Home About us Contact
|
Home About us Contact | ||
|
|
||
Matrix Form (matrix + form)
Selected AbstractsA perturbation analysis of harmonic generation from saturated elements in power systemsELECTRICAL ENGINEERING IN JAPAN, Issue 4 2010Teruhisa Kumano Abstract Nonlinear phenomena such as saturation of magnetic flux have considerable effects in power systems analysis. It is reported that a failure in a real 500-kV system triggered islanding operation, where resultant even harmonics caused malfunctions in protective relays. It is also reported that the major origin of this wave distortion is nothing but unidirectional magnetization of the transformer iron core. Time simulation is widely used today to analyze phenomena of this type, but it has basically two shortcomings. One is that the time simulation takes too much computing time in the vicinity of inflection points in the saturation characteristic curve because certain iterative procedures such as N-R (Newton,Raphson) must be used and such methods tend to be caught in an ill-conditioned numerical hunting. The other is that such simulation methods sometimes do not aid an intuitive understanding of the studied phenomenon because all of the nonlinear equations are treated in matrix form and are not properly divided into understandable parts, as is done in linear systems. This paper proposes a new computation scheme that is based on the so-called perturbation method. Magnetic saturation of iron cores in a generator and a transformer are taken into account. The proposed method has a special feature to deal with the first shortcoming of the N-R-based time simulation method stated above. The proposed method does not use an iterative process to reduce the equation residue, but uses perturbation series, so that it is free of the ill-conditioning problem. The user need only calculate the perturbation terms one by one until the necessary accuracy is attained. In a numerical example treated in the present paper, first-order perturbation can achieve reasonably high accuracy, which means very fast computing time. In a numerical study, three nonlinear elements are considered. The calculation results are almost identical to the conventional N-R-based time simulation, which shows the validity of the method. The proposed method can be effectively used in screening where many case studies are needed. © 2009 Wiley Periodicals, Inc. Electr Eng Jpn, 170(4): 35,42, 2010; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.20895 [source] Diagonalization procedure for scaled boundary finite element method in modeling semi-infinite reservoir with uniform cross-sectionINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2009S. M. Li Abstract To improve the ability of the scaled boundary finite element method (SBFEM) in the dynamic analysis of dam,reservoir interaction problems in the time domain, a diagonalization procedure was proposed, in which the SBFEM was used to model the reservoir with uniform cross-section. First, SBFEM formulations in the full matrix form in the frequency and time domains were outlined to describe the semi-infinite reservoir. No sediments and the reservoir bottom absorption were considered. Second, a generalized eigenproblem consisting of coefficient matrices of the SBFEM was constructed and analyzed to obtain corresponding eigenvalues and eigenvectors. Finally, using these eigenvalues and eigenvectors to normalize the SBFEM formulations yielded diagonal SBFEM formulations. A diagonal dynamic stiffness matrix and a diagonal dynamic mass matrix were derived. An efficient method was presented to evaluate them. In this method, no Riccati equation and Lyapunov equations needed solving and no Schur decomposition was required, which resulted in great computational costs saving. The correctness and efficiency of the diagonalization procedure were verified by numerical examples in the frequency and time domains, but the diagonalization procedure is only applicable for the SBFEM formulation whose scaling center is located at infinity. Copyright © 2009 John Wiley & Sons, Ltd. [source] Vertical dynamic responses of a simply supported bridge subjected to a moving train with two-wheelset vehicles using modal analysis methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 9 2005Ping Lou Abstract The vertical dynamic responses of a simply supported bridge subjected to a moving train are investigated by means of the modal analysis method. Each vehicle of train is modelled as a four-degree-of-freedom mass,spring,damper multi-rigid body system with a car body and two wheelsets. The bridge, together with track, is modelled as a simply supported Bernoulli,Euler beam. The deflection of the beam is described by superimposing modes. The train and the beam are regarded as an entire dynamic system, in which the contact forces between wheelset and beam are considered as internal forces. The equations of vertical motion in matrix form with time-dependent coefficients for this system are directly derived from the Hamilton's principle. The equations of motion are solved by Wilson-, method to obtain the dynamic responses for both the support beam and the moving train. Compared with the results previous reported, good agreement between the proposed method and the finite element method is obtained. Finally, the effects of beam mode number, vehicle number, beam top surface, and train velocity on the dynamic responses of the entire train and bridge coupling system are studied, and the dynamic responses of beam are given under the train moving with resonant velocity. Copyright © 2005 John Wiley & Sons, Ltd. [source] Free vibration analysis of arches using curved beam elementsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 13 2003Jong-Shyong Wu Abstract The natural frequencies and mode shapes for the radial (in-plane) bending vibrations of the uniform circular arches were investigated by means of the finite arch (curved beam) elements. Instead of the complicated explicit shape functions of the arch element given by the existing literature, the simple implicit shape functions associated with the tangential, radial (or normal) and rotational displacements of the arch element were derived and presented in matrix form. Based on the relationship between the nodal forces and the nodal displacements of a two-node six-degree-of-freedom arch element, the elemental stiffness matrix was derived, and based on the equation of kinetic energy and the implicit shape functions of an arch element the elemental consistent mass matrix with rotary inertia effect considered was obtained. Assembly of the foregoing elemental property matrices yields the overall stiffness and mass matrices of the complete curved beam. The standard techniques were used to determine the natural frequencies and mode shapes for the curved beam with various boundary conditions and subtended angles. In addition to the typical circular arches with constant curvatures, a hybrid beam constructed by using an arch segment connected with a straight beam segment at each of its two ends was also studied. For simplicity, a lumped mass model for the arch element was also presented. All numerical results were compared with the existing literature or those obtained from the finite element method based on the conventional straight beam element and good agreements were achieved. Copyright © 2003 John Wiley & Sons, Ltd. [source] Linear stability analysis of flow in a periodically grooved channelINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 6 2003T. Adachi1 Abstract We have conducted the linear stability analysis of flow in a channel with periodically grooved parts by using the spectral element method. The channel is composed of parallel plates with rectangular grooves on one side in a streamwise direction. The flow field is assumed to be two-dimensional and fully developed. At a relatively small Reynolds number, the flow is in a steady-state, whereas a self-sustained oscillatory flow occurs at a critical Reynolds number as a result of Hopf bifurcation due to an oscillatory instability mode. In order to evaluate the critical Reynolds number, the linear stability theory is applied to the complex laminar flow in the periodically grooved channel by constituting the generalized eigenvalue problem of matrix form using a penalty-function method. The critical Reynolds number can be determined by the sign of a linear growth rate of the eigenvalues. It is found that the bifurcation occurs due to the oscillatory instability mode which has a period two times as long as the channel period. Copyright © 2003 John Wiley & Sons, Ltd. [source] Union Formation through Merger: The Case of Ver.di in GermanyBRITISH JOURNAL OF INDUSTRIAL RELATIONS, Issue 2 2005Berndt Keller This article is concerned with the recent merger of five German unions to form the new multi-industry union, ver.di. Its focus is on the effects of the merger and on developments in the post-merger phase. The article explores the various internal problems of the new union, concentrating on those that flow from the adoption of a matrix form of organisation. It deals also with the external relations of ver.di, with other unions and with the central organisation of German trade unions, the DGB. Central conclusions here are that the creation of ver.di is likely to exacerbate competition amongst German unions and further erode the position of the peak association. [source] Full-wave analysis of single cylindrical striplines and microstriplines with multilayer dielectricsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2006Farid Bouttout Abstract In this paper, the spectral-domain method is used to calculate the propagation characteristics of cylindrical microstrip transmission lines. The problem is formulated using an electric field integral equation and the spectral-domain Green's function. The solutions of the field components are obtained in matrix forms, which facilitate the calculations of the Green's function and the power flowing over the lines. The Green's functions are obtained in terms of transition matrices over the dielectric layers. The obtained integral equation is solved by moment method using four kinds of basis functions. The convergence of the method is proven. Based on the power,current definition, a stationary expression for the characteristic impedance has been derived analytically. Numerical results of the effective dielectric constant and the characteristic impedance for various line parameters are calculated and analysed. The computed data are found to be in good agreement with results obtained using other methods. The formulation is then applied to covered microstripline, microstripline and stripline with air gaps, for which data are not found in the literature to date. The presented method is used to guide design of microstrip coil for magnetic resonance imaging. This method is also suitable for investigation of multiconductor strip lines. Copyright © 2006 John Wiley & Sons, Ltd. [source] Volume-dependent pressure loading and its influence on the stability of structuresINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2003T. Rumpel Abstract Deformation-dependent pressure loading on solid structures is created by the interaction of gas with the deformable surface of a structure. Such fairly simple load models are valid for static and quasi-static analyses and they are a very efficient tool to represent the influence of gas on the behaviour of structures. Completing previous studies on the deformation dependence of the loading with the assumption of infinite gas volumes, the current contribution is focusing on the influence of modifications of the size and shape of a finite volume containing the gas in particular on the stability of structures. The linearization of the corresponding virtual work expression necessary for a Newton-type solution leads to additional terms for the volume dependence. Investigating these terms the conservativeness of the problem can be proven by the symmetry of the linearized form. The discretization with finite elements leads to standard stiffness matrix forms plus the so-called load stiffness matrices and a rank-one update for each enclosed volume part, if the loaded surface segments are identical with element surfaces. Some numerical examples show first the effectiveness of the approach and the necessity to take the corresponding terms in the variational expression and in the following linearization into account, and second the particular influence of this term on the stability of structures is shown with some specific examples. Copyright © 2002 John Wiley & Sons, Ltd. [source] Positivity-preserving, flux-limited finite-difference and finite-element methods for reactive transportINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 2 2003Robert J. MacKinnon Abstract A new class of positivity-preserving, flux-limited finite-difference and Petrov,Galerkin (PG) finite-element methods are devised for reactive transport problems. The methods are similar to classical TVD flux-limited schemes with the main difference being that the flux-limiter constraint is designed to preserve positivity for problems involving diffusion and reaction. In the finite-element formulation, we also consider the effect of numerical quadrature in the lumped and consistent mass matrix forms on the positivity-preserving property. Analysis of the latter scheme shows that positivity-preserving solutions of the resulting difference equations can only be guaranteed if the flux-limited scheme is both implicit and satisfies an additional lower-bound condition on time-step size. We show that this condition also applies to standard Galerkin linear finite-element approximations to the linear diffusion equation. Numerical experiments are provided to demonstrate the behavior of the methods and confirm the theoretical conditions on time-step size, mesh spacing, and flux limiting for transport problems with and without nonlinear reaction. Copyright © 2003 John Wiley & Sons, Ltd. [source] | ||||||||||