scholarly journals Computation of Stray Losses in Transformer Bushing Regions Considering Harmonics in the Load Current

2020 ◽  
Vol 10 (10) ◽  
pp. 3527
Author(s):  
Sohail Khan ◽  
Serguei Maximov ◽  
Rafael Escarela-Perez ◽  
Juan Carlos Olivares-Galvan ◽  
Enrique Melgoza-Vazquez ◽  
...  
Keyword(s):  
Differential Equation ◽  
Finite Element ◽  
Electromagnetic Field ◽  
Boundary Conditions ◽  
Eddy Current ◽  
Special Functions ◽  
Separation Of Variables ◽  
Practical Implementation ◽  
Load Current ◽  
Good Agreement

The presence of harmonics in the load current considerably increases stray losses in electric transformers. In this research paper, a new model for computing the electromagnetic field (EMF) and eddy current (EC) losses in transformer tank covers is derived considering harmonics. Maxwell’s equations are solved with their corresponding boundary conditions. The differential equation thus obtained is solved using the method of separation of variables. The obtained expressions do not require the use of special functions, accommodating them for practical implementation in the industry. The obtained formulas are evaluated for different spectrum contents of the load current and losses. The results are in good agreement with simulations carried out using the Altair Flux finite element (FE) software.

scholarly journals Out-of-Plane Vibration of Curved Uniform and Tapered Beams with Additional Mass

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Hamdi Alper Özyiğit ◽  
Mehmet Yetmez ◽  
Utku Uzun
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Variable Cross ◽  
Additional Mass ◽  
Inertia Effects ◽  
Tapered Beam ◽  
Out Of Plane ◽  
Good Agreement

As there is a gap in literature about out-of-plane vibrations of curved and variable cross-sectioned beams, the aim of this study is to analyze the free out-of-plane vibrations of curved beams which are symmetrically and nonsymmetrically tapered. Out-of-plane free vibration of curved uniform and tapered beams with additional mass is also investigated. Finite element method is used for all analyses. Curvature type is assumed to be circular. For the different boundary conditions, natural frequencies of both symmetrical and unsymmetrical tapered beams are given together with that of uniform tapered beam. Bending, torsional, and rotary inertia effects are considered with respect to no-shear effect. Variations of natural frequencies with additional mass and the mass location are examined. Results are given in tabular form. It is concluded that (i) for the uniform tapered beam there is a good agreement between the results of this study and that of literature and (ii) for the symmetrical curved tapered beam there is also a good agreement between the results of this study and that of a finite element model by using MSC.Marc. Results of out-of-plane free vibration of symmetrically tapered beams for specified boundary conditions are addressed.

Unified Solution on Skew Plate Bending with Four Edges Supported under Arbitrary Load

2011 ◽  
Vol 243-249 ◽  
pp. 5994-5998
Author(s):  
Lang Cao ◽  
Xing Jie Xing ◽  
Feng Guang Ge
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Fourier Series ◽  
Boundary Conditions ◽  
Engineering Design ◽  
Plate Bending ◽  
The Finite Element Method ◽  
Arbitrary Load ◽  
Skew Plate ◽  
Good Agreement

According to the bending equation and boundary conditions of skew plate in the oblique coordinates system parallel to the edge of the plate, expanding deflection and load into form of Fourier series, the paper derives and obtains unified solution of bending problem for the four-edge-supported skew plate under arbitrary load. Programmed and calculated by mathematica language, the paper also comes with deflections and moments under the condition of any oblique angles, ratios of side length and Poisson ratios. The results of the paper is compared with those by the finite element method in the example, and they’re in good agreement with each other. The paper extends the bending theory of rectangular plate to the skew plate of any angle. The theory being reliable and the result being accurate, the research of the paper can provide reference for engineering design.

scholarly journals ВІЛЬНІ КОЛИВАННЯ ОРТОТРОПНИХ ПЛАСТИН

2020 ◽  
Vol 138 (5) ◽  
pp. 53-61
Author(s):  
Д. В. Лазарєва ◽  
І. В. Курган
Keyword(s):  
Differential Equation ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Boundary Conditions ◽  
Orthotropic Plate ◽  
Free Vibrations ◽  
Element Analysis ◽  
Method Of Boundary Elements ◽  
Rectangular Orthotropic Plate ◽  
Numerical Analytical Method

The solution of the problem of free vibrations of a rectangular orthotropic plate by the methods of boundary and finite elements under any boundary conditions. Transformation of the two-dimensional differential equation of free vibrations of an orthotropic rectangular plate to one-dimensional. Determination of the complete system of its fundamental solutions using the numerical-analytical method of boundary elements. Implementation of the algorithm on the example of a specific plate and comparison with the results of finite element analysis in ANSYS. The solution to the problem of natural vibrations of a rectangular orthotropic plate is obtained without any restrictions on the nature of the fixing of its sides. A transcendental frequency equation is obtained whose roots give the full spectrum of natural frequencies. The modeling and calculations of the orthotropic plate by the finite element method are performed. An analysis of the numerical results obtained by the author's method shows a very good convergence with the results of finite element analysis. For a plate with rigid fastening of three sides with a free fourth side, the discrepancy is slightly higher than for a plate with a hinged support along the contour. Under both variants of the boundary conditions, the frequency spectrum calculated by the boundary element method is lower than in the finite element calculations. Analytical expressions of fundamental functions are obtained that correspond to all possible solutions to the differential equation of free oscillations. For the first time, a solution to the problem of free vibrations of a rectangular orthotropic plate is presented by the numerical-analytical method of boundary elements. The results allow us to solve the problem of free vibrations of a rectangular orthotropic plate by two methods under any boundary conditions, including inhomogeneous ones.

A Numerical Procedure for Obtaining the Static and Pull-In Deflection and Voltage of Capacitive Microcantilever Beams

2006 ◽  
Author(s):  
Seyed Babak Ghaemi Oskouei ◽  
Aria Alasty
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Numerical Procedure ◽  
Nonlinear Ordinary Differential Equation ◽  
Static Deflection ◽  
Element Analysis ◽  
Fringing Field ◽  
Good Agreement

A numerical procedure is proposed for obtaining the static deflection, pull-in (PI) deflection and PI voltage of electrostatically excited capacitive microcantilever beams. The method is not time and memory consuming as Finite Element Analysis (FEA). Nonlinear ordinary differential equation of the static deflection of the beam is derived, w/wo considering the fringing field effects. The nondimensional parameters upon which PI voltage is dependent are then found. Thereafter, using the parameters and the numerical method, three closed form equations for pull-in voltage are developed. The results are in good agreement with others in literature.

scholarly journals Boundary conditions for the wave equation

1933 ◽  
Vol 141 (843) ◽  
pp. 216-217
Keyword(s):  
Differential Equation ◽  
Wave Equation ◽  
Numerical Methods ◽  
Boundary Conditions ◽  
Existence Theorems ◽  
Theoretical Discussion ◽  
Wave Mechanics ◽  
Eigen Values ◽  
Eigen Solutions ◽  
Good Agreement

A single electron in the field of two fixed nuclei, constituting the idealized hydrogen molecular ion, provides the simplest case for the application of wave mechanics to molecular, as distinct from atomic, problems. The most extensive theoretical discussion of the corresponding wave equation has been given by A. H. Wilson in these 'Proceedings.’ He was led to conclude that this equation possesses no eigen-solutions satisfying the usual boundary conditions for an atomic problem. Subsequent investigators have succeeded, however, in obtaining by numerical methods eigen-values in good agreement with observed values of the energy. But, with the exception of Teller, they appear not to have taken account of Wilson’s result. It is therefore worth while to investigate the existence of their solutions and to clear up, if possible, any doubt as to the applicability of the familiar boundary conditions to this type of problem. The usual existence theorems for eigen-values apply only to boundary conditions at ordinary points of the differential equation. The difficulty in cases like Wilson’s equation is that the conditions are given at singular points.

scholarly journals Criticality dependence on data and parameters for a problem in combustion theory

1986 ◽  
Vol 27 (4) ◽  
pp. 416-441 ◽  
Author(s):  
K. K. Tam
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Boundary Conditions ◽  
Boundary Data ◽  
Main Part ◽  
Original Problem ◽  
Upper And Lower Solutions ◽  
Approximate Solutions ◽  
Central Problem ◽  
Good Agreement

AbstractA central problem in the theory of combustion, consisting of a nonlinear parbolic equation together with initial and boundary conditions, is considered. The influence of the initial and boundary data examined. In the main part of the study, a two-step linearization is developed such that the interesting features of the original problem are given by the solution of a non-liner and ordinary differential equation. Approximate solutions are obtained and upper and lower solutions are used to assess the validity of the approximations. Whenever possible, results are compared with those obtained previously and there is good agreement in all cases.

Sign in / Sign up

Export Citation Format

Share Document