.465-473
• /
• 2023

The higher order shear deformable model and an exact analytical method is used for analytical bending analysis of a cylindrical shell subjected to mechanical loads, in this work. The shell is modelled using sinusoidal bivariate shear strain theory, and the static governing equations are derived using changes in virtual work. The eigenvalue-eigenvector method is used to exactly solve the governing equations for a constrained cylindrical shell The proposed kinematic relation decomposes the radial displacement into bending, shearing and stretching functions. The main advantage of the method presented in this work is the study of the effect of clamping constraints on the local stresses at the ends. Stress, strain, and deformation analysis of shells through thickness and length.

• Journal of the Korean Society of Manufacturing Technology Engineers
• /
• v.9 no.5
• /
• pp.40-46
• /
• 2000

This study predicts the modified structural eigenvector and eigenvalue due to the change in the mass and stiffness of 2-dimesional continuous system by iterative calculation of the sensitivity coefficient using the original dynamic characteristic. The method is applied to examples of a crank shaft by modifing the mass and stiffness. The predicted dynamics characteristics are in good agreement with these from the structural analysis using the modified mass and stiffness. The predicted dynamic characteristics are in good agreement with these from the structural analysis using the modified mass and stiffness.