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1

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.

2

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.

3

Geophysical and analytical determination of overstressed zones in exploited coal seam: a case study

Chlebowski Dariusz, Burtan Zbigniew

Acta Geophysica

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2021

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Vol. 69, no. 2

701--710

EN

A variety of geophysical methods and analytical modeling are applied to determine the rockburst hazard in Polish coal mines. In particularly unfavorable local conditions, seismic profling, active/passive seismic tomography, as well as analytical state of stress calculating methods are recommended. They are helpful in verifying the reliability of rockburst hazard forecasts. In the article, the combined analysis of the state of stress determined by active seismic tomography and analytical mod eling was conducted taking into account the relationship between the location of stress concentration zones and the level of rockburst hazard. A longwall panel in the coal seam 501 at a depth of ca.700 m in one of the hard coal mines operating in the Upper Silesian Coal Basin was a subject of the analysis. The seismic tomography was applied for the reconstruction of P-wave velocity felds. The analytical modeling was used to calculate the vertical stress states basing on classical solutions ofered by rock mechanics. The variability of the P-wave velocity feld and location of seismic anomaly in the coal seam in relation to the calculated vertical stress feld arising in the mined coal seam served to assess of rockburst hazard. The applied methods partially proved their adequacy in practical applications, providing valuable information on the design and performance of mining operations.

4

Analytical calculations of surges caused by direct lightning strike to underground intrusion detection system

Aniserowicz K.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2019

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Vol. 67, nr 2

263--270

EN

The paper presents an analysis of overvoltages caused by a direct lightning strike in intrusion detection system equipped with underground radiating cable sensors. Waveforms of currents and voltages in the system components are calculated using analytical formulas basing on a transmission-line model in the frequency domain. The time-domain waveforms are computed using the inverse fast Fourier transform (IFFT). Three network configurations of the intrusion detection system are analyzed.

5

The experimental and the theoretical analysis of the serviceability behavior of a deployable footbridge

Benjeddou O., Limam O., Ouezdou M. B.

Archives of Civil and Mechanical Engineering

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2017

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Vol. 17, no. 2

293--306

EN

This study presents a new concept of a deployable footbridge. The structural solution of the proposed footbridge comprises two parallel deployable beams as main girders and wooden boards which constitute the deck. The two beams were composed by several softwood blocks bonded to a unidirectional carbon fiber sheets layers by using an epoxy resin. In the first part of this study; we present the principle of the developed deployable footbridge. Thereafter, small-scale section prototype of the footbridge was tested under a vertical static nondestructive load on the Serviceability Limit State. The purpose of the tests is mainly to evaluate the vertical displacement responses under the static load, in every location of the prototype deck. The second purpose of these tests is to verify the deployment of the footbridge. Finally, a theoretical model based on the classical beam theory and on the theoretical structural behavior of the deployable beams was developed. The model presents the theoretical relationship between the load and the vertical displacement, under static loads, in every point of the footbridge. The predicted and the experimental results show a good agreement.

6

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.

7

Symulator przenośnika taśmowego z uwzględnieniem uszkodzeń

Cenacewicz K., Przystałka P.

Modelowanie Inżynierskie

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2015

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T. 24, nr 55

13--20

PL

Przedstawiono aktualny stan prac w zakresie symulacyjnego modelu przenośnika taśmowego, w którym uwzględniono wpływ uszkodzeń. W ramach opracowania skupiono się na wybranych aspektach teoretycznych modelowania analitycznego oraz pokazano implementację symulatora obiektu badań z wykorzystaniem środowiska MATLAB®/Simulink®. Zalety i wady utworzonego symulatora zostały omówione przy uwzględnieniu wyników testów weryfikacyjnych, jakie uzyskano podczas badań.

EN

The paper presents the current state of the research dealing with the conveyor belt simulator, in which selected faults can be introduced. This study focuses on the most important aspects of analytic modelling of this kind of systems as well as on the implementation of the conveyor simulator with the use of MATLAB®/Simulink® software. The advantages and limitations of the simulator were investigated taking into account the verification results obtained at this stage of the research.

8

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.

9

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.

10

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.

11

Wybrane problemy modelowania przewodzenia ciepła w badaniach nieniszczących materiałów kompozytowych

Świderski W., Vavilov V.

Problemy Techniki Uzbrojenia

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2012

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R. 41, z. 123

17--32

PL

W pracy przeprowadzono porównanie analitycznych i numerycznych metod stosowanych przy badaniu wymiany ciepła w materiałach kompozytowych, zawierających ukryte defekty typu naruszenia jednolitości (ciągłości). Poddano ocenie wykorzystywane oprogramowanie komputerowe oraz przedstawiono przewidywane kierunki rozwoju modeli badań termicznych.

EN

Analysis using analytical and numerical methods in investigation of exchange of heat in composite materials including hidden defects of disarrangement or uniformity (continuity) is carried out in the paper. The computer software used in this modeling is evaluated and future directions of development of thermal investigation models are presented too.

12

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.

13

Analityczna ocena cyklu cieplnego w procesie spawania w strefie wpływu ciepła przy wykorzystaniu różnych modeli źródeł ciepła

Ranatowski E., Poćwiardowski A.

Zeszyty Naukowe. Mechanika / Akademia Techniczno-Rolnicza w Bydgoszczy

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1998

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Z. 42 (212)

33-45

PL

Efektywną metodą do szybkich obliczeń pól termicznych możemy uznać analityczne modelowanie połączone z numerycznymi obliczeniami. W niniejszym artykule przedstawiono liniową, analityczno - numeryczną metodę obliczeń. Podstawą obliczeń jest matematyczny, trójwymiarowy model źródła ciepła o charakterze uniwersalnym, pozwalający opisać również inne ich formy, poprzez jego transformację. Obliczenia objęły płyty o dowolnej grubości wraz z uwzględnieniem wymiany ciepła na powierzchni ograniczającej. W pierwszej kolejności założono ruchome źródło o działaniu impulsowym, wywołując nieustalone pole cieplne, a następnie sumowano ich oddziaływanie. W pracy przedstawiono również kilka analitycznych przykładów.

EN

A method that effectively joins mathematical modelling with numerical calculation seems to be the idea for fast computing thermal fields. In this article a linear, analytic, numerically computed method would be presented. The basis of this method is mathematical, universal, three dimensional heat source model that can successfully describe all necessary welding heat sources. For the plate with optional thickness, the changeable radiative heat transfer on both surface is taken under consideration. It is assumed that moving heat source, during avery short period of time, generates impulse of energy which induces an instantaneous thermal field plate area. These fields are being fluently summed up giving resultant thermal field. There also was made some analytical examples.