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  1. 4 Archives of Civil and Mechanical Engineering
  2. 3 Acta Scientiarum Polonorum. Architectura
  3. 3 Engineering Transactions
  4. 2 Archives of Civil Engineering
  5. 2 Journal of Theoretical and Applied Mechanics
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  1. 1 2023
  2. 1 2022
  3. 3 2020
  4. 1 2019
  5. 6 2018
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  1. 4 Magnucki K.
  2. 3 Obara P.
  3. 3 Wstawska I.
  4. 3 Zenkour A. M.
  5. 2 Bril J.
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1
Content available The use of modelling of impacts exerted by means of transport on the environment for ensuring safety
100%
Bril J. , Rydygier E.
Scientific Journal of the Military University of Land Forces
|
2018
|
tom 50
|
nr 2(188)
162-175
EN
The article presents the model research on impacts exerted by means of transport on the structures. In modelling the dynamics of transport systems the dynamic properties of the ground forming the foundation soil for tracks or roadways have been taken into account. The ground has been modelled as an elastic half-space. The dynamics of an infinite mass band being in contact with an elastic half-space has been investigated. As part of the research on impacts exerted by means of transport on structures a model of a problem has been examined where an automotive vehicle, representing a concentrated force in motion, is in contact with a roadway described as a rigid body coupled with an elastic half-space. It has been demonstrated that a surface (Rayleigh) wave propagates in the ground, being a continuous (elastic) medium, and acts on a structure modelled as a rigid body. The research results have been presented in the form of vertical and horizontal transmittances of the ground for different frequencies of loading with different unit forces.
2
Content available The use of modelling of impacts exerted by means of transport on the environment for ensuring safety
100%
Bril J. , Rydygier E.
Scientific Journal of the Military University of Land Forces
|
2018
|
tom Vol. 50, No. 2(188)
162--175
EN
The article presents the model research on impacts exerted by means of transport on the structures. In modelling the dynamics of transport systems the dynamic properties of the ground forming the foundation soil for tracks or roadways have been taken into account. The ground has been modelled as an elastic half-space. The dynamics of an infinite mass band being in contact with an elastic half-space has been investigated. As part of the research on impacts exerted by means of transport on structures a model of a problem has been examined where an automotive vehicle, representing a concentrated force in motion, is in contact with a roadway described as a rigid body coupled with an elastic half-space. It has been demonstrated that a surface (Rayleigh) wave propagates in the ground, being a continuous (elastic) medium, and acts on a structure modelled as a rigid body. The research results have been presented in the form of vertical and horizontal transmittances of the ground for different frequencies of loading with different unit forces.
3
Content available Analytical solutions for free oscillations of beams on nonlinear elastic foundations using the Variational Iteration Method
100%
Younesian D. , Saadatnia Z. , Askari H.
Journal of Theoretical and Applied Mechanics
|
2012
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tom Vol. 50 nr 2
639-652
EN
Closed form expressions are obtained for the dynamic response of an elastic beam rested on a nonlinear foundation in this paper. The nonlinear governing equation is solved using the Variational Iteration Method (VIM). An iteration formulation is constructed based on the VIM and the dynamic responses are then obtained. Frequency responses are presented in a closed form and their sensitivity with respect to the initial amplitudes are investigated. A number of numerical simulations are then carried out and performance and validity of the solution procedure is evaluated in the time domain. It is proved that the VIM is quite a reliable and straightforward technique to solve the corresponding set of coupled nonlinear differential equations.
PL
W pracy przedstawiono zamknięte formy rozwiązań opisujących odpowiedź dynamiczną elastycznej belki spoczywającej na nieliniowo sprężystym podłożu. Równanie ruchu rozwiązano przy pomocy iteracyjnej metody wariacyjnej (VIM). Sformułowanie iteracyjne skonstruowane w oparciu o tę metodę pozwoliło na wyznaczenie odpowiedzi dynamicznej belki. Charakterystyki częstościowe przedstawiono w zamkniętej formie i podkreślono ich wrażliwość na wartość amplitud początkowych. Następnie zaprezentowano wyniki kilku symulacji numerycznych w celu oszacowania wydajności i dokładności zastosowanej procedury rozwiązywania równań ruchu w dziedzinie czasu. Wykazano, że metoda VIM jest wystarczająco prosta i wiarygodna w rozwiązywaniu układu sprzężonych, nieliniowych równań różniczkowych.
4
On the interaction between elastic ponderable layer and ceiling plate
100%
Małachowski M. , Pauk V.
Zeszyty Naukowe Politechniki Świętokrzyskiej. Nauki Techniczne
|
2007
|
tom Z. 6
129-141
EN
In this paper, the interaction between soil subgrade and a ceiling plate is studied. The two bodies are assumed to be in frictionless contact. The subgrade is modeled by the elastic, homogenous layer and the Kirchhoff hypotheses for the plate is assumed. Different types of plate support are considered. The interaction problem is reduced to the integral equation, which is solved numerically. Some results are presented on diagrams.
PL
Niniejsza praca traktuje o współpracy pomiędzy warstwą gruntową i płytą stropową. Założono, że oba ciała znajdują się w kontakcie, bez tarcia. Podłoże modelowane jest za pomocą jednorodnej, elastycznej warstwy, natomiast dla płyty przyjęto założenia Kirchhoffa. W pracy zostały przeanalizowane różne sposoby podparcia płyty. Zagadnienie interakcji zostało sprowadzone do rozwiązania równania całkowego, które zostało rozwiązane numerycznie. Niektóre z wyników zostały zaprezentowane w postaci wykresów.
5
Content available remote Approximate estimation of stability of homogeneous beam on elastic foundation
100%
Wstawska I. , Kędzia P. , Magnucki K.
Engineering Transactions
|
2019
|
tom Vol. 67, iss. 3
429--440
EN
The paper deals with a proposition of obtaining an analytical solution for a beam on elastic foundation. The main objective of presented work was stability analysis of the axially compressed beam. The analytical model was proposed. Shape function for inhomogeneous properties of the foundation was assumed. The Galerkin method was used to calculate the values of critical forces. Main conditions have been defined. The critical loads as a function of geometric and mechanical properties of the beam as well as inhomogeneous properties of the elastic foundation have been calculated.
6
Analityczne rozwiązanie zagadnienia belki o zmiennych w funkcji jej długości parametrach, współdziałających z podłożem sprężystym
100%
Gorczyński H.
Zeszyty Naukowe Katedry Mechaniki Stosowanej / Politechnika Śląska
|
2000
|
tom nr 13
93-98
PL
Problem zginania belek współdziałających z ciągłym podłożem potykamy przy modelowaniu różnorodnych konstrukcji technicznych. W takich przypadkach na wartość liczbową ugięcia liniowego i kątowego, a także na wartości liczbowe sił wewnętrznych (momentów zginających i sił poprzecznych) ; występujących w belce wywierają wpływ: własności podłoża, sztywność belki oraz obciążenia przyłożone z zewnątrz (ich rodzaj, wartość liczbowa oraz miejsce przyłożenia). Uwzględniając, że parametry belki oraz podłoża mogą zmieniać się w funkcji długości belki jak również fakt, że liczba obciążeń może być duża oraz to, ze całość zagadnienia opisuje równanie różniczkowe czwartego rzędu rozwiązanie zagadnienia staje się bardzo skomplikowane, aczkolwiek możliwe do wykonania. Poniżej przedstawiono sposób rozwiązania tego zagadnienia w oparciu o metody numeryczne.
EN
Bending of beams cooperating with continuous foundation is encountered at modeling different technical structures. In such cases the numerical values of the linear and angular deflections, and these of internal forces (bending moments and transverse forces), are influenced by the foundation properties, beam rigidity and the external loads (their type, value and point of apphcation). Taking into account that both the beam and foundation parameters can vary with the beam length and that the number of loads may be significant, as well as the fact that the complete problem is described by the differential equation of fourth order, the solution of this problem becomes very complicated, although nQt impossible. Presented below is the solution based on numerical methods.
7
Content available Analytical investigation of a beam on elastic foundation with nonsymmetrical properties
100%
Wstawska I. , Magnucki K. , Kędzia P.
Engineering Transactions
|
2022
|
tom Vol. 70, iss. 1
77--93
EN
The subject of presented analytical and numerical investigation is the stability of an axially compressed beam on an elastic foundation. The shape function of the foundation was assumed. The formula was supplemented with the offset parameter. The critical values of loads were calculated and presented as a function of geometric and mechanical properties of the beam and nonsymmetrical properties of the elastic foundation. The highest values of critical loads can be obtained for the highest values of shape parameter and the lowest values of amplitudes of shape function. The values of critical loads increase with the increase of the value of the offset parameter.
8
Content available Effect of damages on crack development in coating on elastic foundation
100%
Mirsalimov V. M. , Hasanov S. G.
Journal of Theoretical and Applied Mechanics
|
2015
|
tom Vol. 53 nr 4
823--836
EN
A fracture mechanics problem for a coating linked to the basis made of another elastic material is considered. It is assumed that in the vicinity of technological defect (crack) in the process of loading in the coating, there will arise prefracture zones (damages) that are modeled as the areas of weakened interparticle bonds of the material. In the prefracture zones (interlayers of the overstressed material), the coating material is deformed beyond the limit of elasticity. It is considered that during loading in the cross section of the coating in the vicinity of the crack, there is an arbitrary number of rectilinear prefracture zones. The condition determining the limiting value of the external load at which the crack growth happens is obtained.
9
Content available Free flexural vibration of a sandwich beam on an elastic foundation with variable properties
88%
Magnucki K. , Wstawska I. , Kedzia P.
Archives of Mechanics
|
2023
|
tom Vol. 75, nr 6
619--646
EN
Free flexural vibration of a simply supported sandwich beam on an elastic foundation is the main purpose of the presented investigation. An analytical model of multi-layered beam on elastic foundation has been prepared. The authors submitted an original beam-foundation interaction model which based on variable parameters of the foundation and their influence on the beam response. This explanation leads to the possibility of continuous characterization of the beam-foundation interplay. A nonlinear mathematical function for symmetrical properties of the foundation has been adopted. The frequency equation as a function of geometric and mechanical properties of the beam and the parameters of the elastic foundation was derived using the Galerkin method. The analytical investigation has been divided into two parts: the analysis of elastic foundation with constant and variable properties. The unconventional shape function and the function of deflection have been introduced and employed. Moreover, the finite element analysis has been performed. Sample analytical and numerical calculations have been performed, demonstrating a good concurrence between both models. The difference between analytical and numerical values of the fundamental natural frequency did not exceed 0:5%.
10
Content available remote Approximate fundamental solutions of equilibrium equations for thin plates on elastic foundation
88%
Myślecki K.
Archives of Civil and Mechanical Engineering
|
2004
|
tom Vol. 4, no 1
31-40
EN
In this paper, a new approximate method of determining fundamental solutions for thin plates on elastic foundation is considered. Various models of foundations (Winkler, Pasternak, elastic half-space) are analysed. The approximate fundamental solutions are obtained through the analysis of power series of their Fourier's transform images. In the inversion procedure from images to originals, the well-known fundamental solutions of the n-th power of the Laplace operator are used. The effectiveness of the approximate fundamental solutions is veritied by some test examples.
PL
Podano przybliżoną metodę wyznaczania rozwiązań podstawowych równań równowagi dla płyt cienkich na podłożu sprężystym. Rozpatrzono jednoparametrowe podłoże Winklera, dwuparametrowe podłoże Pasternaka i półprzestrzeń sprężystą. Przybliżone rozwiązania podstawowe otrzymano, rozwijając transformaty Fouriera ścisłych rozwiązań podstawowych względem małego parametru. Do odwracania obrazów transformat Fouriera wykorzystano znane rozwiązania podstawowe n-tej potęgi operatora Laplace'a. Otrzymana postać przybliżonych rozwiązań podstawowych (szeregi podstawowe) jest dużo prostsza od postaci ścisłych rozwiązań podstawowych (funkcje specjalne Bessela i Struvego). Znalezione przybliżone rozwiązania podstawowe zastosowano w metodzie elementów brzegowych w wersji Kupradzego. Zaletą tej wersji jest to, że nie musi się obliczać osobliwych całek na brzegu obszaru płyty, a brzegowe równania całkowe mają prostą postać. Dla każdego rodzaju podłoża wykonano przykład numeryczny rozwiązania płyty metodą elementów brzegowych z zastosowaniem przybliżonych rozwiązań podstawowych. Prezentowane wyniki obliczeń porównano z opublikowanymi literaturze wynikami otrzymanymi dzięki zastosowaniu metody różnic skończonych. Część wyników porównano z wynikami otrzymanymi metodą elementów skończonych w systemie COSMOSIM. Analiza przykładów wykazuje użyteczność przybliżonych rozwiązań podstawowych w praktycznych zastosowaniach oraz szybką zbieżność szeregów potęgowych reprezentujących te rozwiązania - wystarcza 5-7 wyrazów, aby osiągnąć zadowalającą zbieżność.
11
Content available Research of work of a rotor crush machine on elastic foundation with the use of graphs
75%
Zinko R.
Vibrations in Physical Systems
|
2014
|
tom Vol. 26
343--350
EN
The use of graphs for the research of a rotor crush machine work on elastic foundation is offered. For machines the structure graph of its design is being written. The graph of levels structure of the generalized coordinates of mathematical model is being formed on the basis of structure graph of machine design. It allows building of the mathematical model, which describe the physical processes of the machine work quickly and qualitatively.
12
Content available Trigonometric solution for an exponentially graded thick plate resting on elastic foundations
75%
Zenkour A. M.
Archive of Mechanical Engineering
|
2018
|
tom Vol. LXV, nr 2
193--208
EN
This article investigates the solution of exponentially graded (EG) thick rectangular plates resting on two-parameter elastic foundations according to a trigonometric plate theory (TPT). This theory includes the effect of both shear and normal strains thickness without needing to any shear correction factor. The displacement fields contains initial terms of a power series across plate thickness as well as additional trigonometric terms. The material properties of plate is graded such that Lamé’s coefficients convert exponentially in a given constant orientation.Equilibrium equations according to the EG plate resting on Pasternak’s foundations are derived. The solution is obtained by using Navier’s technique. Numerical results for the EG thick plate on elastic foundations are presented, and compared with those available in the literature. The influences of Winkler’s and Pasternak’s parameters, side-to-thickness ratio, inhomogeneity parameter and aspect ratio on the bending responses of EG plates are investigated.
13
Content available remote Free And Forced Vibrations of a Post-Buckled Delaminated Beam-Plate Resting on a Two Parameter Elastic Foundation
75%
Bichir S. , Esmaeel R. A. , Nassar M. M.
Mechanics and Mechanical Engineering
|
2005
|
tom Vol. 9, nr 2
207--222
EN
In this study, the free and forced vibrations of a delaminated beam-plate resting on a two-parameter (Pasternak type) elastic foundation are investigated. We consider a homogeneous isotropic clamped beam-plate compressed axially and subject to an external time dependent force. In order to study the vibration of the delaminated beam-plate relative to a post-buckled state we should solve the static deformations. This has been accomplished by the successive substitution method.The free and forced vibration analysis are then performed. Results are represented in both graphical and tabulated forms and shows that the natural frequencies are affected by the change in the delamination length, depth and location and also affected by the change in the elastic foundation parameters.
14
Content available remote Stability of slightly wrinkled plates interacting with an elastic subsoil
75%
Michalak B.
Engineering Transactions
|
1999
|
tom Vol. 47, iss. 3
269-283
EN
The fisrt aim of the contribution is to formulate an engineering theory describing the linear stability of periodically waved shallow shell-like structures (slightly wrinkled plates, cf. Fig. 1) interacting with a Winkler foundation. On the basis of the proposed theory, the effect of elactic foundation on the value of a critical force is investigated. The second aim is to compare the proposed model of wrinkled plates resting on elastic medium with the known theories of orthotropic plates. It is shown that the obtained solution depend on the shell wavelength parameter l. The general results are illustrated by an example.
15
Content available remote Compressive study of functionally graded plates resting on Winkler–Pasternak foundations under various boundary conditions using hyperbolic shear deformation theory
75%
Zenkour A. M. , Radwan A. F.
Archives of Civil and Mechanical Engineering
|
2018
|
tom Vol. 18, no. 2
645--658
EN
Equilibrium equations of a functionally graded plate resting on two-parameter elastic foundations are derived using hyperbolic shear deformation theory. This theory takes into account the hyperbolic distribution of transverse shear deformation and satisfies that the corresponding shear stresses equal to zero on upper and lower surfaces of the plate without requiring any shear correction factors. Eight different types of boundary conditions are considered. Governing equations are obtained including the plate-foundation interaction. The present results are compared well with the corresponding available in the literature. Effects of boundary conditions, linear (Winkler) modulus and shear foundation (Pasternak) modulus, gradient index, plate aspect ratio, side-to-thickness ratio on the stresses and deflections are all discussed. It is established that the present model is more accurate than some theories developed previously.
16
Content available Free axisymmetric flexural vibrations of circular plate with symmetrically varying mechanical properties supported on elastic foundation
63%
Magnucki K.
Vibrations in Physical Systems
|
2020
|
tom Vol. 31, nr 2
art. no. 2020217
EN
The subject of the paper is a circular plate with clamped edge supported on elastic foundation. Mechanical properties of the plate symmetrically vary in its thickness direction. Free axisymmetric flexural vibration problem of the plate with consideration of the shear effect is analytically studied. Two partial differential equations of motion based on the Hamilton principle are obtained. The system of equations is analytically solved and the fundamental natural frequency of axisymmetric vibration for example plates is derived.
17
Content available Układ dwóch nieskończenie długich belek z wypełnieniem sprężystym pod obciążeniem ruchomym
63%
Ataman M. , Szcześniak W.
Autobusy : technika, eksploatacja, systemy transportowe
|
2018
|
tom R. 19, nr 12
285--288
PL
W artykule omówiono analityczne rozwiązanie zadania z dynamiki układu dwóch nieskończenie długich belek z wypełnieniem sprężystym. Układ spoczywa na podłożu Winklera i jest obciążony ruchomą siłą skupioną. Ponieważ zagadnienie jest stacjonarne dla obserwatora poruszającego się z obciążeniem, cząstkowe równania różniczkowe opisujące drgania układu transformowano na równania różniczkowe zwyczajne w układzie współrzędnych związanym z ruchomą siłą. Układ równań doprowadzono do jednego równania różniczkowego, zawyżonego rzędu, na ugięcie dolnej belki. Rozwiązanie zadania doprowadzono do prostej całki nieskończonej Fouriera. W pracy przedstawiono obszerny wykaz publikacji z literatury przedmiotu [1-45].
EN
The paper discussed the analytical solution of a dynamic problem of a system of two infinite beams separated by an elastic core. The beams’ system rests on the Winkler foundation and is loaded with a moving concentrated force. Because the problem is stationary for an observer moving with the load, partial differential equations, describing the vibrations of the system, were transformed into ordinary differential equations in the coordinate system related to the moving force. The system of equations was transformed to one differential equation of an eighth order. The equation defines deflection of the lower beam. The solution of the problem was resulted to the simple infinite Fourier integral. An extensive list of publications on the related literature is presented in the paper [1-45].
18
Analiza stateczności pręta smukłego spoczywającego na dwuparametrowym podłożu sprężystym
63%
Obara P.
Zeszyty Naukowe Politechniki Świętokrzyskiej. Nauki Techniczne
|
2007
|
tom Z. 2
135-148
PL
W pracy analizie poddano smukłą belkę spoczywającą na dwuparametrowym podłożu sprężystym. Wyprowadzone zostało różniczkowe równanie równowagi dynamicznej belki ściskanej zachowawczą siłą osiową oraz została przeprowadzona analiza rozwiązania tego równania w zależności od wzajemnych relacji między jego współczynnikami. Wyprowadzona została również ścisła macierz sztywności podstawowego elementu belkowego, a rozwijając otrzymana macierz w szereg potęgowy względem argumentów występujących w niej funkcji wyznaczona została macierz sztywności elementu pracującego z udziałem sprężystego podłoża i stałej siły osiowej.
EN
Analysis in work was subjected slender rod resting on elastic foundation. It was led out squeezed the differential equation of dynamic equilibrium of rod conservative axial strength as well as analysis of solution of this equation was conducted in dependence from mutual reports between his coefficiens. The also exact matrix of stiffness of basic rodelement was led out, and unreeling received matrix in power series in relation to arguments of occurrent in her functions was appointed the matrix of stiffness of element working with part of elastic foundation and solid strength axial.
19
Content available remote Numerical analysis of beams on unilateral elastic foundation
63%
Torbacki W.
Archives of Materials Science and Engineering
|
2008
|
tom Vol. 29, nr 2
109-112
EN
Purpose: The main issue of this paper is to present results of finite element analysis of beams elements on unilateral elastic foundation received with a use of special finite elements of zero thickness designated for foundation modelling. Design/methodology/approach: Computer strength analysis with a use of Finite Element Method (FEM) was carried out. Findings: The paper presents possibilities of special finite elements of zero thickness which enable taking into consideration unilateral contact in construction-foundation interaction as well as an impact of surrounding construction environment to its behaviour. Research limitations/implications: Further researches should concentrate on taking into consideration a multi-layer aspects as well as elasto-plasticity of foundation. Practical implications: Modern engineering construction on elastic foundation analyze require not only standard analysis on Winkler (one parameter) foundation but also calculation of construction on two-parameter foundation which will take into consideration a possibility of loosing contact between construction and foundation (unilateral contact). Originality/value: The paper can be useful for person who performs strength analysis of beams on elastic foundation with a use of finite element method.
20
Content available remote Bending and buckling analysis of FGM plates resting on elastic foundations in hygrothermal environment
63%
Zenkour A. M. , Radwan A. F.
Archives of Civil and Mechanical Engineering
|
2020
|
tom Vol. 20, no. 4
198--220
EN
The present paper deals with the effect of exponential temperature and moisture concentration on the bending and buckling analysis of functionally graded plates resting on two-parameter elastic foundations via a four-variable exponential shear deformation theory. The mechanical properties of the plates are assumed to vary through the thickness. The equations of equilibrium are derived using Hamilton’s principle. The present solutions are derived using Navier’s method. Using Navier’s solution the numerical results are presented and compared well with those available in the literature. Discussions are made to show how the foundation stiffness, hygrothermal loading and other parameters have a significant influence on the bending and buckling analysis of FG plates under hygrothermal and mechanical loading.
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