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1
Content available remote On the mass discretization approach to elastodynamics of periodically stratified composites
Szlachetka O., Wągrowska M., Witkowska-Dobrev J., Woźniak C.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2012
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Vol. 11, nr 4
143-150
EN
The object of analysis are two component periodically stratified linear elastic multilayered composites. The aim of contribution is elastodynamics of these composites subjected to the mass discretization on the interfaces between adjacent homogeneous layers. Two specific cases of the mass discretizations are taken into account. In the first case the mass is assigned uniformly to every interface. It is shown that this kind of mass discretization leads to physically completely wrong results. In the second case, the mass is discretized uniformly but on the every second interface. In this case it is shown that the obtained elastodynamics equations have a physical sense provided that the wave are sufficiently long.
2
On the boundary effect in elastodynamics of laminated solids
Wierzbicki E., Łacińska L.
Zeszyty Naukowe Politechniki Świętokrzyskiej. Nauki Techniczne
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2007
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Z. 6
45-54
EN
The object of the contribution is the analysis of a certain aspects of the boundary effect behaviour in elastodynamics of FGM-type multiphase laminated composites. The aim of the paper is to answer the question what kind of assumptions are enough to be taken into account in the framework of the simplified tolerance model for the elastodynamics of the considered laminates the boundary effect will be observed. The answer to this question is obtained for a certain class of two-phased FGM-type laminates and for tolerance description based on the exclusively one arbitrary shape function.
PL
Przedmiotem rozważań jest analiza zjawisk typu warstwy brzegowej w elastodynamice wielofazowych laminatów z gradacją własności efektywnych. Celem pracy jest odpowiedź na pytanie, przy jakich założeniach przyjętych w ramach uproszczonego tolerancyjnego modelu elastodynamiki takich laminatów efekt brzegowy jest obserwowany. Odpowiedź na to pytanie uzyskano dla pewnej klasy dwufazowych laminatów typu FGM i tolerancyjnego modelu z jedną funkcją kształtu, której postać nie musi być precyzowana dla realizacji celu pracy.
3
Content available remote On tolerance averaged model of the propagation of boundary displacement fluctuations in FGM-type laminated composite
Łacińska L., Wierzbicki E.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2007
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Vol. 6, nr 1
133-140
EN
The object of the contribution is the analysis of a certain initial-boundary problems in elastodynamics of FGM-type multiphased laminated composites. The aim of the paper is to formulate an answer to the question what kind of assumptions are enough to be taken into account in the framework of the simplified tolerance model for the elastodynamics of the considered laminates the boundary effect will be observed.
4
Content available remote On the null condition for nonlinearly elastic solids
Domański W., Ogden R. W.
Archives of Mechanics
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2006
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Vol. 58, nr 4-5
339-361
EN
Smooth solutions to the Cauchy problem for the equations of nonlinear elastodynamics exist typically only locally in time. However, under the assumption of small initial data and an additional restriction, the so-called null condition, global existence and uniqueness of a classical solution can be proved. In this paper, we examine this condition for the elastodynamic equations and study its connection with the property of genuine nonlinearity as well as its relation with the phenomenon of self-resonance of nonlinear elastic waves. Using a special structure of plane waves elastodynamics [13], we provide an alternative and simple formulation of the null condition. This condition is then evaluated for some examples of elastic constitutive laws in order to determine the nature of the restrictions that it imposes.
5
Content available remote Boundary layer phenomena in elastodynamics of functionally graded laminates
Rychlewska J., Woźniak Cz.
Archives of Mechanics
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2006
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Vol. 58, nr 4-5
431-444
EN
The object of considerations are micro-laminated two-phase solids having macroscopic properties continuously varying in the direction normal to the layering (functionally graded laminates, FGL). The main question posed in this contribution is how to investigate both micro- and macro- dynamic response of the linear-elastic FGL. To answer this question, a new approximate mathematical model of FGL is proposed. This model is represented by a certain refined homogenized equation of motion for averaged displacements and a boundary-layer equation for intrinsic displacement fluctuations. Main attention is given to the investigations of near-initial and near-boundary dynamic phenomena in FGL, which are related to the specific form of initial and boundary conditions. For a periodically laminated medium the obtained results reduce to those derived in [7].
6
Content available remote Boundary and initial fluctuation effect on dynamic behaviour of a laminated solid
Łacińska L., Wierzbicki E.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2005
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Vol. 4, nr 1
110-122
EN
In the paper an approximate description of the evolution of boundary traction fluctuations in the two-component linear-elastic laminates is discussed. In the paper [1] it has been shown that in the framework of the tolerance averaged model of linear elastodynamics of the aforementioned laminates, cf. [2], in the first approximation such evolution is independent of the mean (averaged) displacement. The aim of this contribution is to discuss solutions to the boundary problem formulated in [1].
7
Simplified models for the vibration analysis of micro-periodic elastic media
Rychlewska J., Szymczyk J., Woźniak C.
Journal of Technical Physics
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2004
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Vol. 45, no 2
91-104
EN
The aim of this paper is to propose and apply a new approach to the formation of simplified models for the vibration analysis of a micro-periodic linear-elastic composite medium. First, we propose a discrete model which can be used to investigations of both long and short waves. The main feature of the obtained discrete model is the finite-difference form of governing equations. The continuum models are derived directly from the discrete one under the assumption that the macroscopic wavelength is large when compared to the length dimension of a periodicity cell. The proposed models describe both the low-frequency and high-frequency vibration problems and can be formulated on different levels of accuracy. The reliability of the procedure leading from discrete to continuum models is discussed on the illustrative example.
8
Content available remote Trefftz polynomials reciprocity based boundary element formulations for elastodynamics
Konkol F., Kompiš V.
Computer Assisted Mechanics and Engineering Sciences
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2004
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Vol. 11, No. 2-3
239-245
EN
In this paper Trefftz polynomials are used for the BEM (Boundary Element Method) based on the reciprocity relations. BEM provides a powerful tool for the calculation of dynamic structural response in the frequency and time domains. Field equations of motion and boundary conditions are cast into boundary integral equations (BIE), which are discretized only on the boundary [1]. Trefftz polynomials or other non-singular (e.g. harmonic), Trefftz functions [2] (i.e. functions satisfying all governing differential equations but not the boundary conditions) used in the Betti's reciprocity relations lead to corresponding BIE that do not contain any (weak, strong, hyper) singularities. Fundamental solutions are not needed and evaluation of the field variables inside the domain is simpler.
9
Content available remote Two approaches to the formation of a tolerance averaged equations for elastodynamics of periodic solids
Augustowska L., Wierzbicki E.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2002
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Vol. 1, nr 1
5--13
EN
The aim of this contribution is to formulate two different approaches to the computation of averaged moduli in the equations of the tolerance averaged model of microperiodic linear-elastic composites. In the first approach, which will be called basis function approach, we shall use some of the FEM concepts in order to establish the basis functions in the Galerkin approximation to the non-stationary periodic cell problem of elastodynamics. In the second approach, which will be called mode shape function approach, we shall also use FEM concepts in order to determine functions describing the character of free vibrations of the periodicity cell. This approach makes it possible to reduce a large number of unknowns occuring in the first approach.
10
Content available remote Ciągły model dynamiki płyt siatkowych
Cielecka I.
Vibrations in Physical Systems
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2000
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Vol. 19
82--83
11
Różnicowe i ciągłe modele elastodynamiki dyskretnych układów periodycznych o złożonej strukturze
Lewandowska J., Szymczyk J., Woźniak C.
Zeszyty Naukowe Katedry Mechaniki Stosowanej / Politechnika Śląska
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1999
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z. 9
147-152
PL
W pracy przedstawiono nową, różnicową postać równań elastodynamiki dyskretnych układów periodycznych o złożonej strukturze. Pokazano sposób bezpośredniego przejścia od opisu dyskretnego do modelu ciągłego. Sformułowano odpowiednie równania dynamiki w asymptotycznym modelu deformacji długofalowych.
EN
A new finite difference formulation of elastodynamics of polyatomic lattices is presented. A way of transition from a nonlocal model to a continuum one is shown. Finite difference and continuum formulations of the asymptotic model for the long wave deformations are formulated.
12
Drilling rotations in elastodynamics of thin-walled periodic structures
Wierzbicki E., Woźniak C.
Zeszyty Naukowe Katedry Mechaniki Stosowanej / Politechnika Śląska
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1999
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z. 9
273-278
EN
The aim of this contribution is to obtain an averaged continuum model of linear-elastic spatial periodic thin-walled structures, cf. Figure 1. Considerations are restricted to problems independent on z-coordinate; hence the plain stress in plates and the cylindrical bending of walls in 0x1x2-plane are postulated. Under assumption that all joints interconnecting wall elements are rigid the concept of drilling rotations in 0x1x2-plane as independent dynamic variables was introduced.
PL
Celem pracy jest otrzymanie uśrednionego modelu ciągłego liniowo-sprężystych przestrzennych cienkościennych konstrukcji periodycznych (por. rys. 1). Rozważania ograniczono do zagadnień niezależnych od zmiennej z, zakładając płaski stan naprężenia w płytach oraz walcowe zginanie ścianek w płaszczyźnie 0x1x2. Przyjmując, że wszystkie połączenia ścianek są sztywne, wprowadzono pojęcie obrotów owinięcia w płaszczyźnie 0x1x2 jako niezależnych zmiennych dynamicznych.
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