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EN
The dynamic behavior of a typical viscoelastic material in wide ranges of frequency and tem- perature is characterized. A four-parameter fractional derivative model was considered in the frequency domain along with the Arrhenius and WLF models, also for including tempera- ture as a source of variation. A Bayesian framework is adopted and inferences on parameters governing the model quantities of interest are based on samples from posterior distributions obtained by Monte Carlo Markov Chain (MCMC) methods. Posterior predictive checks were conducted to ensure the goodness-of-fit of the model. Based on the results we argue that the Bayesian framework allows more complete and suitable inference about dynamic properties of typical viscoelastic materials, as required for broad and sound vibration control actions.
EN
Viscoelastic materials are used to reduce vibrations in mechanical systems due to their con- trol efficacy. Considering that the dynamic behavior of those materials may be described by means of complex moduli, and experimental data may present ucertainties, an alternative is to use probabilistic methods, especially the Bayesian inference approach. By that approach, probability distribution functions are obtained for parameters of a model which describes the behavior of a given material. The present work employs a viscoelastic material modeled by the Bayesian approach in two vibration control actions, namely: a) use of vibration isolators; b) use of dynamic neutralizers. Transmissibility and receptance curves are displayed as well as dimensions of the control devices. Performance predictions are carried out in both cases. It is shown that the Bayesian approach can favourably reflect the presence of the uncertain- ties and advance their effects. Thus, more information can be provided for the designer of viscoelastic vibration control devices to anticipate eventual corrective measures.
EN
The supplemental energy dissipation system is a practical approach to attenuate the structural response under extreme loading. Viscoelastic damping used to reinforce the structure against the seismic vibration, Viscoelastic material (VEM) most commonly used in viscoelastic dampers (VEDs). In this paper, dynamic mechanical analysis (DMA) approach is used to investigate the performance index of VEM. It is demonstrated that the performance index, such as storage modulus, loss modulus, and loss factor decrease noticeably as the temperature increases, which reflects the low stiffness at high temperature. Excitation frequency also influenced the performance index, and the reaction has correspondence to temperature. As the temperature increases, the VEM dynamic properties decreases, which represents the rubbery region, and it is found that higher to low-temperature dynamic properties increases, which the glassy region is. DMA is a particularly flexible approach, and it characterizes the properties of VEM simultaneously at various conditions.
EN
We consider a mathematical model which describes the dynamic evolution of a viscoelastic body in frictional contact with an obstacle. The contact is modelled with normal damped response and unilateral constraint for the velocity field, associated to a version of Coulomb’s law of dry friction. Our aim is to present a detailed description of the numerical modelling of the problem. To this end, we use a penalty method to approximate the constraint. Then, we provide numerical simulations in the study of a two-dimensional example and compare the penalty model with the original one.
5
Content available remote Skurcz i pełzanie betonu w ujęciu norm. Cz.1 PN-B 0364:2002, PN-EN 1992-1-1
PL
W pracy przedstawiono i porównano sposoby uwzględniania zjawisk reologicznych w obliczeniach konstrukcji betonowych proponowane przez normy PN-B 03264:2002, PN-EN 1992-1-1 oraz wydaną w 2013 roku "Pre-normę konstrukcji betonowych fib Model Code 2010". Przegląd zilustrowano przykładem liczbowym. W pracy omówiono także podstawowe modele lepkosprężyste i ich przydatność w ocenie zjawisk reologicznych.
EN
Purpose: In this study, short-term tensile creep and recovery behaviors of medical grade ultra-high molecular weight polyethylene (UHMWPE) were investigated to contribute deformation behaviour of UHMWPE components in knee and hip prosthesis during daily life activities of patients. Design/methodology/approach: Tensile test specimens were machined from compression molded UHMWPE sheets having commercial brand name: Chirulen 1020 and they were prepared according to ASTM 527-2. The tensile creep tests were performed at constant stress levels of 5, 9, 13, 18 and 21 MPa as long as 1 hour for each test. Then, the specimens were allowed to recover unloaded for 1 hour. Automatic extensometer was used to measure the deformations precisely for each test. Findings: Results show that creep rate linearly increased with increasing the stress levels. Permanent deformations were observed after recovery. Recovery of the material became difficult with increasing the applied load at intended time interval. Research limitations/implications: UHMWPE components used in prosthesis have been subjected to complex loading conditions during service life. Polymeric materials show the viscoelastic material properties like strain rate sensitivity, relaxation, creep and recovery at room temperature. Because of the viscoelastic material properties of the UHMWPE, it makes difficult to predict the failure of the UHMWPE components in hip and knee prosthesis. Therefore, deformation behavior of medical grade UHMWPE should be investigated in many different loading conditions. Practical implications: Medical grade ultra-high molecular weight polyethylene (UHMWPE) have been used commonly in total hip replacements as acetabular cup and in total knee replacements as tibial insert since early 1960s.
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Content available remote Drgania tłumione układu zmiany wysięgu żurawia
EN
In the present work a problem pertaining to the damped lateral vibrations of the truck crane radius change system has been formulated and solved. In the adopted model the vibration energy dissipation derives from the internal damping of the viscoelastic material (the Kelvin– Voigt rheological model) of beams that model the system and from the resistance motion in the supports of a telescopic boom and the hydraulic cylinder.
PL
W niniejszej pracy rozważa się tłumione drgania układu zmiany wysięgu żurawia samochodowego DST0285. Obszerną literaturę dotyczącą drgań żurawi samochodowych i ich elementów zawarto w monografiach [1, 2]. Badania drgań swobodnych układu zmiany wysięgu żurawia przedstawiono w pracy [3]. W zbudowanym modelu przyjęto, że rozproszenie energii drgań w czasie zmiany wysięgu powstaje na skutek tłumienia wewnętrznego materiału lepkosprężystego układu oraz poprzez wprowadzenie do modelu rotacyjnych tłumików wiskotycznych w miejscach mocowania siłownika i wysięgnika do ramy nadwozia.
EN
Modern machine tools must achieve a high precision for a better surface texture and higher flexibility for wide range of machining requirements. To fulfill these requirements, a semi-active damping system for a new generation of machine tools is proposed. The new concept is partially based on the Amplified Piezo Actuators APA® from CEDRAT Technologies. With these actuators, the dynamic behavior (stiffness and damping) of structural body components of machine tools can be controlled and adjusted to the optimum parameters. To reduce the transfer of vibrations through the active elements, a viscoelastic material was used. This article presents test results performed on the APA® with viscoelastic material. A significant reduction of the vibrational amplitude at resonance frequency was observed with additional material. The optimized quantity of viscoelastic material reduces the full stroke of the actuator only by 10 percent. At the same time, the viscoelastic material has red the tests performed on the machine tool showed significant surface texture improvement with use of the amplified piezoelectric actuator.
EN
Epoxy resins filled with dielectric mineral particles are frequently used as insulating materials in power industry applications. Due to their excellent dielectric properties and relatively good thermal performance (resistance, ageing and conductivity) their usability is common and extensive. However, processing of epoxy resin based products is quite difficult, and often results in quality problems or even cracks. Normally, for such as complex products, manufacturing-induced residual stresses cannot be totally avoided, but numerical simulations may provide good estimation of their level. This paper deals with mechanical problems of power industry products and explains the methodology for numerical modeling of failure in silica fllled epoxy systems subjected to severe temperature gradients. The exemplary product cast of Huntsman's CY228 epoxy system was simulated using commercial ABAQUS software package. Special subroutines describing progress of polymerization, exothermic effects of the reaction, as well as viscoelastic-driven stress relaxation process were implemented into general purpose FEM code. In addition, the model describing probability of epoxy cracking was proposed, calibrated and introduced into the software package. This approach allowed modeling the authentic phenomena taking place during real production processes, and studying the influence of design and manufacturing parameters on product quality. The outcome of numerical analysis was compared with the results of strain-gauge measurements, showing good agreement. As a result the optimal settings of curing and post-curing operations could be evaluated, driving to minimal cast product distortion and low probability of failure.
PL
Żywica wypełniona cząstkami krzemionki jest w urządzeniach elektrycznych powszechnie stosowanym materiałem izolacyjnym, spełniającym nierzadko również funkcje konstrukcyjne. Wynika to z bardzo dobrych właściwości dielektrycznych tego typu kompozytów, dobrych właściwości mechanicznych oraz ich powszechnej dostępności i stosunkowo łatwej technologii otrzymywania. Częstym problemem związanym z zastosowaniem tych materiałów są jednak przypadki zniszczenia aparatów zainicjowane na granicy faz metal-osnowa, a wywołane przez naprężenia resztkowe powstające już podczas schładzania po procesie odlewania żywicy. Prezentowana praca dotyczy oceny i modelowania naprężeń resztkowych przy użyciu metody elementów skończonych, z uwzględnieniem lepko-sprężystych właściwości materiału polimerowego. W artykule przedstawiono podstawowe modele zjawisk towarzyszących procesowi produkcyjnemu elementów z żywicy epoksydowej z napełniaczem mineralnym, a więc kinetykę sieciowania żywicy wraz z reakcją egzotermiczną, zjawisko relaksacji naprężeń w materiale lepko-sprężystym, a także opis prawdopodobieństwa rozwoju pęknięcia w wyrobie. Zaproponowane podejście pozwoliło wyjaśnić termo-mechaniczne zachowanie się wyrobu w procesie produkcyjnym i wskazać na naprężenia obwodowe występujące w pobliżu karbu jako główne źródło zniszczenia podczas testów niskotemperaturowych. Zaproponowano zmiany konstrukcyjne mające na celu ograniczenia prawdopodobieństwa pękania wyrobów podczas testów.
10
Content available remote Determination of the elasticity range of paper
EN
This research work presents a method for the determination of the limit of elasticity of paper considered as a variable dependent on stress and the time of its duration. For plane stress it was found that in the case of a low share of permanent strain in the total strain, we can assume that the highest value of its share appears on one of the principal axes of stress. Such an assumption allowed to use a one-dimensional rheological model to define the permanent range in a two dimensional state of stresses for paper.
PL
W ramach pracy zaproponowano sposób wyznaczania granicy sprężystości papieru, traktowanej jako zmienna zależna od wartości naprężeń i czasu ich działania. Dla płaskich stanów naprężeń, występujących w płaszczyźnie papieru wykazano, że w przypadku małego udziału odkształceń trwałych w całkowitych można przyjąć, że największa wartość udziału odkształceń trwałych w całkowitych występuje dla jednego z kierunków naprężeń głównych. Takie założenie, pozwoliło na wykorzystanie jednowymiarowego modelu reologicznego do określenia zakresu sprężystości w dwukierunkowym stanie naprężeń papieru.
EN
The load capacity of homogeneous, isotropic viscoelastic materials subjected to multiaxial stresses is considered. For this purpose uniaxial equivalent stresses in selected load cases are determined and relevant criteria applied. It is shown that in the case of constant load the yield criterion does not differ from that for perfectly elastic materials. Similar conclusion has been drawn for the fatigue and yield criteria at in-phase and out-of-phase stresses. On the contrary, the criteria derived for viscoelastic materials subjected to periodic loads do not coincide with those for perfectly elastic materials.
EN
On the basis of modified Hooke’s law for multiaxial stress in viscoelastic solids, threedimensional constitutive equations for strains have been derived. It is shown that after application or removal of triaxial static load, normal and shear strain components vary in course of time proportionally to each other and that in-phase stress components produce in-phase strain components. Harmonic out-of-phase stress as well as multiaxial periodic and stationary random stresses are also considered. The matrix of dynamical flexibility of viscoelastic materials is determined which depends on three material constants (Young modulus, Poisson’s ratio and coefficient of viscous damping of normal strain) and load circular frequency.
EN
On the basis of Hooke’s law for multiaxial stress in elastic solids, similar relationships for viscoelastic materials are considered. It is assumed that the material is homogeneous and isotropic, and that the Kelvin-Voigt’s model is applicable to normal strain components. An analogous model is also taken for shear strain components. It is shown that the ratio of coefficients of viscous damping of normal and shear strain components is equal to the ratio of Young modulus and shear modulus. As a result, the modified Hooke’s law for multiaxial stress in viscoelastic materials has been formulated which includes three material constants: Young modulus, Poisson’s ratio and coefficient of viscous damping of normal strain.
EN
On the basis of the three-dimensional constitutive equations for strains resulting from the Kelvin-Voigt’s model and modified Hooke’s law for multiaxial stress in viscoelastic solids, the formulae for the energy dissipated in a given time per unit volume have been derived. It is shown that after application or removal of triaxial static load there is no difference in the time functions governing the dissipation of strain energy of volume change and the dissipation of strain energy of distortion. Harmonic in-phase stress and harmonic out-of-phase stress as well as multiaxial periodic stress are also considered. It is demonstrated that in the process of energy dissipation due to normal and shear stress components the role of the latter is dominant.
EN
The problem of onset of convective instability in a dielectric micropolar viscoelastic fluid (Walters' liquid B') heated from below confined between two horizontal plates under the simultaneous action of the rotation of the system, vertical temperature gradient, one relaxation time and vertical electric field is considered. Linear stability theory is used to derive an eigenvalue of twelve order, and an exact eigenvalue equation for a neutral instability is obtained. Under somewhat artificial boundary conditions, this equation can be solved exactly to yield the eigenvalue relationship from which various critical values are determined in detail. Critical Rayleigh heat numbers and wave number for the onset of instability are presented graphically as a function of rotation at a certain value of the Prandtl number, for various values of the relaxation time, the Rayleigh electric number, the elastic parameter and micropolar parameters.
EN
This paper presents constitutive equations of viscoelastic materials subjected to complex loading conditions. The standard rheological model is used and its 3-D generalization is considered. In the case of sudden application of loads and higher strain rates the momentary modulus of elasticity in tension-compression and the momentary modulus of elasticity in shear as well as the momentary coefficients of viscous damping of normal and shear strain components have been taken into account. The ratios of these moduli and of these coefficients are investigated.
PL
W artykule przedstawiono równania konstytutywne materiałów lepkosprężystych poddanych obciążeniom złożonym. Użyto standardowego modelu reologicznego i rozpatrzono jego uogólnienie na przestrzeń trójwymiarową. W przypadku nagłego przyłożenia obciążeń i większych prędkości deformacji uwzględniono chwilowe moduły sprężystości i chwilowe współczynniki tłumienia wiskotycznego odnoszącego się do rozciągania - ściskania i skręcania. Analizowane są ilorazy tych modułów i tych współczynników.
17
PL
W artykule przedstawiono model MES do analizy rozwoju zarysowania ścian zbiorników żelbetowych powstałego w wyniku rozwoju naprężeń termicznych w okresie dojrzewania betonu. Przedstawiono przykład ściany prostokątnego zbiornika żelbetowego zrealizowanego podczas rozbudowy oczyszczalni ścieków. Model uwzględnia rozwój ciepła hydratacji i wpływ temperatury otoczenia na rozwój pola temperatury. Zastosowano sprężysto-lepki model materiału z zarysowaniem.
EN
In the paper it was presented FEM model to an analysis of the crack width development in the walls of RC tanks, which appeared as a result of thermal stresses during hardening period of concrete. It was presented an example of the rectangular RC tank wall which was realized during the extension of the sewage treatment plant. The influence of the heat of the hydration and ambient temperature of the air on the development of the temperature are included in the proposed model. Viscoelastic material with cracking was used in the calculation.
18
Content available remote Three-parameter optimization of an axially loaded beam on a foundation
EN
A beam of circular cross-section, made of viscoelastic material of Kelvin-Voigt type, is considered. The beam is symmetric with respect to its center, the length and volume of the beam are fixed and its ends are simply supported. The radius of the cross-section is a cubic function of co-ordinate. The beam interacts with a foundation of Winkler, Pasternak or Hetknyi a, type and is axially loaded by a non-conservative force P(t) = PO + PI cos vt. Only the first instability region is taken into account. The shape of the beam is optimal if the critical value of P1 is maximal. A few numerical examples are presented on graphs.
19
Content available remote Naprężenia termiczne w dojrzewającym betonie ściany zbiornika żelbetowego
PL
W artykule przedstawiono model MES do analizy rozwoju naprężeń termicznych w młodym betonie. Przedstawiono przykład ściany cylindrycznego zbiornika żelbetowego zrealizowanego podczas rozbudowy oczyszczalni ścieków. Model uwzględnia rozwój ciepła hydratacji i wpływ temperatury słonecznej powietrza na rozwój niejednorodnego pola temperatury. Zastosowano liniowo-sprężysto-lepki model materiału.
EN
In the paper a FEM model for an analysis of the development of the thermal stresses at early age concrete was presented. An example of the cylindrical RC tank wall, which was realized during an extension of the sewage treatment plant was shown. The influence of the hydration heat and solar temperature of the air on the development of the non-uniform temperature field were included in the proposed model. A linear visco-elatic model for concrete was used in the calculations.
EN
This paper presents a new method for measuring the low magnitude friction forces in biojoints and polymers. It provides a basis for facilitating the control of friction and viscoelastic properties of biomaterials, especially for tissue cultivation process in bioreactors. This method is based on forced vibration of a two-ball actuator and sensor which are directed parallel to the sample surface. A tuning piezoelectric fork device is introduced for exciting the system, when simultaneously it is used as a sensor. Variation of vibration parameters are induced through energy dissipation of indentor system which has the same friction force and viscoelastic behaviour as the sample. In this regard, the mathematical model of excited oscillations including variation of generated friction forces and viscolelastic characteristics is presented.
PL
Referat przedstawia nową koncepcję dotyczącą pomiaru małych sił tarcia oraz właściwości materiałów lepko-sprężystych. Zaprezentowano: ogólny zarys metody pomiaru, wskazania dotyczące projektowania i budowy urządzenia pomiarowego, model matematyczny oraz sposób identyfikacji parametrów modelu. Metoda ta jest szczególnie przydatna w przypadku analizy właściwości materiałowej polimerów oraz tkanki chrząstki stawowej człowieka zarówno in vitro, jak i podczas hodowania w bioreaktorach.
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