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1
Content available Tolerance modelling of nonstationary problems of microheterogeneous media and structures
Jędrysiak J., Domagalski Ł., Marczak J., Pazera E.
Vibrations in Physical Systems
|
2018
|
Vol. 29
art. no. 2018001
EN
In this note a certain review of applications of a non-asymptotic modelling approach, called the tolerance modelling, is presented. Some objects and thermomechanical problems are shown, with a general outline of this method and an example of application for nonlinear vibrations of periodic beams.
2
Content available Nonlinear vibrations of a slender beam interacting with a periodic viscoelastic subsoil
Świątek M., Jędrysiak J., Domagalski Ł.
Vibrations in Physical Systems
|
2018
|
Vol. 29
art. no. 2018030
EN
The paper describes nonlinear vibrations of Euler-Bernoulli beams interacting with a periodic viscoelastic foundation. The original model equations with highly oscillating periodic coefficients are transformed using the tolerance modelling technique. Newly delivered equations have constant coefficients and describe macro-dynamics of the beam including the effect of the microstructure size. The main purpose of this paper is to propose an equivalent approximate model describing the nonlinear vibrations of a beam interacting with a periodic viscoelastic subsoil.
3
Content available Linear vibrations of periodic Timoshenko and Rayleigh beams
Świątek M., Jędrysiak J., Domagalski Ł.
Vibrations in Physical Systems
|
2018
|
Vol. 29
art. no. 2018035
EN
Elastic periodic structures with variable material and geometrical properties exhibit dynamic characteristics that are investigated in this contribution. The paper is devoted to analysis of geometrically linear vibrations of Rayleigh and Timoshenko beams with cross-sections and material properties periodically varying along the longitudinal axis. The period of inhomogeneity is assumed to be sufficiently small when compared to the beam length. Equations of motion in both beam theories under consideration have highly-oscillating coefficients. In order to derive the averaged model equations with constant coefficients for vibrations, the tolerance averaging approach is applied. The method of averaging differential operators with rapidly varying coefficients is applied to obtain averaged governing equations with constant coefficients. An assumed tolerance and indiscernibility relations and the definition of slowly varying function found the applied technique. Numerical results from the tolerance Rayleigh and Timoshenko beam model equations are compared.
4
Content available Effect of temperature on vibrations of laminated layer
Pazera E., Jędrysiak J.
Vibrations in Physical Systems
|
2018
|
Vol. 29
art. no. 2018032
EN
In this note the influence of temperature on vibrations of laminated layer made of two different materials is presented. The macroscopic properties of this layer are changing continuously along one direction x1, perpendicular to the laminas. To obtain the equations describing this problem, the tolerance averaging technique is used [1]. In this work, three models are proposed: the tolerance and the asymptotic-tolerance model, taking into account the effect of the microstructure size on the overall behaviour of this type of structures, and the asymptotic model, which equations omit this effect. To solve the equations of these three models the finite difference method is used.
5
Content available remote On thermoelasticity in FGL - tolerance averaging technique
Pazera E., Ostrowski P., Jędrysiak J.
Mechanics and Mechanical Engineering
|
2018
|
Vol. 22, nr 3
703--717
EN
In this paper the problem of linear thermoelasticity in a laminate with functional gradation of properties is considered. In micro level this laminate is made of two different materials, microlaminas, distributed non-periodically but also not randomly along one of directions, what in macro level results in aforementioned functionally gradation of laminate properties. In order to describe behavior of such structure, equations of two models are here presented - the tolerance and the tolerance-asymptotic model. Both are obtained by the tolerance averaging technique. The basic aim of this work is to analyse the influence of some terms from these averaged equations on the distribution and the values of the displacements and the temperature functions. To solve the equations of two proposed models the finite difference method is used.
6
Niestacjonarne zjawisko termosprężystości w nieperiodycznym laminacie
Jędrysiak J., Pazera E
Modelowanie Inżynierskie
|
2017
|
T. 32, nr 63
65--71
PL
W niniejszej pracy rozpatrywany jest efekt termosprężystości w zagadnieniu niestacjonarnym w laminacie nieperiodycznym. Własności takiego laminatu na poziomie makro zmieniają się w sposób ciągły wzdłuż osi prostopadłej do lamin, natomiast na poziomie mikro są opisane funkcjami tolerancyjnie-periodycznymi, nieciągłymi. W celu otrzymania równań o ciągłych współczynnikach funkcyjnych zastosowano metodę tolerancyjnego modelowania, czyli tzw. tolerancyjne modelowanie, oraz modelowanie asymptotyczne. Pierwsze z tych podejść pozwala uwzględnić w wyprowadzonych równaniach wpływ wielkości mikrostruktury laminatu. Zastosowanie otrzymanych równań pokazano na przykładzie jednokierunkowego przepływu ciepła prostopadle do lamin.
EN
In this work the thermoelasticity effect in a non-stationary heat problem for non-periodic laminates is considered. On the macro-level properties of this laminate are continuously varied along a direction normal to laminas, but on the micro-level they are described by tolerance-periodic, non-continuous functions. In order to obtain equations with continuous coefficients the tolerance method is applied, the tolerance modelling and the asymptotic modelling. The first of these approaches allows to take into account the effect of the microstructure size of the laminate in derived equations. An application of these model equations is shown on an example of one-directional problem along a direction perpendicular to laminas.
7
Drgania periodycznych struktur trójwarstwowych z rdzeniem Murakamiego
Marczak J., Jędrysiak J.
Modelowanie Inżynierskie
|
2017
|
T. 32, nr 63
97--106
PL
Przedmiotem rozważań jest analiza dynamiczna struktur trójwarstwowych o periodycznie zmiennych własnościach. Konstrukcja tego typu została wymodelowana jako układ dwóch płyt cienkich, połączonych ze sobą za pomocą materiału sprężystego Murakamiego. W tym celu rdzeń konstrukcji zastąpiono szeregiem jednorodnych prętów o stałych przekrojach, wykonujących niezależnie od siebie drgania podłużne. Dodatkowo założono, że każda z warstw konstrukcji może mieć periodycznie zmienną grubość i/lub własności materiałowe. Równania różniczkowe ruchu rozpatrywanej struktury są równaniami o periodycznie zmiennych, nieciągłych i silnie oscylujących współczynnikach, które z wykorzystaniem metody tolerancyjnego uśredniania da się sprowadzić do wygodnej do rozwiązania postaci o stałych współczynnikach.
EN
In this work the vibrations of periodic sandwich structures are considered. The model of such structure consists of two thin plates (outer layers), undergoing transverse vibrations, connected with each other by the inner layer, so called core, which is being modelled as a Murakami's type elastic material. Additionally, it is assumed, that every each of those layers can be characterised by certain periodic microstructure (both periodically varying thickness and material properties). The governing equations of such structure are partial differential equations with periodic, non-continuous and highly oscillating coefficients, which are very difficult to solve. In this work, the tolerance averaging technique is used to transform the mentioned system of equations into the form with constant coefficients, which is very convenient in solving many engineering problems.
8
Content available Vibrations of periodic sandwich plates with inert core
Marczak J., Jędrysiak J.
Vibrations in Physical Systems
|
2016
|
Vol. 27
265--272
EN
In this note a free vibration analysis of periodic three-layered sandwich structures is performed. The equations of motion of such structures, which are derived basing on Kirchhoff's thin plate theory, contain periodic, non-continuous and highly oscillating coefficients, which makes them difficult to solve. In this work, the tolerance averaging technique is applied in order to transform the mentioned system of equations into a form with constant coefficients, which takes into account the effect of the microstructure size. The differences between two modelling procedures are shown and discussed. Eventually, formulas for free vibration frequencies of an exemplary 2D structure are derived and an analysis of influence of certain varying material properties is performed.
9
Content available Vibrations of non-periodic thermoelastic laminates
Jędrysiak J., Pazera E.
Vibrations in Physical Systems
|
2016
|
Vol. 27
175--180
EN
Vibrations of non-periodic thermoelastic laminates, which can be treated as made of functionally graded material with macroscopic properties changing continuously along direction, x1, perpendicular to the laminas on the macrolevel are considered. Three models of these laminates are presented: the tolerance, the asymptotic-tolerance and the asymptotic. Governing equations of two first of them involve terms dependent of the microstructure size. Hence, these models (the tolerance, the asymptotic-tolerance) describe the effect of the microstructure. Averaged governing equations of these laminates can be obtained using the tolerance modelling technique, cf. Jędrysiak [1]. Because the model equations have functional, but slowly-varying coefficients calculations for examples can be made numerically or by using approximated methods.
10
Content available Influence of substructure properties on natural vibrations of periodic Euler-Bernoulli beams
Świątek M., Jędrysiak J., Domagalski Ł.
Vibrations in Physical Systems
|
2016
|
Vol. 27
377--384
EN
In this paper there are considered vibrations of Euler-Bernoulli beams with geometrical and material properties periodically varying along the axis. The basic exact equations with highly oscillating periodic coefficients are replaced by the system of averaged equations with constant coefficients. The new model is based on the tolerance modelling technique, which describes macro-dynamics of the beam including the effect of the microstructure size. The purpose of this paper is to present an approximately equivalent model, which describe vibrations of periodic beams taking into account length of the periodicity cell.
11
Content available Higher order vibrations of thin periodic plate bands with various boundary conditions
Jędrysiak J., Wyrwa P.
Vibrations in Physical Systems
|
2016
|
Vol. 27
181--186
EN
In this contribution there are considered thin periodic plates. The tolerance averaging method, cf. [12, 13, 4], is applied to model problems of vibrations of these plates. Hence, the effect of the microstructure size is taken into account in model equations of the tolerance model. Calculations are made for periodic plate bands using this model and the asymptotic model for various boundary conditions.
12
Content available Free vibrations of medium thickness microstructured plates
Jędrysiak J.
Vibrations in Physical Systems
|
2016
|
Vol. 27
169--174
EN
A problem of free vibrations of medium thickness microstructured plates, which can be treated as made of functionally graded material on the macrolevel is presented. The size of the microstructure of these plates is of an order of the plate thickness. Averaged governing equations of these plates can be obtained using the tolerance modelling technique, cf. [18, 19, 9]. Because, the derived tolerance model equations have the terms dependent of the microstructure size, this model describes the effect of the microstructure size. Results can be evaluated introducing the asymptotic model. Calculated results can be compared to those from the finite element method or a similar tolerance model of thin plates, cf. [9].
13
Content available A study on natural frequencies of Timoshenko beam with rapidly varying stiffness
Świątek M., Domagalski Ł., Jędrysiak J.
Vibrations in Physical Systems
|
2016
|
Vol. 27
369--376
EN
Vibrations of Timoshenko beams with properties periodically varying along the axis are under consideration. The tolerance method of averaging differential operators with highly oscillating coefficients is applied to obtain the governing equations with constant coefficients. The dynamics of Timoshenko beam with the effect of the cell length is described. A asymptotic model is then constructed, which is further studied in analysis of the low order natural frequencies. The proposed model is able to describe dynamics of beams made of non-slender cells.
14
Content available Nonlinear vibrations of periodic beams
Domagalski Ł., Jędrysiak J.
Journal of Theoretical and Applied Mechanics
|
2016
|
Vol. 54 nr 4
1095--1108
EN
Geometrically nonlinear vibrations of beams with properties periodically varying along the axis are investigated. The tolerance method of averaging differential operators with highly oscillating coefficients is applied to obtain governing equations with constant coefficients. The proposed model describes dynamics of the beam with the effect of microstructure size. In an example, an analysis of undamped forced nonlinear vibrations of the periodic beam is shown. Moreover, the results obtained for undamped free vibrations of periodic beams by the tolerance model are justified by those results from the finite element method. These results can be used as a benchmark in similar problems.
15
Content available Geometrically nonlinear vibrations of thin visco-elastic periodic plates on a foundation with damping: non-asymptotic modelling
Jędrysiak J.
Journal of Theoretical and Applied Mechanics
|
2016
|
Vol. 54 nr 3
945--961
EN
The objects under consideration are thin visco-elastic periodic plates with moderately large deflections. Geometrically nonlinear vibrations of these plates are investigated. In order to take into account the effect of microstructure size on behaviour of these plates a non- -asymptotic modelling method is proposed. Using this method, called the tolerance modelling, model equations with constant coefficients involving terms dependent on the microstructure size can be derived. In this paper, only theoretical considerations of the problem of nonlinear vibrations of thin visco-elastic periodic plates resting on a foundation with damping are presented.
16
Content available On free vibrations of thin functionally graded plate bands resting on an elastic foundation
Jędrysiak J., Kaźmierczak-Sobińska M.
Journal of Theoretical and Applied Mechanics
|
2015
|
Vol. 53 nr 3
629--642
EN
In this note free vibrations of plate bands with functionally graded properties, resting on an elastic foundation, are investigated. On the micro-level, these plate bands have a tolerance- -periodic structure. It can be shown that in dynamic problems of those objects, the effect of the microstructure size plays a role. This effect can be described in the framework of the tolerance model, which is presented here for these bands. Obtained results are evaluated introducing the asymptotic model. Both fundamental and higher free vibration frequencies of these plate bands are calculated using the Ritz method. The effects of differences of material plate properties in the cell on the microlevel and of the foundation are shown.
17
Content available remote Vibrations of plate strips with internal periodic structure
Marczak J., Jędrysiak J.
Engineering Transactions
|
2015
|
Vol. 63, iss. 1
93--108
EN
In this note vibrations of thin periodic plate strips with periodically distributed systems of three concentrated masses are analysed. Results of the non-asymptotic tolerance model are compared to those by the exact discrete model. In an example, these models are used to calculate lower and higher frequencies of the travelling wave related to the internal periodic structure.
18
Content available „Mała Wojna” w pruskiej myśli wojskowej 1815-1848
Jędrysiak J.
Zeszyty Naukowe / Wyższa Szkoła Oficerska Wojsk Lądowych im. gen. T. Kościuszki
|
2014
|
Nr 3
34--54
PL
Współczesne dyskusje nad naturą wojny bardzo często odwołują się do dorobku Carla von Clausewitza. Poszczególni pisarze wojskowi próbują potwierdzić lub odrzucić użyteczność jego dla różnych koncepcji „nowych wojen”. Badacze ci pomijają niestety zwykle kontekst epoki w której żył pruski filozof wojny, jak również fakt, że problem działań nieregularnych oraz „małej wojny” był istotnym tematem rozważań środowiska, w którym tworzył. Podobnie jak teoretycy u progu XXI stulecia, pruscy pisarze wojskowi stanęli po zakończeniu wojen napoleońskich przed problemem warunkowanych społecznie dynamicznych przemian w sztuce wojennej. Jednym z ważnych elementów tej refleksji była koncepcja „małej wojny”, znana wprawdzie w czasach ancien regime, lecz nabierająca nowego znaczenia w postrewolucyjnej Europie. Celem artykułu jest prezentacja najważniejszych przejawów tej refleksji, mająca w zamierzeniu pełnić funkcję pomocniczą w próbach zarówno oceny samych koncepcji Clausewitza, jak również ich użyteczności we współczesnej refleksji nad wojną.
EN
Contemporary discussions on the nature of war very often refer to Carl von Clausewitz's achievements. Military writers are trying to confirm or deny his utility for the different concepts of "new wars". Unfortunately, researchers usually overlook the context of the era in which the Prussian philosopher of war lived, as well as the fact that the problems of irregular actions and the "small wars" were major discussion topics in the environment in which he created. Just as the theorists at the beginning of XXI century, at the end of the Napoleonic wars the Prussian military writers faced the problem of socially conditioned dynamic changes in the art of war. One of the important elements of this reflection was the concept of "small wars", although known at the time of the ancient regime, but they take on new significance in the post-revolutionary Europe. The aim of the article is the presentation of the most important signs of this reflection, which is intended to assist in every attempt of evaluating Clausewitz's concept, as well as their usefulness in contemporary reflections on war.
19
Content available Vibrations of thin functionally graded plates with tolerance-periodic microstructure
Kaźmierczak-Sobińska M., Jędrysiak J.
Vibrations in Physical Systems
|
2014
|
Vol. 26
99--104
EN
This paper presents a problem of vibrations of thin functionally graded plates. To describe this kind of plates three averaged models are proposed: a tolerance model, an asymptotic model and a combined asymptotictolerance model, cf. [10]. Calculational results obtained for a functionally graded plate band using the proposed models are compared to each other.
20
Content available Nonlinear vibrations of periodic beams
Domagalski Ł., Jędrysiak J.
Vibrations in Physical Systems
|
2014
|
Vol. 26
73--78
EN
Geometrically nonlinear vibrations of beams with properties periodically varying along the axis are investigated. The tolerance method of averaging differential operators with highly oscillating coefficients is applied to obtain the governing equations with constant coefficients. The proposed model describes the dynamics of the beam with the effect of the microstructure size.
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