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Eigenvalue Analysis (eigenvalue + analysis)

Distribution by Scientific Domains
Engineering87%

Selected Abstracts

Initialization Strategies in Simulation-Based SFE Eigenvalue Analysis

COMPUTER-AIDED CIVIL AND INFRASTRUCTURE ENGINEERING, Issue 5 2005
Song Du
Poor initializations often result in slow convergence, and in certain instances may lead to an incorrect or irrelevant answer. The problem of selecting an appropriate starting vector becomes even more complicated when the structure involved is characterized by properties that are random in nature. Here, a good initialization for one sample could be poor for another sample. Thus, the proper eigenvector initialization for uncertainty analysis involving Monte Carlo simulations is essential for efficient random eigenvalue analysis. Most simulation procedures to date have been sequential in nature, that is, a random vector to describe the structural system is simulated, a FE analysis is conducted, the response quantities are identified by post-processing, and the process is repeated until the standard error in the response of interest is within desired limits. A different approach is to generate all the sample (random) structures prior to performing any FE analysis, sequentially rank order them according to some appropriate measure of distance between the realizations, and perform the FE analyses in similar rank order, using the results from the previous analysis as the initialization for the current analysis. The sample structures may also be ordered into a tree-type data structure, where each node represents a random sample, the traverse of the tree starts from the root of the tree until every node in the tree is visited exactly once. This approach differs from the sequential ordering approach in that it uses the solution of the "closest" node to initialize the iterative solver. The computational efficiencies that result from such orderings (at a modest expense of additional data storage) are demonstrated through a stability analysis of a system with closely spaced buckling loads and the modal analysis of a simply supported beam. [source]

Non-linear version of stabilized conforming nodal integration for Galerkin mesh-free methods

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2002
Jiun-Shyan Chen
Abstract A stabilized conforming (SC) nodal integration, which meets the integration constraint in the Galerkin mesh-free approximation, is generalized for non-linear problems. Using a Lagrangian discretization, the integration constraints for SC nodal integration are imposed in the undeformed configuration. This is accomplished by introducing a Lagrangian strain smoothing to the deformation gradient, and by performing a nodal integration in the undeformed configuration. The proposed method is independent to the path dependency of the materials. An assumed strain method is employed to formulate the discrete equilibrium equations, and the smoothed deformation gradient serves as the stabilization mechanism in the nodally integrated variational equation. Eigenvalue analysis demonstrated that the proposed strain smoothing provides a stabilization to the nodally integrated discrete equations. By employing Lagrangian shape functions, the computation of smoothed gradient matrix for deformation gradient is only necessary in the initial stage, and it can be stored and reused in the subsequent load steps. A significant gain in computational efficiency is achieved, as well as enhanced accuracy, in comparison with the mesh-free solution using Gauss integration. The performance of the proposed method is shown to be quite robust in dealing with non-uniform discretization. Copyright © 2002 John Wiley & Sons, Ltd. [source]

Eigenvalue analysis of temperature distribution in composite walls

INTERNATIONAL JOURNAL OF ENERGY RESEARCH, Issue 13 2001
Galip Oturanç
Abstract The transient heat conduction problem in two-layer composite wall is solved analytically using spectral analysis. Eigenvalues and corresponding eigenfunctions of the spectral problem for the temperature distribution in composite walls are analysed using the Rouche Theorem. The number of eigenvalues is obtained and the temperature distribution of this complicated problem is given by a formula with calculated eigenvalues. The analytical solution obtained is in explicit form and provides easy determination of temperature rise in heating and thawing applications of composite materials. Copyright © 2001 John Wiley & Sons, Ltd. [source]

Initialization Strategies in Simulation-Based SFE Eigenvalue Analysis

COMPUTER-AIDED CIVIL AND INFRASTRUCTURE ENGINEERING, Issue 5 2005
Song Du
Poor initializations often result in slow convergence, and in certain instances may lead to an incorrect or irrelevant answer. The problem of selecting an appropriate starting vector becomes even more complicated when the structure involved is characterized by properties that are random in nature. Here, a good initialization for one sample could be poor for another sample. Thus, the proper eigenvector initialization for uncertainty analysis involving Monte Carlo simulations is essential for efficient random eigenvalue analysis. Most simulation procedures to date have been sequential in nature, that is, a random vector to describe the structural system is simulated, a FE analysis is conducted, the response quantities are identified by post-processing, and the process is repeated until the standard error in the response of interest is within desired limits. A different approach is to generate all the sample (random) structures prior to performing any FE analysis, sequentially rank order them according to some appropriate measure of distance between the realizations, and perform the FE analyses in similar rank order, using the results from the previous analysis as the initialization for the current analysis. The sample structures may also be ordered into a tree-type data structure, where each node represents a random sample, the traverse of the tree starts from the root of the tree until every node in the tree is visited exactly once. This approach differs from the sequential ordering approach in that it uses the solution of the "closest" node to initialize the iterative solver. The computational efficiencies that result from such orderings (at a modest expense of additional data storage) are demonstrated through a stability analysis of a system with closely spaced buckling loads and the modal analysis of a simply supported beam. [source]

Analysis of effects of contracts on the stability of dynamic power markets

EUROPEAN TRANSACTIONS ON ELECTRICAL POWER, Issue 1 2009
Jia Yan-Bing
Abstract Experiences with operations of power markets show that contracts may affect stability of markets. Therefore, it is necessary to consider whether the market with bilateral contracts will lead to a stable equilibrium conditions after the market is exposed to certain kinds of disturbances. In this paper, the dynamic behaviour of power markets is expressed by differential/algebraic equations, and eigenvalue analysis is used to study effects of contracts on stability of the model. Results of the analysis show that suitable relative ratio of contracts can improve the stability of power markets and even make the unstable markets stable. On the other hand, unsuitable relative ratio of contracts may deteriorate the stability of markets. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Analysing subsynchronous resonance phenomena in the time- and frequency domain

EUROPEAN TRANSACTIONS ON ELECTRICAL POWER, Issue 4 2000
X. Lei
Subsynchronous resonance (SSR) is a condition that can exist in a power system, especially for long-distance transmission systems with series compensated line. It can cause shaft fatigue and possible damage or failure of the generator involved. The analysis of the SSR phenomenon can be performed usually by using three individual analytical methods -frequency scanning, eigenvalue analysis in the frequency domain and transient torque analysis in the time domain. In this paper the comprehensive simulation program NETOMAC with a complete solution for analysing SSR is presented. Based on a common data set of the system concerned, both frequency and transient torque analysis can be performed, taking interactions among the spring-mass system of the turbine-generator units and the electrical network into consideration. Two case studies are demonstrated in the paper. The results achieved validate the functionality of the program for SSR analysis. [source]

Barotropic instability in the tropical cyclone outer region

THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 641 2009
Jiayi Peng
Abstract The growth of asymmetric perturbations and their interactions with the symmetric flow are investigated for wind profiles in a tropical cyclone with instability in its outer region. Three tangential wind profiles are examined: TC1, a strong barotropic instability profile in the outer region; TC2, a stable wind profile; and TC3, a weaker instability profile comparing to TC1 with a larger distance between the inner negative and the outer positive vorticity gradient centres. An eigenvalue analysis indicates that azimuthal wave-number two is the most unstable mode in both TC1 and TC3, with an e-folding time-scale of about 1 and 9 days, respectively. Numerical simulations using a linear barotropic model, with an initial asymmetry specified in the outer region, confirm the eigenvalue analysis. A mechanism is provided to explain the difference between simulations in TC1 and TC2. In both the stable and unstable case, an inner asymmetry is induced by the initial outer asymmetry acting on the symmetric vorticity gradient. Subsequently, the newly generated inner asymmetry feeds back positively to the outer asymmetry with the unstable profile. Because of this positive feedback, the inner and the outer asymmetries maintain an up-shear phase tilting, leading to a continuous energy transfer from the symmetric flow to the asymmetric perturbation. In the stable TC2, the inner asymmetry could not amplify the outer initial asymmetry as there is no basic-state radial vorticity gradient there. Also due to this feedback process, disturbances grow faster where the (absolute) basic-state vorticity gradients are large. Therefore, the position of an initial disturbance plays a minor role in determining the outcome of the system. Simulations with a nonlinear barotropic model and a primitive equation model further confirm the significant weakening of the maximum tangential wind due to the positive feedback process in TC1. Simulations for TC3 show a smaller change of the symmetric tangential wind, as expected. Copyright © 2009 Royal Meteorological Society [source]

Field simultaneous measurements, modeling, and simulation of harmonic components in a small generation-transmission network

EUROPEAN TRANSACTIONS ON ELECTRICAL POWER, Issue 1 2007
S. Ríos M
Abstract This paper presents a detailed deterministic model for a small electrical transmission network (110,kV), representing a large (150,MVA) industrial Copper mine production plant. This model is developed and validated with simultaneous field measurements. The network topology allows two operating modes, ring and open ring operation, without disturbing the busbar loads. Experimental results of,simultaneous,measurements at the three load busbars confirm the simulation results obtained with a state space deterministic model. A sensitivity assessment of busbar harmonic distortions, based on singular and eigenvalues analysis, is also presented. Copyright © 2006 John Wiley & Sons, Ltd. [source]