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1

Effect of the number of shells on selected mechanical properties of parts manufactured by FDM/FFF technology

Szot Wiktor, Rudnik Mateusz

Advances in Materials Science

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2024

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Vol. 24, nr 1(79)

86--103

EN

The technological parameters of 3D printing have an influence on the mechanical properties of the manufactured components. The purpose of the article was to study the comparative influence of the technological parameter of the number of shells variable in two stages (2 and 10) on selected mechanical properties. The maximum tensile stress for the number of shells 10 was 39.80 MPa, which is higher compared to the number of shells 2: 30.98 MPa. In the case of the maximum bending stress for the number of shells 10, an average value of 61.02 MPa was obtained, which is higher compared to the number of shells of 2: 37.46 MPa. Furthermore strong fit of the Kelvin-Voight model was obtained, as confirmed by the values of the 𝐶ℎ𝑖2:0.0001 and 𝑅2:0.997 coefficients.

2

About one problem of finding equal strength contour inside a viscoelastic rectangle

Kapanadze Giorgi, Kipiani Gela, Rajczyk Marlena

Zeszyty Naukowe Politechniki Częstochowskiej. Budownictwo

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2023

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Z. 29 (179)

41--47

EN

The problem of finding an equal-strength contour inside a viscoelastic rectangle according to the Kelvin-Voigt model is considered. It is assumed that constant normal compressive forces with given principal vectors act on the sides of the rectangle (or the values of constant normal displacements are known), and the inner boundary (the desired equal-strength contour) is free from external forces. The methods of the theory of conformal reflections, Cauchy type integral and boundary value problems of analytic functions are used to study the plate bending problems discussed in the paper. Which in turn are based on the task of constructing a conformally mapping function on a doubly linked circular ring bounded by broken line. The latter is reduced to the Riemann-Hilbert problem for a circular ring based on the solution of which it becomes possible to present the mentioned function in a defective form. It is worth noting that when considering mixed problems of plate bending for doubly connected areas bounded by broken line, it is possible to decompose them into two independent problems, each of which is a Riemann-Hilbert problem.

PL

Rozważono problem znalezienia konturu o stałej wytrzymałości wewnątrz lepko sprężystego prostokąta zgodnie z modelem Kelvina-Voigta. Zakłada się, że na boki prostokąta działają stałe normalne siły ściskające o danych wektorach głównych (lub znane są wartości stałych przemieszczeń normalnych), a wewnętrzna granica (żądany kontur o jednakowej wytrzymałości) jest wolna od sił zewnętrznych. Do badania omawianych w artykule problemów zginania płyt wykorzystano metody teorii odbić konforemnych, zagadnienia całki typu Cauchy’ego i wartości brzegowych funkcji analitycznych, które z kolei opierają się na zadaniu skonstruowania funkcji odwzorowującej konformalnie na podwójnie połączonym pierścieniu kołowym ograniczonym linią przerywaną. To ostatnie sprowadza się do problemu Riemanna-Hilberta dla pierścienia kołowego na podstawie rozwiązania, które możliwe jest jako przedstawienie wspomnianej funkcji w postaci wadliwej. Warto zauważyć, że rozpatrując mieszane problemy zginania blachy dla obszarów podwójnie połączonych ograniczonych linią przerywaną, można je rozłożyć na dwa niezależne problemy, z których każdy jest problemem Riemanna-Hilberta.

3

Nonlinear hygrothermal effects on the vibrations of a magnetostrictive viscoelastic laminated sandwich plate resting on an elastic medium

Zenkour Ashraf M., El-Shahrany Hela D.

Archives of Civil and Mechanical Engineering

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2021

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Vol. 21, no. 2

692--706

EN

In engineering applications, composite structures supported by elastic foundations are being vastly utilized in various operating environmental conditions. The nonlinear hygrothermal effect on vibration analysis of a magnetostrictive viscoelastic laminated composite sandwich plate rested on two-parameter Pasternak’s foundations is studied in the present article. The material properties of the viscoelastic plate’s layers are considered based on the Kelvin–Voigt model. The governing equation system is derived according to Hamilton’s principle. The analytical solution is obtained to study influences of the hygrothermal change, half wave number, magnitude of the feedback control gain, aspect ratios, thickness ratio, and structural viscoelastic damping coefficients on vibration damping characteristics of the plate including the frequencies, the damping rate, and the deflection. The obtained results indicate that the natural frequency and deflection reduce with increasing the structural viscoelastic damping value. The plate takes a long time for suppressing its vibration due to increasing the hygrothermal factor.

4

Theoretical studies of dynamic soil compaction by wheeled forestry machines

Grigorev Igor, Kunickaya Ol'ga, Burgonutdinov Albert, Ivanov Viktor, Shuvalova Svetlana, Shvetsova Viktoria, Stepanishcheva Marina, Tikhonov Evgeniy

Diagnostyka

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2020

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Vol. 21, No. 4

3--13

EN

The impact of forest skidding machine tires on the soil differs depending on topography, soil properties, and type of the wheel system. The development of a mathematical model describing the entire dynamic process is a challenging but relevant task to assess the level of impact. The work aims mathematical modeling of the impact caused by the skidding system on the forest soil employing Kelvin-Voigt theory with additional elastic element and Laplace transform equations. A dynamic model represents the "traktor-timber bundle– soil" system. According to the results of mathematical modeling, it was found that studying the vertical vibrations and vibrations of sprung mass in longitudinal and transverse planes is sufficient for examining dynamic soil compaction. Developed methods of statistical dynamics with the presentation of the track surface microroughness and the theory of linear elastic and viscous soil deformation showed that each pass of the skidding system is ac-companied by additional dynamic soil compaction. Its maximum value depends on the properties of the soil and skidding system, as well as on the presence of resonant zones in the frequency spectrum. The results of these studies provide an opportunity to predict the exposure level of skidders and establish new solutions to minimize negative consequences for the environment and productivity of the forest industry.

5

Modelling of erythrocyte behaviour in blood capillaries by structural model combined with Lattice-Boltzmann approach

Przekop R., Majewski I., Moskal A.

Chemical and Process Engineering

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2018

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Vol. 39, nr 4

411–-426

EN

A microstructural model of Red Blood Cell (RBC) behaviour was proposed. The erythrocyte is treated as a viscoelastic object, which is denoted by a network of virtual particles connected by elastic springs and dampers (Kelvin-Voigt model). The RBC is submerged in plasma modelled by lattice Boltzmann fluid. Fluid – structure interactions are taken into account. The simulations of RBC behaviour during flow in a microchannel and wall impact were performed. The results of RBC deformation during the flow are in good agreement with experimental data. The calculations of erythrocyte disaggregation from the capillary surface show the impact of RBC structure stiffness on the process.

6

Wpływ wyższych harmonicznych na nieliniowe drgania belek wykonanych z meteriału Kelvina-Voigta

Wielentejczyk P., Lewandowski R.

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

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2017

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z. 64, nr 2/I

39--48

PL

W pracy analizuje się geometrycznie nieliniowe drgania ustalone belek wymuszone siłami harmonicznie zmiennymi w czasie. Belki wykonane są z materiału lepkosprężystego opisywanego za pomocą modelu Kelvina-Voigta. Do opisu geometrycznej nieliniowości deformacji zastosowano teorię von Karmana oraz teorię belek Eulera-Bernoulliego. Pominięto wpływ osiowych sił bezwładności oraz założono nieprzesuwność osiową końców belek. Sformułowano związki fizyczne wyrażone za pomocą sił przekrojowych i uogólnionych odkształceń. Równania ruchu oraz równania amplitud zapisano stosując metodę prac wirtualnych, metodę bilansu harmonicznych oraz metodę elementów skończonych. Nieliniowe równania amplitud rozwiązano metodą kontynuacji. W rozwiązaniach okresowych równań ruchu uwzględniono wyższe harmoniczne, co pozwala na analizę rezonansów pobocznych, ale znacząco skomplikowało sformułowanie i rozwiązanie problemu. Za pomocą krzywych rezonansowych przedstawiono dynamiczne zachowanie się belek wykonanych z materiału Kelvina – Voigta. Wyniki porównano z rozwiązaniami dla belek sprężystych. Przeanalizowano istotność wyższych harmonicznych w opisie drgań nieliniowych.

EN

The problem of geometrically non-linear steady state vibrations of beams excited by harmonic forces is considered in this paper. The beams are made of a viscoelastic material defined by the classic Kelvin-Voigt rheological model. The von Karman theory and the Euler-Bernoulli theory are applied to describe the effects of geometric nonlinearities of beam deformations. The influence of axial inertial forces are neglected. The immovable ends of beam system are assumed. The physical relationships for internal forces and general deformations are defined. The equations of motion and amplitudes are derived using the virtual work method, the harmonic balance method and the finite element methodology. Non-linear amplitude equations are solved applying the continuation method. In the steady-state solution of equations of motion, the higher harmonics are taken into account what enables one to examine an secondary resonances but significantly complicates the formulation and solution of the problem. Using resonance curves the dynamic behaviour of beam systems made of the viscoelasticity Kelvin-Voigt material are presented. The results are compared with these ones for elastic beams. The significance of higher harmonics for the description of steady-state non-linear vibrations are briefly discussed.

7

The effect of pulsed laser radiation on a thermoviscoelastic semi-infinite solid under two-temperature theory

Othman M. I., Abouelregal A. E. E.

Archives of Thermodynamics

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2017

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Vol. 38, no. 3

77--99

EN

The purpose of this paper is to study the thermoviscoelastic interactions in a homogeneous, isotropic semi-infinite solid under two-temperature theory with heat source. The Kelvin-Voigt model of linear viscoelasticity which describes the viscoelastic nature of the material is used. The bounding plane surface of the medium is subjected to a non-Gaussian laser pulse. The generalized thermoelasticity theory with dual phase lags model is used to solve this problem. Laplace transform technique is used to obtain the general solution for a suitable set of boundary conditions. Some comparisons have been shown in figures to estimate the effects of the phase lags, viscosity, temperature discrepancy, laser-pulse and the laser intensity parameters on all the studied fields. A comparison was also made with the results obtained in the case of one temperature thermoelasticity theory.

8

Zastosowanie ułamkowego modelu reologicznego Kelvina-Voigta w badaniach nad zdrową żywnością

Jóźwiak B., Orczykowska M., Dziubiński M.

Inżynieria i Aparatura Chemiczna

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2016

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Nr 4

139--141

PL

Dokonano kompleksowej oceny struktury i właściwości reologicznych 3% kleików skrobiowych z japońskiego kuzu, w zależności od długości trwania procesu kleikowania. Do opisu uzyskanych danych doświadczalnych w postaci modułów zachowawczego i stratności w funkcji częstości oscylacji zaproponowano 7-parametrowy model reologiczny będący modyfikacją ułamkowego modelu Kelvina-Voigta z dwoma wbudowanymi elementami typu springpot. Wyznaczone parametry modelu były jednocześnie stałymi materiałowymi, przydatnymi dla specjalistów z dziedziny inżynierii materiałowej.

EN

In the paper, there has been made a comprehensive assessment of data in the form of storage modulus and loss modulus in a function of oscillation frequency, a new 7-parameter rheological model - which was a modification of the fractional Kelvin-Voigt model with two built-in springpot elements - was proposed. Determined parameters of the model were also material constants, useful for specialists in the field of materials science.

9

Collision Modeling in Mechanical Systems on the Example of Impact Vibration Eliminators

Golec Z., Golec M.

Vibrations in Physical Systems

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2004

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Vol. 21

159--162

EN

The work presents modeling of collisions of mechanical bodies using two basic models of the collision: the Newton model, in which dynamics of the collision is described by the coefficient of restitution, and the model considering the elastic dissipative properties of colliding bodies, i.e. the non-linear Kelvin-Voigt model. Quantitative similarity of both models was described using the energetic method.