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1
Content available remote Zastosowanie formalizmu Hamiltona do modelowania układów energetycznych z silnikami synchronicznymi o podatnej transmisji ruchu
Czaban A., Lis M.
Przegląd Elektrotechniczny
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2018
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R. 94, nr 1
21--24
PL
W pracy rozpatrywano zasady interdyscyplinarnego modelowania procesów nieustalonych w zespole elektrycznym. Składa się on z napędów z silnikami synchronicznymi o złożonej transmisji ruchu, które są zasilane z transformatora mocy. Wały napędowe silników przedstawiono jako ciągły układ o rozłożonych parametrach mechanicznych z uwzględnieniem sprężystości układu transmisji ruchu. Równania stanu elektrycznego oraz dyskretyzowane równania stanu mechanicznego przedstawiono w postaci Causze’go, które rozwiązano wykorzystując metody numeryczne. Wyniki symulacji komputerowej przedstawiono w postaci graficznej.
EN
In the paper the principles of interdisciplinary modelling of transient processes in an electrical set are considered. This electrical set consists of synchronous motors with a complex transmission of mechanical power and power transformer which energizes the motors. Transmission shafts of the motors are described as the system with the continuously distributed mechanical parameters taking into account the elasticity of transmission of mechanical power. Equations of electrical state and digitized equations of mechanical state are given in Cauchy’s form and solved using numerical methods. Results of computer simulations are presented in a graphic form.
2
Content available remote Modelling of three-phase transformer’s operation using variational methods
Czaban A., Lis M., Popenda A., Patro M., Śliwiński T.
Przegląd Elektrotechniczny
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2015
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R. 91, nr 5
88-91
EN
This paper presents a mathematical model of power system. The interdisciplinary method, based on a modification of Hamilton’s integral variational principle, is used in order to model the system. The analyzed system consists of a nonlinear power transformer that is connected to the unbalanced energy source via asymmetric cable line. The unbalanced RLC circuit is considered as a load of the transformer. The operation of the transformer in transient states is analyzed using the formulated model. The results of computer simulations are presented as graphs.
PL
W pracy przedstawiono model matematyczny układu elektroenergetycznego stosując interdyscyplinarną metodę modelowania, która wykorzystuje modyfikację integralnej zasady wariacyjnej Hamiltona. Analizowany układ składa się z nieliniowego transformatora mocy, który jest podłączony przez asymetryczną linię kablową do niesymetrycznego źródła energii. Transformator pracuje obciążony niesymetrycznym obwodem RLC. Wykorzystując sformułowany model przedstawiono analizę pracy transformatora w stanach przejściowych. Wyniki symulacji komputerowych przedstawiono w postaci graficznej.
3
Content available remote Some theorems of incremental thermoelectroelasticity
Montanaro A.
Archives of Mechanics
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2010
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Vol. 62, nr 1
49-72
EN
We extend to incremental thermoelectroelasticity with biasing fields certain classical theorems, which have been stated and proved in linear thermopiezoelectricity referred to a natural configuration. A uniqueness theorem for the solutions to the initial boundary value problem, the generalized Hamilton principle and the theorem of reciprocity of work are deduced for incremental fields, superposed on finite biasing fields in a thermoelectroelastic body.
4
Content available Run-Up of Linear Long Waves on Uniform Slope in Lagrangian Description
Chybicki W.
Archives of Hydro-Engineering and Environmental Mechanics
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2006
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Vol. 53, nr 2
97-104
EN
The case of linear, two-dimensional long waves on a uniform slope is considered. It is assumed that the fluid is nonviscous and incompressible. In the present paper the description of the long wave proposed by Wilde (Wilde, Chybicki 2004) is based on the fundamental assumption that the vertical material lines of fluid remain vertical during the entire motion. The equations of motion are derived with the help of a variational formulation of the problem. The Lagrangian is the difference between the kinetic and potential energy of the fluid. In the paper a correction followed from dispersion to the results obtained by Shuto is presented.
5
Content available Modelling of gravity waves in water of finite depth
Chybicki W.
Archives of Hydro-Engineering and Environmental Mechanics
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2004
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Vol. 51, nr 3
205-224
EN
An extension of shallow water theory proposed by Wilde (Wilde, Chybicki 2000), for finite water depth and based on the Lagrangian type formalism is presented. As in Bussinesq-type models the vertical dimension is being eliminated and the horizontal displacement is expanded in the even power series of vertical variable Y, but only two terms - with power null and two are taken into account. Based on continuity equation, vertical displacement is expressed in terms of horizontal displacement and its derivatives. The equations of motion are derived from a Hamilton principle applied to Lagrangian function being a difference of kinetic and potential energy. In order to solve the set of governing equations a direct method of variational calculus has been applied. The solutions preserve total energy. The numerical simulations have been verified experimentally, in terms of wave measurements in the flume, for various wave heights and ratios of wavelength to water depth, showing good conformity between measured and calculated values. The theory presented here can also be applied for the case of varying depth.
6
Content available Long water waves as a structure fluid interaction problem
Wilde P., Chybicki W.
Archives of Hydro-Engineering and Environmental Mechanics
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2004
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Vol. 51, nr 2
95-118
EN
The paper describes a new formulation of the theory of long shallow water waves, which is based on the fundamental assumption that vertical material lines of fluid remain vertical during the entire motion. To make the problem consistent from the point of view of physics the case of waves in a flume due to the motion of a piston type generator is considered. At the piston the material line of water particles remains vertical during the entire motion and thus the generation follows the assumption in the description of the motion of water in the flume. Wave equations are derived with the help of a variational formulation of the problem in a material description. The Lagrangian is the difference between the kinetic and potential energies of the fluid and the mechanical system that describes a very simplified wave generator. The basic assumption simplifies the geometry of the displacement field. The definitions of generalized forces follow from variational calculus. The procedure ensures that the energy is preserved. A simple discrete formulation of the problem is based on the finite element method and the corresponding approximate expressions for energies.
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