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1
Content available An approach to free vibration analysis of axially graded beams
Kukla S., Rychlewska J.
Journal of Theoretical and Applied Mechanics
|
2016
|
Vol. 54 nr 3
859--870
EN
In this study, the solution to the free vibration problem of axially graded beams with a non-uniform cross-section has been presented. The proposed approach relies on replacing functions characterizing functionally graded beams by piecewise exponential functions. The frequency equation has been derived for axially graded beams divided into an arbitrary number of subintervals. Numerical examples show the influence of the parameters of the functionally graded beams on the free vibration frequencies for different boundary conditions.
2
Content available Metoda wyznaczania obszaru dobrej widoczności na przejściach dla pieszych w Polsce
Jamroz K., Kempa J., Rychlewska J., Mackun T.
Transport Miejski i Regionalny
|
2015
|
nr 4
10--21
PL
Jednym z istotnych czynników wpływających na wypadki z pieszymi przekraczającymi jezdnię są ograniczenia obszarów dobrej widoczności pieszych i pojazdów na przejściach dla pieszych. W Polsce ten problem jest niedoceniany. W niniejszym artykule przedstawiono propozycję metody wyznaczania obszaru dobrej widoczność na przejściach dla pieszych w Polsce. Metodę tę opracowano, korzystając z doświadczeń zagranicznych i badań własnych. Metoda zawiera: sposób szacowania odległości widoczności pojazdu zbliżającego się do przejścia dla pieszych z punktu widzenia pieszego chcącego przekroczyć jezdnię, sposób szacowania odległości widoczności pieszego przechodzącego przez jezdnię lub wykazującego zamiar wejścia na przejście dla pieszych z punktu widzenia kierowcy pojazdu zbliżającego się do przejścia oraz zasady sprawdzania obszaru dobrej widoczności i postępowania w celu ewentualnego jej polepszenia.
EN
One of the important factors affecting accidents with pedestrians crossing the road are limitations of areas of good visibility of pedestrians and vehicles at pedestrian crossings. In Poland this issue is underestimated. This paper proposes a method of determining area of good visibility at pedestrian crossings in Poland. The method has been developed on the basis of international experiences and own studies. The method includes: a measure to estimate vehicle sight distance approaching the crossing from the point of view of pedestrians willing to pass the road, measure to estimate a distance of the visibility of pedestrians crossing the road or demonstrating intention to enter a crossing from the point of view of the driver of approaching vehicle and rules of verification the area of good visibility in order to possible improvement.
3
Content available A new approach for buckling analysis of axially functionally graded beams
Rychlewska J.
Journal of Applied Mathematics and Computational Mechanics
|
2015
|
Vol. 14, nr 2
95--102
EN
The object of considerations are axially functionally graded (FG) beams, which are loaded by an axial force varying along the length of the beam. The main idea presented here is to approximate FG beams by an equivalent beam with piecewise exponentially varying material properties, geometrical properties and axial load. Numerical solutions of the buckling analysis are obtained for four various types of boundary conditions associated with pinned and clamped ends. The usefulness of the proposed method is confirmed by comparing numerical results with those available for graded beams of special polynomial non-homogeneity.
4
Content available Zagrożenia dla uczestników ruchu drogowego stwarzane przez reklamy widziane z drogi
Mackun T., Jamroz K., Żukowska J., Rychlewska J.
Drogownictwo
|
2015
|
nr 4-5
134--142
PL
Na podstawie przeprowadzonych audytów i ocen planowanych reklam w pobliżu miejsc krzyżowania się dużych potoków pojazdów zidentyfikowano problemy, które mają rozwiązywać zarządcy dróg. Scharakteryzowano podstawowe cechy fizyczne i psychomotoryczne oka ludzkiego i wskazano występujące reakcje bezwarunkowe pod wpływem ekspozycji otoczenia. Badania treści i parametrów świetlnych reklam dynamicznych LED w Gdańsku wskazują, że spoty reklamowe trwają zbyt długo, a jasność nośników LED w nocy przekracza wielokrotnie normy jasności przyjmowane dla znaków i sygnałów drogowych.
EN
Based on audits and assessments of planned advertising in the vicinity of crossings of large streams of traffic, the paper identifies issues which have to be solved by the road manager. It characterizes the basic physical and psychomotor properties of the human eye and points out the unconditional reactions occuring under the influence of ambient exposure. Examining the content and parameters of dynamic LED light commercials in Gdansk indicate that the commercials take too long, and the brightness of the LED media repeatedly during the night than the brightness accepted standards for traffic signs and signals.
5
Content available Widoczność na przejściach dla pieszych
Jamroz K., Gumińska L., Rychlewska J., Mackun T.
Drogownictwo
|
2015
|
nr 4-5
142--149
PL
Przyczyną powstawania większości wypadków drogowych z udziałem pieszych są w Polsce błędy popełniane przez użytkowników dróg, a także błędy planistyczne i projektowe oraz bardzo często źle utrzymana infrastruktura drogowa. Jednym z istotnych czynników wpływających na wypadki z pieszymi przekraczającymi jezdnię są ograniczenia obszarów dobrej widoczności pieszych i pojazdów na przejściach dla pieszych. W Polsce ten problem jest niedoceniany. W artykule przedstawiono charakterystykę problemu ograniczonej widoczności na przejściach dla pieszych. Przedstawiono przykłady wyznaczania obszaru dobrej widoczności w wybranych krajach oraz podstawy teoretyczne wyznaczania obszaru dobrej widoczność na przejściach dla pieszych.
EN
The cause of most road accidents involving pedestrians in Poland mistakes made by road users, as well as planning and design errors, and often poorly maintained road infrastructure. One of the important factors affecting the accidents with pedestrians in excess of the road are the limitations of areas of good visibility of pedestrians and vehicles at pedestrian crossings. In Poland, the problem is underestimated. This paper presents the characteristics of the problem of limited visibility at pedestrian crossings. Also shows examples of the determination of the area of good visibility in selected countries and the theoretical basis for determining the area of good visibility at pedestrian crossings.
6
Content available Free vibration of axially functionally graded Euler-Bernoulli beams
Kukla S., Rychlewska J.
Journal of Applied Mathematics and Computational Mechanics
|
2014
|
Vol. 13, nr 1
39--44
EN
In this contribution, free vibration of axially functionally graded beams is analysed within the framework of the Euler-Bernoulli beam theory. The beams with uniaxial variation of the elasticity modulus and mass density are approximated by an equivalent beam with piecewise exponentially varying geometrical and material properties. A numerical example for a beam with pinned ends is presented.
7
Content available Buckling analysis of axially functionally graded beams
Rychlewska J.
Journal of Applied Mathematics and Computational Mechanics
|
2014
|
Vol. 13, nr 4
103--108
EN
In this paper critical buckling loads for axially functionally graded (FG) beams are studied. It is assumed that material properties of the beam vary exponentially through the axial direction. Solutions are derived for three types of boundary conditions: a beam that is clamped at both ends, pinned at both ends and a beam that is clamped at one end and pinned at the other.
8
Content available A system of linear recurrence equations for determinant of pentadiagonal matrix
Borowska J., Łacińska L., Rychlewska J.
Journal of Applied Mathematics and Computational Mechanics
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2014
|
Vol. 13, nr 2
5--12
EN
In this paper we present an application of the system of two homogeneous linear recurrence equations to evaluate the determinant of pentadiagonal matrix. The general considerations are illustrated by two examples. It is shown that the proposed approach is suited for implementation using computer algebra systems.
9
Content available On determinant of certain pentadiagonal matrix
Borowska J., Łacińska L., Rychlewska J.
Journal of Applied Mathematics and Computational Mechanics
|
2013
|
Vol. 12, nr 3
21--26
EN
In this paper, using the LU factorization, the relation between the determinant of a certain pentadiagonal matrix and the determinant of a corresponding tridiagonal matrix will be derived. Moreover, it will be shown that determinant of this special pentadiagonal matrix can be calculated by applying the fourth order homogeneous linear difference equation.
10
Content available Free vibration analysis of functionally graded beams
Kukla S., Rychlewska J.
Journal of Applied Mathematics and Computational Mechanics
|
2013
|
Vol. 12, nr 2
39--44
EN
In this paper free vibration of axially functionally graded (FG) beams consisting of two segments is studied. The FG beams under consideration are characterized by axially varying cross-section areas and/or functionally grading material properties. Numerical example for a beam that is clamped at both ends is presented.
11
Content available remote Application of difference equations to certain tridiagonal matrices
Borowska J., Łacińska L., Rychlewska J.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
|
2012
|
Vol. 11, nr 3
15-20
EN
In this paper we present an application of second order homogeneous linear difference equations with constant coefficients to evaluate the determinant of tridiagonal matrices. Comparing the obtained results with a certain alternative approach [1] some formulae for the finite sum are derived.
12
Content available remote On the certain asymptotic approach to the modelling of microheterogeneous media
Borowska J., Rychlewska J., Woźniak C.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
|
2009
|
Vol. 8, nr 1
5-12
EN
The object of analysis is mathematical modelling of thermomechanical problems of microheterogeneous media. The aim of this contribution is to propose a certain asymptotic modeling technique. The proposed approach is realized both in consistent and semiconsistent form.
13
Content available remote On the tolerance overaging for differential operators with periodic coefficients
Borowska J., Łaciński Ł., Rychlewska J., Woźniak C.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
|
2008
|
Vol. 7, nr 1
17-21
EN
The aim of this contribution is to propose the tolerance averaging for differential operators with periodic coefficients. The averaging technique presented in this paper is based on proper limit passages with tolerance parameter to zero. This approach is a certain generalization of that presented in [1].
14
Simplicial modelling of dynamic problems in microstructured composite solids
Rychlewska J.
Zeszyty Naukowe Politechniki Świętokrzyskiej. Nauki Techniczne
|
2007
|
Z. 6
35-44
EN
The aim of this paper is to propose a certain new approach to the formulation of both discrete and continuum models for the analysis of dynamic problems in elastic composite solids with a periodic microstructure. The proposed approach is based on a periodic simplicial division of the unit cell and on the assumption of a uniform strain in every simplex. The main feature of the obtained discrete model is the finite-difference form of the governing equations. By applying smoothing operation the continuum models are derived directly from the discrete ones.
PL
W pracy zostało zaproponowane nowe podejście do modelowania zagadnień dynamiki w liniowo–sprężystych mikroperiodycznych ośrodkach ciągłych, które za punkt wyjścia przyjmuje periodyczny podział symplicjalny elementu reprezentatywnego struktury. Podejście to umożliwia wyprowadzenie pewnej hierarchii modeli ciągłych, które opisują zagadnienia dynamiki z różną dokładnością. Za pomocą operacji wygładzania zaproponowane modele ciągłe zostały wyprowadzone bezpośrednio z modeli dyskretnych.
15
Content available remote On a certain extension of the principle of stationary action and its applications
Łaciński Ł., Rychlewska J., Szymczyk J., Woźniak C.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
|
2007
|
Vol. 6, nr 1
141-145
EN
The aim of this contribution is to propose a certain extension of the principle of stationary action which can be applied to derive the hyperbolic and elliptic PDEs with quasi-linear operators. The proposed generalized form of the above principle will be used to formations of mathematical models for solids and structures.
16
Content available remote A contribution to the modeling of nonstationary processes in functionally graded laminates
Łaciński Ł., Rychlewska J., Szymczyk J., Woźniak C.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
|
2006
|
Vol. 5, nr 1
83-94
EN
The considerations are concerned with mathematical modeling of nonstationary thermomechanical processes in functionally graded laminates (FGL). The proposed modeling procedure is an extension of that based on the tolerance averaging technique [13].
17
Content available On the modelling and optimization of functionally graded laminates
Rychlewska J.
Journal of Theoretical and Applied Mechanics
|
2006
|
Vol. 44 nr 4
783-795
EN
The object of investigations are Functionally Graded Materials (FGM) which on the microstructural level are made of two kinds of very thin laminae. These FGM will be referred to as the Functionally Graded Laminates (FGL). The aim of this contribution is to formulate discrete-continuum and continuum 3D-models of elastodynamics of FGL. The proposed modelling procedure constitutes a certain generalization of the approach to the modelling of periodic structures leading to a system of finite difference equations and then to their continuum approximation, Rychlewska and Woźniak (2003). The obtained results are applied to the analysis of a certain layered structure with a FGL transition zone. The optimization problem related to the position of the transition zone is discussed.
PL
Przedmiot rozważań stanowi szczególna klasa materiałów gradientowych, tzw. laminatów o strukturze gradientowej, które na poziomie mikrostrukturalnym złożone są z dużej liczby bardzo cienkich wartewek. celem pracy jest zaproponowanie modelu dyskretno-ciągłego i ciągłego zagadnień elastodynamiki takich laminatów. Sformułowany model ciągły został zastosowany do analizy drgań ośrodka obciążonego inercyjnie, złożonego z dwóch jednorodnych wartw, pomiędzy którymi znajduje się strefa przejściowa. Przedyskutowano zagadnienie optymalizacji położenia strefy przejściowej.
18
Content available remote Boundary layer phenomena in elastodynamics of functionally graded laminates
Rychlewska J., Woźniak Cz.
Archives of Mechanics
|
2006
|
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].
19
Content available remote On the modelling of functionally graded laminated structures
Rychlewska J., Szymczyk J., Woźniak C.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
|
2005
|
Vol. 4, nr 1
230-238
EN
The object of analysis is a functionally graded material (FGM). The aim of this paper is threefold. Firstly, we outline and recall basic technological motivations and physical foundations of FGM concept. Secondly, we propose a certain special kind of FGM, which on the microstructural level are made of very thin laminae (a functionally graded laminate-FGL). Thirdly, a new approach to the formulation of averaged models for the analysis of dynamic problems in FGL is proposed. Example of applications of the proposed models will be discussed separately.
20
Content available remote Discrete and continuum models in elastodynamics of micro-periodic solids
Rychlewska J.
Vibrations in Physical Systems
|
2004
|
Vol. 21
319--322
EN
The aim of this paper is to propose a new alternative approach to the formulation of both discrete and continuum models for the analysis of dynamic problems in elastic composite solids with a periodic microstructure. The proposed approach is based on a periodic simplicial division of the unit cell, [1], and on the assumption of a uniform strain in every simplex. The main feature of the obtained discrete model is the finite-difference form of the governing equations. The proposed discrete model can be formulated on different levels of accuracy. Considerations are restricted to problems in which the typical wavelength of the macroscopic deformation pattern is sufficiently large when compared to the unit cell diameter By applying smoothing operation the continuum models are derived directly from the discrete ones. The general equations obtained in the models proposed here are applied in order to investigate dispersion phenomena in the wave propagation problems.
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