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1

Application of graphs in the analysis of vibrating 3-dimensional systems

Wojnarowski J.

International Journal of Applied Mechanics and Engineering

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2016

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Vol. 21, no. 3

761--766

EN

Vibrating 3-dimensional mechanical systems are described by hybrid graphs. By dividing the hybrid graph into a tree and associated co-tree it is possible to describe in terms of matrices: across-flow-variables, stiffness and flexibility. The application of the formalism of graphs makes it possible to analyze mechanical systems in terms of dynamic characteristic and trajectory motion of determinate points.

2

XII Sympozjum "Podstawowe Problemy Energoelektroniki, Elektromechaniki i Mechatroniki" PPEEm '07

Kluszczyński K.

Nowa Elektrotechnika

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2008

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nr 3 (43)

34--35

3

Seminarium "Problemy eksploatacyjne elektroenergetyki, elektromechaniki i energoelektroniki" 8SPE-2007

Hickiewicz J.

Napędy i Sterowanie

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2007

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R. 9, nr 7/8

109-110

PL

Podobnie jak w latach ubiegłych, w dniach 17-19 kwietnia br., tym razem w Zespole Turystyczno-Wypoczynkowo-Rehabilitacyjnym Caritas Diecezji Opolskiej Sebastianeum Silesiacum w Kamieniu Śląskim k. Opola, odbyło się seminarium 8SPE-2007. Seminarium nie rozpoczęło się w Elektrowni Opole, jak to się odbywało tradycyjnie od 1994 r., ze względu na remont tamtejszej wielkiej sali konferencyjnej.

4

Rayleigh-Taylor instability in electrohydrodynamics bounded by rough surface in the presence of an electric field

Rudraiah N., Venkatachalappa M., Siddalinga Prasad M.

International Journal of Applied Mechanics and Engineering

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2007

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Vol. 12, no 1

183-196

EN

The effects of slip due to roughness of nanostructured silicon, transverse time invariant but space variant electric field due to embedded electrodes and surface tension due to free surface on Rayleigh - Taylor instability (RTI) in electrohydrodynamics are investigated using a linear stability analysis. A simple theory based on considering a rough nanostructured silicon interface bounding a light poorly conducting liquid is proposed to find an analytical expression for the growth rate n of RTI, in the presence of suitably strong of electric field, in the form [...] is the cIassical growth rate in the absence of both electric field and roughness of the substrate [...] is the normal velocity, delta represents the effect of electric field, [...] the slip coefficient, [...] the wave number, B the Bond number and [...] will depend on whether the electric field is in the direction of gravity or opposing its direction. It is shown that the combined effect of electric field and roughness af the substrate is to reduce the growth rate of RTI considerably over the value it would have in the cIassical case.

5

Governing equations for the coupled electromagnetics and acoustics of clay and clay like porous media

Drzewiecki A., Sypniewska-Kamińska G.

Vibrations in Physical Systems

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2002

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Vol. 20

138--139

6

Dynamika maszyny elektrycznej obciążonej siłami procesu technologicznego

Stępniewski A. A.

Inżynieria Rolnicza

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2002

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R. 6, nr 9

271--277

PL

Stosując równania wektorów strumieni stojana i twornika oraz równania dynamiki układu dwumasowego, zbudowano model matematyczny układu elektromechanicznego, składającego się z silnika prądu zmiennego oraz reduktora, którego wał odbiorczy połączony jest z urządzeniem napędzanym podatnym wałem. W modelach uwzględniono podatność skrętną wału napędowego, tłumienie drgań i sterowanie ze sprzężeniem zwrotnym względem położenia, prędkości i przyśpieszenia. Pominięto histerezę mechaniczną i magnetyczną, wpływ prądów wirowych i nasycenie magnetyczne. Wykonano badania symulacyjne, których wyniki przedstawiono w postaci czasowych przebiegów parametrów kinematycznych, dynamicznych i elektrycznych.

EN

At application of flux vector equations for the stator and armature as well as an equation of two-mass system dynamics, a mathematical model of electromechanical system was developed. The system consisted of an alternating-current motor and reducer, the driving shaft of which was connected to driven shaft of the machine. Torsial flexibility of the driving shaft, vibration damping, related to position feedback control of the velocity and acceleration, were included into models. However, the mathematical and magnetic hysteresis, the effect of rotating currents and magnetic saturation, were neglected. The simulation studies were carried out and the results were presented in form of time depended courses of kinematic, dynamic and electric parameters.

7

Analiza zjawisk elektromagnetycznych w przetwornikach elektromechanicznych na podstawie modeli polowych symulacja stanów dynamicznych

Demenko A., Nowak L., Szeląg W.

Prace Instytutu Elektrotechniki

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2001

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Z. 208

47-60

PL

W pracy przedstawiono algorytmy analizy dynamicznych stanów pracy przetworników elektromechanicznych na podstawie trójwymiarowych modeli polowych. Rozpatrzono układy z masywnymi elementami przewodzącymi o uzwojeniach wykonanych z cienkich przewodów. Szczególną uwagę poświęcono zagadnieniom związanym z symulacją ruchu na modelu o elementach skończonych. Przedstawiono wyniki obliczeń dla dwóch przykładów. Analizowano zjawiska w silniku magnetoelektrycznym o magnesach wykonanych z materiału przewodzącego oraz zjawiska w silniku liniowym o masywnej części wtórnej.

EN

The paper presents algorithms for dynamic analysis of electromechanical converters - on the basis of three dimensional field models. Systems containing solid conducting parts and filamentary windings have been considered. Special attention for movement finite element modelling has been paid. In this case, the equation of the mechanical motion must be taken into consideration. In order to solve this equation, the explicit or implicit time-stepping algorithm can be applied - expressions (2) and (3). The implicit procedure is unconditionally stable but it requires the iterative calculations. During the movement, the geometric structure of the considered region is changing. Therefore, the grid remeshing is required. Method of remeshing depends on the type of problem. Two main approaches are possible to applied: (a) the nodes within moving region are fixed and (b) the nodes move in accordance with this region. In case of infinitely long moving part with constant permeability, as for example in linear induction motor, the movement modelling is relatively simple task. During the dynamic process, the entirely constant mesh can be applied. The additional term in equation (1), proportional to velocity of the moving body may be omitted if the special procedure of estimation of derivative dA/dt - according to formulae (6) - is applied. Problem is still more complicated in case of short moving part. In such case, the polynomial or Fourier's interpolation of the FE matrices is proposed. The grid is entirely constant. On the basis of "grid positions", the Newton polynomial or Fourier's series is constructed. If the total displacement of the moving body is limited, then the distorted element method may be applied. However, the distortion of the elements causes additional formal changes of the magnetic stored energy and therefore causes additional parasitic components of the electromagnetic force or torque. As an illustration of the elaborated algorithms, the operation of the synchronous motor with conducting permanent magnet and start-up operation of the linear induction motor have been investigated.

8

Analiza zjawisk elektromagnetycznych w przetwornikach elektromechanicznych na podstawie modeli polowych dwu i trójwymiarowe modele dyskretne

Demenko A., Nowak L., Szeląg W.

Prace Instytutu Elektrotechniki

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2001

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Z. 208

61-73

PL

W pracy przedstawiono zarys historii stosowania numerycznych metod analizy pola elektromagnetycznego w obliczeniach przetworników elektromechanicznych. Zwrócono uwagę na dwa główne nurty prac wykorzystujących te metody: (a) prace polegające na stosowaniu metod polowych do obliczania parametrów schematów zastępczych przetworników, (b) prace nad modelami polowo-obwodowymi i algorytmami, w których równania pola są rozwiązywane równocześnie z równaniami stanu przetwornika. Omówiono badania nad dwuwymiarowymi modelami polowo-obwodowymi. Przedstawiono ogólną postać równań modeli trójwymiarowych.

EN

The paper presents shortly the history of the applications of the numerical methods of electromagnetic field analysis in the electromechanical converter calculations. Attention is paid to the finite difference (FD) and finite element (FE) methods. It has been shown that there are two main lines of the application of these method: (a) the methods are applied in the calculations of integral parameters of the equivalent electric and magnetic circuits, and (b) the equations of FD or FE method are combined with the circuit equations of converter windings and with circuit equations of supply system (the circuit and field equations create the so called coupled field-circuit model of the converter). Summarily, the research works in relation to the 2D field-circuit models are discussed in the section 2. The 3D field-circuit models are presented in the section 3. In the considered models, the magnetic vector potential formulation is applied. First, the equations for the models with the edge element (EE) are presented. The finite elements are assumed to be edge elements in relation to magnetic vector potential A. The EE equations of the magnetic field are combined with the equations that describe the distribution of the electric field of conducting currents. In the case of the region with filamentary conductors, the EE equations are combined with the voltage equations which describe the winding currents i(c), see Eq. (1). These currents represent the edge values of current vector potential T. However, for the regions with solid conductors, the electric scalar potential V formulation is applied, see Eq. (3). Matrix equation (3) can be represented by the equations of the reluctance-conductance network. The network representation of tetrahedron is shown in Fig. 1 (reluctance network - Fig. 1a), conductance network - Fig. 1b). The edge element method has been compared with the classical nodal element method for the magnetic vector potential formulation. Finally, the unifed matrix of the equations for the 3D field models have been proposed, see Eq. (6). Equations (6a), (6b) are related to A-T formulation and A-V formulation, respectively. In the case of A-T formulation the finite elements are assumed to be nodal or edge elements in relation to A and T. However, for A-V formulation the finite elements are assumed be nodal in relation to V and are assumed to be nodal or edge elements in relation to A.

9

On the plane steady flows of a viscous incompressible fluid of finite electrical conductivity in the presence of a magnetic field

Naeem R. K., Shad Ahsan S. M.

Applied Mechanics and Engineering

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2000

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Vol. 5, no 4

897-911

EN

Basic equations describing the motion of a viscous incompressible fluid of finite electrical conductivity in the presence of a magnetic field (1) for constant vorticity flows are recast in a new form. It is indicated that the other flow variables can be expressed either in terms of the magnetic flux function 'fi' or the stream function 'psi' where these functions satisfy a partial differential equation whose every solution, including Naeem (1996), is a solution to the basic flow equations and (2) for variable vorticity flows an unknown function f(r) is introduced in the basic flow equations. The solutions are determined and one solution admits, as a particular case, Naeem's solution by appropriately choosing the arbitrary constants therein. Some applications of the solutions to physically possible situations are also presented.

10

Macroscopic description of the non-linear electro-mechanical coupling in ferroelectrics

Bohle U., Kamlah M., Munz D., Tsakmakis C.

Applied Mechanics and Engineering

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2000

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Vol. 5, no 4

959-970

EN

Our objective is the construction of a phenomenological ferroelectricity model for general electro-mechanical loading histories, which is simple enough to be implemented in an FE-code with reasonable expenditure. In this paper, we motivate and verify the one-dimensional formulation of such a model. This is done by introducing remanent polarization and remanent strain as internal variables besides stress, strain, electric field and polarization. Polarization induced anisotropy is taken into account to the extent deemed necessary. For the sake of simplicity, no rate effects are included. By bilinear approximation the following characteristic phenomena of macroscopic ferroelectricity are represented: dielectric hysteresis, polarization induced piezoelectricity, butterfly hysteresis, ferroelastic hysteresis, mechanical depolarization, field dependent coercitive stress.