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1

Stability of thin-walled square tubes with intermediate stiffeners under torsion

Kołakowski Zbigniew, Jankowski Jacek

Journal of Theoretical and Applied Mechanics

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2019

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Vol. 57 nr 3

655--663

EN

The present paper deals with the buckling of thin-walled square tubes with intermediate stiffeners under torsion when the shear lag phenomenon and distortional deformations are taken into account. A plate model (2D) was adopted for the tube. The tubes were assumed to be simply supported at their ends. The values of critical loads of the tubes were determined with three methods, namely: analytical-numerical method (ANM), finite difference method (FDM) and finite element method (FEM).

2

Mathematical model of oscillations of bearing body frame of emergency and repair railcars

Khromova G., Mukhamedova Z., Yutkina I.

Transport Problems

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2017

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T. 12, z. 1

93--102

EN

Nowadays, the importance of maintenance and effective use of available railcars in the railway transport is growing, and researchers and technical experts are working to address this issue with the use of various techniques. The authors address the use of analytical technique, which includes mathematical solutions for flexural and longitudinal fluctuations of the bearing framework of a railcar body frame. The calculation is performed in connection with the modernization of the body frame of emergency and repair rail service car, taking into account the variability in section, mass, longitudinal stiffness, and bending stiffness. It allows for extension of the useful life of their operation, with special focus on vehicles owned by Joint-Stock Company "Uzbekistan Railways". The simulation of equivalent bearing body frame of emergency and repair rail service car was carried out using an elastic rod with variable parameters including stiffness and mass. The difference between the proposed model and the existing ones is due to the variability in cross section, mass, and the longitudinal and bending stiffness along the length of equivalent beam, which corresponds to the actual conditions of operation and data of the experimental studies conducted by the authors on the bearing frames of electric locomotives’ variable sections. The frequency analysis that was carried out with the use of the Mathcad 14 programming showed that the frequencies of natural oscillations change on n harmonicas = 1, 2, 3 … 5. As regards longitudinal oscillations of system, in case of introduction of the damping subfloor, the frequency of natural oscillations of the upgraded rail car frame λ1mn increases on comparing with standard λ1n (for example, in case of n = 5 the frequency is 0.587 and 0.602 Hz/m, respectively).

3

Numerical model for calculation of fluctuations in the main-bearing frame of railcar with changing stiffness and physical parameters

Mukhamedova Z.

Journal of KONES

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2016

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Vol. 23, No. 2

255--259

EN

This article covers the use of analytical technique of solutions for flexural and longitudinal fluctuations of the bearing framework of a railcar body frame in the form of an elastic core of variable section with a variable weight, flexural and longitudinal rigidity. The calculation is performed for the modernization of the body frame of emergency and repair rail service car, taking into account the variability of section, mass, longitudinal and bending stiffness along the length to prolong the service life of their useful operation. Problems of increasing the reliability and strength of the frames, load-bearing body structure and components for rail vehicles during their design, operation and modernization are extensively studied. An analytical-numerical method based on the dynamic strength of the bearing body frame of emergency and repair rail service car, assuming a beam-type pattern of its fluctuations with elastic fixing of the ends under harmonic load as it moves along the track with periodic joint roughness.

4

Coupled static and dynamic buckling modelling of thin-walled structures in elastic range review of selected problems

Kołakowski Z., Teter A.

Acta Mechanica et Automatica

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2016

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Vol. 10, no. 2

141--149

EN

A review of papers that investigate the static and dynamic coupled buckling and post-buckling behaviour of thin-walled structures is carried out. The problem of static coupled buckling is sufficiently well-recognized. The analysis of dynamic interactive buckling is limited in practice to columns, single plates and shells. The applications of finite element method (FEM) or/and analytical-numerical method (ANM) to solve interaction buckling problems are on-going. In Poland, the team of scientists from the Department of Strength of Materials, Lodz University of Technology and co-workers developed the analytical-numerical method. This method allows to determine static buckling stresses, natural frequencies, coefficients of the equation describing the post-buckling equilibrium path and dynamic response of the plate structure subjected to compression load and/or bending moment. Using the dynamic buckling criteria, it is possible to determine the dynamic critical load. They presented a lot of interesting results for problems of the static and dynamic coupled buckling of thin-walled plate structures with complex shapes of cross-sections, including an interaction of component plates. The most important advantage of presented analytical-numerical method is that it enables to describe all buckling modes and the post-buckling behaviours of thin-walled columns made of different materials. Thin isotropic, orthotropic or laminate structures were considered.

5

Zagadnienie brzegowe pola elektromagnetycznego struktury cylindrycznej z nieliniowym obszarem - rozwiązanie otrzymane metodą analityczno-numeryczną

Sowa M., Spałek D.

Prace Naukowe Politechniki Śląskiej. Elektryka

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2012

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z. 1

7--31

PL

W artykule jest rozważane nieliniowe zagadnienie z teorii pola elektromagnetycznego: struktura cylindryczna z powłoką o nieliniowej konduktywności umiejscowiona w polu sinusoidalnie zmiennym w czasie. Podjęto próbę określenia rozkładu wektorowego potencjału magnetycznego dla zadanych warunków brzegowych pierwszego rodzaju (warunek Dirichleta) i drugiego rodzaju (warunek brzegowy Neumanna). W tym celu zastosowano metodę wykorzystującą rozwinięcie w szereg względem "małego parametru". Cechą charakterystyczną wybranej metody są obliczenia symboliczne. W dalszej kolejności, w celu sprawdzenia dokładności rozwiązania, zdefiniowano błędy równania różniczkowego (błąd całkowy i błąd maksymalny) i określono ich wartości oraz sprawdzono bilans mocy. Celem artykułu jest przedstawienie metody pozwalającej otrzymać rozwiązanie wzorcowe dla wybranych zagadnień teorii pola elektromagnetycznego, uwzględniających nieliniową konduktywność.

EN

A nonlinear problem in the electromagnetic field theory is considered: a cylindrical structure with a nonlinear conductive layer placed in a uniform sinusoidal field. An attempt was made to determine the magnetic vector potential distribution for imposed boundary conditions of the first (Dirichlet boundary condition) and second (Neumann condition) kind. For this purpose, a method that bases on the "small parameter" expansion is used. A characteristic feature of the chosen method is that it includes the need for symbolic calculation. Furthermore, in order to verify the solution, differential equation errors were defined and evaluated (integral error and maximum error). Additionally, the power balance was verified. The aim of this paper is to present a method allowing obtainment of a model solution for chosen problems in the electromagnetic field theory which involve nonlinear conductivity.

6

Modeling magnetic field in the vicinity of single wire helix

Budnik K., Machczyński W.

Computer Applications in Electrical Engineering

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2011

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Vol. 9

69--77

EN

Transmission of the electric power is accompanied with generation of low - frequency electromagnetic fields. Electromagnetic compatibility studies require that the fields from sources of electric power be well known. Many of these sources are not defined to the desired degree of accuracy. This applies e.g. to the case of helical current conductors of finite length. The paper presents an analytical-numerical method of the calculation of the 3D magnetic fields in vicinity of conductors having helical structure. The method is based on the Biot-Savart law and a software tool to model the magnetic fields generated by e.g. twisted wires, helical coils, etc can use the formulas obtained.