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1

Influence of rail track foundation parameters on the nonlinear dynamic response of a railway track

Kozioł Piotr, Pilecki Zenon

Technical Transactions

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2025

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Vol. 122, iss. 1

art. no. e2025021

EN

The dynamic response of railway tracks is a key factor influencing the operational safety and reliability of rail transport. Classical analytical methods for modelling track dynamics become insufficient at higher operating speeds, as they typically assume linear behaviour and cannot account for nonlinearities present in the fastening system or in the rail track foundation response. This increases the risk of damage, leading to traffic interruptions, financial losses, and reduced safety. To support predictive maintenance, it is necessary to develop databases based on in-situ measurements, complemented with synthetic data obtained from validated analytical and semi-analytical models. This paper presents such a model, designed to analyse how the parameters of the track foundation – including stiffness and damping – affect the track's dynamic response to loads generated by a moving railway vehicle. The model incorporates experimentally confirmed nonlinear stiffness of the fastening system, represented by a viscoelastic layer that provides continuous support for the rails.

2

Współczynnik ścinania w warstwowych płytach z tektury falistej

Garbowski Tomasz, Graczyk Julia

Przegląd Papierniczy

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2025

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R. 81, nr 12

686--690

PL

Płyty warstwowe z rdzeniem pofalowanym stanowią istotną grupę lekkich konstrukcji stosowanych w opakowaniach, przegrodach budowlanych, konstrukcjach transportowych oraz panelach inżynierskich. Odpowiedź mechaniczna takich układów w dużej mierze zależy od geometrii periodycznego rdzenia, która determinuje podatność na ścinanie poprzeczne, a tym samym efektywną sztywność postaciową płyty. Podczas gdy klasyczne współczynniki korekcyjne ścinania są dobrze znane w rdzeniach płaskich, brak jest ujednoliconej formuły analitycznej dla rdzeni pofalowanych o dowolnym kształcie. W niniejszej pracy przedstawiono zwartą formułę matematyczną umożliwiającą wyznaczenie współczynnika korekcyjnego ścinania ks dla płyt warstwowych z periodycznym rdzeniem pofalowanym o różnych kształtach, takich jak: fala sinusoidalna, trapezowa, półkolista, elipsoidalna i trójkątna. Podstawą analizy jest zasada równoważności energii odkształcenia postaciowego przekroju rzeczywistego i jego odpowiednika w teorii Timoshenki. Pole naprężeń stycznych rekonstruowane jest na podstawie ogólnego opisu geometrycznego profilu fali i całkowane w obrębie jednej komórki periodycznej. Zaproponowana metoda pokazuje, w jaki sposób kształt pofalowania wpływa bezpośrednio na mechanizm przenoszenia ścinania poprzez rozkład szerokości efektywnej oraz moment statyczny. Bez wchodzenia w zagadnienia optymalizacji, czy szczegółowej walidacji numerycznej, praca koncentruje się na strukturze matematycznej współczynnika ks oraz jego wrażliwości geometrycznej. Uzyskane zależności stanowią przejrzyste narzędzie do analiz porównawczych oraz projektowania nowych rdzeni w płytach warstwowych, takich jak tektura falista.

EN

Sandwich plates with corrugated cores represent an important class of lightweight structural systems used in packaging, building envelopes, transport structures and engineered panels. The mechanical response of such systems is strongly influenced by the geometry of the periodic core, which governs transverse shear deformation and, consequently, the effective shear stiffness of the plate. While classical shear correction factors are well established for flat sandwich cores, no unified analytical framework exists for corrugated cores of arbitrary shape. This short contribution presents a concise mathematical formulation for the evaluation of the shear correction factor ks in sandwich plates with periodic corrugated cores of various geometries, including sinusoidal, trapezoidal, semicircular, elliptical and triangular waveforms. The formulation is based on energetic equivalence between the true cross-sectional shear strain energy and the corresponding Timoshenko plate idealization. The shear-stress field is reconstructed using a generalized geometric description of the corrugation profile and integrated over one periodic cell. The proposed framework highlights how the corrugation shape directly influences the shear-transfer mechanism through the first moment of area and the effective material width distribution. Without focusing on numerical optimization or detailed finite element validation, the paper emphasizes the mathematical structure of ks and its geometric sensitivity. The derived expressions provide compact analytical insight into the role of corrugation shape and may serve as a transparent tool for preliminary design and comparative studies of new cores in corrugated bords.

3

Analytical model of a composite girder with flexible adhesive bondline

Szeptynski P.

Archives of Mechanics

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2024

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Vol. 76, nr 1-2

155--189

EN

The paper presents a linear elastic one-dimensional Discrete Layer–Wise (DLW) analytical model of a composite girder consisting of two beams bonded together with a layer of a flexible adhesive. The model takes into account both longitudinal and transverse deformation of component beams, the First Order Shear Deformation Theory (FSDT) for these adherends as well as extensibility of the adhesive layer. A system of governing equations is derived and a general solution is found with the use of the method of generalized eigenvectors. Two examples are analyzed both with the use of the considered 1D analytical model and a 3D Finite Element Analysis (FEA) in order to validate predictions of the introduced theory. Satisfactory agreement is found between theoretical and numerical results.

4

Free flexural vibrations of an expanded-tapered sandwich beam

Magnucki Krzysztof, Kustosz Joanna, Goliwąs Damian

Vibrations in Physical Systems

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2023

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Vol. 34, nr 1

art. no. 2023114

EN

The paper is devoted to the analytical modelling of a simply supported expanded-tapered sandwich beam. The simplified analytical model of this beam with omitting the shear effect is elaborated. Based on Hamilton’s principle, the differential equation of motion of this beam is obtained. This equation is analytically solved with consideration of the deflection line of this beam subjected to its own weight. The fundamental natural frequencies for exemplary beams are derived. Moreover, the FEM model of the beam in the ABAQUS is developed. The calculation results of the fundamental natural frequency of exemplary beams of these two methods are presented in tables and figures.

5

Effective shaping of a stepped sandwich beam with clamped ends

Magnucki Krzysztof, Kustosz Joanna, Goliwąs Damian

Acta Mechanica et Automatica

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2023

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Vol. 17, no. 2

200--204

EN

The aim of this work is to propose a sandwich beam with stepped layer thickness in three parts along its length. The total depth, width of the cross-section and its mass are constant. The beam is under a uniformly distributed load. The system of two equilibrium equa-tions was formulated for each part based on the literature. This system was analytically solved for the successive parts of the beam and the functions of the shear effect and deflection were determined in them. The effective stepped layer thicknesses was determined on the basis of the adopted criterion for minimizing the maximum deflection of the beam. The example calculations were made for two elected beams. The effective shapes of these beams are shown in the figures. Moreover, FEM numerical calculations of the deflections of these beams are performed.

6

Modelling of linear elasticity and viscoelasticity of thermosets and unidirectional glass fibre-reinforced thermoset-matrix composites. Part 1, Theory of modelling

Klasztorny Marian, Nycz Daniel B.

Composites Theory and Practice

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2022

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R. 22, nr 1

3--15

EN

The paper presents advanced analytical modelling of the linear elasticity and viscoelasticity of thermosets and unidirectional long glass fibre-reinforced thermoset-matrix (UFRT) composites. New non-aging materials fully relaxed after the curing and post-curing processes are considered. Quasi-static long-term isothermal reversible viscoelastic processes under normal conditions are modelled. The thermosets are isotropic materials with viscoelastic shear strains and elastic bulk strains, and the fibres are isotropic and elastic. New rheological models for thermosets and UFRT composites, described by the smallest possible number of material constants, are developed. The viscoelastic generic function for shear/quasi-shear stresses is assumed as the Mittag-Leffler fractional exponential function in an integral form. The thermoset is described by two elastic and three viscoelastic parameters. The homogenized UFRT composite is described by five elastic and five viscoelastic parameters. Conjugated/unconjugated standard/inverse constitutive equations of the linear elasticity/elasticity-viscoelasticity governing thermosets and UFRT composites are formulated. The equations are mutually analytically transformable.

7

On the approach to the analysis of the growth of epitaxial layers by pulsed laser deposition

Pankratov Evgeny L.

Computer Methods in Materials Science

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2021

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Vol. 21, No. 4

203--208

EN

This paper considers an analytical approach for the prognosis of mass and heat transport during the growth of epitaxial layers by means of pulsed laser deposition. The approach provides the opportunity to make a prognosis which takes into account the spatial and temporal variations of their parameters and, at the same time, the nonlinearity of these processes. Based on this approach, the influence of the variation of several parameters on the growth process is investigated.

8

On the method of changing the temperature of liquids and gases in a transportation system by local heating or cooling

Pankratov Evgeny L.

Computer Methods in Materials Science

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2020

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Vol. 20, No. 3

107--112

EN

In this paper we consider an approach of changing the temperature of liquids and gases in a pipeline by local heating and cooling. The approach based on changing of temperature of series sections of the pipeline due to external modification of temper-ature of these sections. This situation could be used for heat sink or increasing of temperature. A model of heat transfer based on transfer of heat in a pipeline with account convection due to liquid/gas transport has been introduced. We also introduce an ana-lytical approach for analysis of liquid/gas transport with account transport of heat due to convection. The approach gives a possi-bility to take into account spatial and temporal variation of parameters of transport and at the same time to take into account non-linearity of considered processes.

9

Designing a monolithic tip-tilt-piston flexure manipulator

Hao G., He X.

Archives of Civil and Mechanical Engineering

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2017

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Vol. 17, no. 4

871--879

EN

This paper deals with the design of a monolithic tip-tilt-piston flexure manipulator for high-precision applications. The manipulator is first proposed with consideration of actuation isolation, which is a symmetrical and compact design and can be monolithically fabricated without using additive manufacturing. Kinematic and kinetostatic models are then analytically derived for quick parameter assessments. A case study is discussed finally, where a monolithic prototype has been made using CNC milling machining, comparisons among analytical, FEA and testing results are also undertaken.

10

Analytical model end plate bolted joint under bending moment and axial force load

Pisarek Z.

Czasopismo Inżynierii Lądowej, Środowiska i Architektury / Journal of Civil Engineering, Environment and Architecture

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2015

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z. 62, nr 3/II

325--336

EN

In typical buildings with steel-concrete composite floors, joints are designed to transmit only hogging bending moment. In case of the large horizontal loads due to wind, earthquake or accidental events, sagging bending moments in the joint and not to neglect axial force can also occur. Additionally, large deformations of the structure cause tying and prying effects. The joints loaded in this way are changing their characteristics, and their strength for the bending moment is decreased. In global analysis of the structures, the accurate knowledge of the characteristics of the joints allows for determine accurate internal forces in the structural elements. Procedures presented in literature and standards [1] allow for appointing of characteristics of the joint only for bending moment without taking into account axial loads. In the paper, a mechanical model based on “component method” for evaluation of characteristics of the composite joint under bending and axial loads is presented. The influence of tying and prying actions on distribution of the internal forces in a joint is also analyzed. The procedure for calculation of the characteristics of the composite joint with bolted end-plate connection is elaborated too.

PL

W typowych budynkach ze stropami zespolonymi stalowy-betonowy, węzły są projektowane głownie do przenoszenia momentów zginających. W przypadku dużych obciążeń poziomych powstałych w wyniku oddziaływań wiatru, trzęsień ziemi lub zdarzeń wyjątkowych, w węzłach pojawia się moment dodatni i siła osiowa o niezaniedbywalnej wartości. Dodatkowo, duże odkształcenia konstrukcji mogą wywoływać siłę skleszczenia efekt cięgnowy w ryglach ramy. Obciążone w taki sposób węzły zmieniają swoją charakterystykę, a ich nośność na zginanie maleje. W analizie globalnej konstrukcji, znajomość rzeczywistych charakterystyk węzłów pozwala na określenie dokładnego rozkładu sił wewnętrznych w elementach konstrukcji. Procedury przedstawione w literaturze i normie [1] pozwalają na wyznaczanie charakterystyki węzłów jedynie obciążonych momentem zginającym bez uwzględnienia siły osiowej. W artykule przedstawiono, oparty na metoda składnikowej, model mechaniczny, przydatny do określenia charakterystyki węzła zespolonego poddanego obciążeniu momentem zginającym i siłą osiową. Przeanalizowano również wpływ efektu kleszczenia i efektu cięgnowego na rozkład i wartość sił wewnętrznych w połączeniu. Opracowano procedury do obliczania takich połączeń i na przykładzie wykonano porównanie otrzymanej z modelu charakterystyki węzła z wynikami badań doświadczalnych.

11

Material model and revealing the truth

Czarnecki L., Sokołowska J. J.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2015

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Vol. 63, nr 1

7--14

EN

The paper refers to the approach used in science, specifically in building materials engineering, assuming the possibility of material modeling, including modeling of the technical characteristics of building materials of various compositions as well as modeling phenomena/processes that occur during the use of materials and structures made from them. The authors analyze the merits of the approach of modeling in the context of compliance computational models to reality, consider the significance of the selection of the proper model (type of mathematical function, number of input data) which should be based on the knowledge of modeled material or phenomenon and later adequate verification of the model. The authors also underline importance of proper interpretation of results obtained by calculation. Misrepresentation may result in a misstated model of the studied phenomenon and lead to incorrect conclusions, which puts the researcher far from the truth, that he or she should always seek for.

12

Stress intensity factor against fracture toughness in functionally graded geopolymers

Nazari A., Sanjayan J. G.

Archives of Civil and Mechanical Engineering

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2015

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Vol. 15, no. 4

1007--1016

EN

The benefits of producing functionally graded geopolymer in terms of their modified stress intensity factor and fracture toughness are discussed in the present paper. Pre-notched functionally graded geopolymer beams were fabricated by two different fly ash-based geopolymer mixtures. The load was applied parallel to the functionally graded region; two different structures were evaluated by changing the position of the notch. The obtained results indicated that the crack nucleation and growth depend on the interaction between stress intensity factor and fracture toughness. According to the notch position, a crack experience upward or downward variations of properties. When the crack is located in the mixture with the lowest toughness, the variation of properties is called upward and vice versa. A crack facing an upward fracture toughness region is arrested, when the applied stress is equal to the weakest strength of the constituent materials. On the other hand, the fracture toughness of a crack facing a downward fracture toughness gradient is more than that facing an upward one, without any subsequent arresting. It was shown that the position of the notch, and experiencing of downward or upward gradient in mechanical properties mainly determine the final flexural strength of the specimens.

13

Dobór parametrów płyty dociskowej układu wibroizolacji podtorza na podstawie jego modelu dyskretno-ciągłego

Bednarz J., Targosz J.

TTS Technika Transportu Szynowego

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2012

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R. 19, nr 9

4039--4046, CD

PL

W pracy przedstawiono metodę analitycznego modelowania wibroizolowanych torowisk pojazdów szynowych z wykorzystaniem modelu dyskretnego-ciagłego. W pracy przedstawiono analizę układu wibroizolacji torowiska oraz przykład doboru optymalnych parametrów mechanicznych płyty dociskowej będącej jednym z podstawowych elementów systemu wibroizolacji. Rozwiązano zagadnienie wartości własnych i przedstawiono funkcjonał w oparciu o który istnieje między innymi możliwość doboru parametrów masowych i sztywności płyt dociskowych różnego typu. Praca wykonana w ramach projektu badawczego 4875/B/TO2/2010/38 finansowanego przez Ministerstwo Nauki i Szkolnictwa Wyższego.

EN

In the paper the method of analytical modelling of vibration isolated railways track based on discrete-continuous models is presented. The paper presents an analysis of track vibration isolation system and selection of optimal mechanical parameters of platen which is one of the basic elements of vibration isolation system. In the paper the eigenvalue problem solution is presented and the functional on which there is a possibility to select the parameters of mass and stiffness of the platen of different types. The work was done in the framework of a research project funded by the Ministry of 4875/B/TO2/2010/38 of Science and Higher Education.

14

Analysis of effects of magnetic slot wedges on characteristics of large induction motor

Dems M., Komęza K., Sykulski J. K.

Przegląd Elektrotechniczny

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2012

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R. 88, nr 7b

73-77

EN

Magnetic slot wedges are often used to improve starting performance of large induction motors. In this paper we have investigated – through simulation – the effects of the wedges on the performance characteristics of the motor and core losses under no load condition. Both analytical and hybrid two-dimensional field-circuit models have been used. In order to reliably establish the parameters of the end connections of the rotor cage, whose values significantly influence the results of simulation, a three-dimensional model was developed, also useful for verification purposes at standstill. The simulation has demonstrated the effects of the wedges on the starting performance but revealed little influence on the core losses.

PL

W artykule przedstawiono wpływ zastosowania klinów magnetycznych na charakterystyki eksploatacyjne i straty w rdzeniu silników indukcyjnych dużej mocy w warunkach obciążenia. Obliczenia zostały wykonane z wykorzystaniem hybrydowego modelu obwodowo-polowego 2D oraz metodami analitycznymi. Wyniki obliczeń porównano z wynikami pomiarów.

15

Analytical modelling cargoes displacement in wagon and tension in fastening

Turanov K., Timukhina E.

Transport Problems

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2008

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T. 3, z. 3

69-76

EN

The article deals with the conclusions of analytical modeling cargoes displacement relative wagon and tension in fastening on exposure to spatial system of forces.

16

A studyon liquefaction susceptibility of some soils from the coast of Marmara sea

Sawicki A., Świdziński W.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2006

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Vol. 54, nr 4

405-418

EN

The paper presents an estimation of liquefaction susceptibility of some soils from the coast of the Marmara Sea, which was heavily striken by the Kocaeli earthquake in 1999. Firstly, the results of field investigations are summarized. Then, the results of laboratory investigations of physical and mechanical properties of the soils collated from the sites investigated are presented. The mechanical properties relate to the compaction/liquefaction model of saturated soils. This model is briefly outlined, then respective experimental procedures dealing with its calibration described, and values of material parameters listed. Liquefaction potential of investigated soils is analysed using standard procedures, based on the grain size distribution curves and SPTs. Finally, the simulation of pore-pressure generation and onset of liquefaction of Turkish soils is carried out, using the compaction/liquefaction model. Discussion of some standard empirical procedures of estimation of liquefaction potential of saturated soils, conducted from the analytical point of view, is also presented.