PL
 |
EN
Preferencje help
Polish version English version Język
Widoczny [Schowaj] Abstrakt
Liczba wyników

Znaleziono wyników: 10

Liczba wyników na stronie
first rewind previous Strona / 1 next fast forward last
Wyniki wyszukiwania
Wyszukiwano:
w słowach kluczowych:  slender systems
help Sortuj według:

help Ogranicz wyniki do:
first rewind previous Strona / 1 next fast forward last
1
Content available Analiza drgań poprzecznych smukłej kolumny o zmiennym przekroju poprzecznym przy obciążeniu uogólnionym z siłą skierowaną do bieguna dodatniego
Szmidla J., Jurczyńska A.
Czasopismo Inżynierii Lądowej, Środowiska i Architektury / Journal of Civil Engineering, Environment and Architecture
|
2017
|
z. 64, nr 2/I
191--202
PL
W pracy zawarto wyniki rozważań teoretycznych oraz analizę numeryczną zagadnienia drgań swobodnych smukłego układu o zmiennym przekroju poprzecznym poddanego działaniu wybranego przypadku obciążenia swoistego. Analizowane obciążenie uogólnione z siłą skierowaną do bieguna dodatniego realizowane jest poprzez strukturę zbudowaną z głowic z zarysie kołowym: wywołującą i przejmującą obciążenie. W celu zamodelowania niepryzmatyczności kolumny, układ podzielono na n pryzmatycznych segmentów o równej długości i grubości oraz zmiennej szerokości opisanej za pomocą funkcji liniowej oraz wielomianu drugiego stopnia, przy zachowaniu warunku stałej objętości sumarycznej. W oparciu o model fizyczny układu zdefiniowano zależności określające energię mechaniczną struktury. Problem sformułowano na podstawie zasady Hamiltona (metoda drgań, kinetyczne kryterium utraty stateczności). Biorąc pod uwagę geometryczne warunki brzegowe oraz geometryczne warunki ciągłości wyznaczono różniczkowe równania ruchu poszczególnych segmentów kolumny oraz brakujące do opisu układu naturalne warunki brzegowe i naturalne warunki ciągłości. W oparciu o tak zdefiniowany model matematyczny opracowano autorskie algorytmy obliczeniowe umożliwiające badania numeryczne drgań poprzecznych układu. W ramach przeprowadzonych obliczeń określono zakres zmian częstości drgań własnych w funkcji obciążenia zewnętrznego. Dyskusji poddano wpływ zmiennych parametrów geometrycznych kolumny na wartość częstości drgań oraz typ układu, uwzględniając parametry określające kształt kolumny oraz geometrię struktury realizującej obciążenie.
EN
The results of the theoretical considerations and numerical analysis of the issue of the free vibration of the slender system of the variable cross-section under selected case of the specific load were included in this work. Analyzed generalized load with a force directed towards the positive pole is realized by the structure built of heads of the circular outlines: loading and receiving heads. In order to model the variable cross-section of the column, the system was divided into n prismatic segments of the equal length and thickness and the variable width described by the linear function and the polynomial of degree 2, fulfilling the condition of the constant total volume. On the basis of the physical model of the system, the mechanical energy of the structure was defined. The issue of the free vibration was formulated taking into account the Hamilton’s principle (energetic method, kinetic criterion of the stability loss). Taking into consideration the geometric boundary conditions and the geometric continuity conditions, the differential equations of motion of particular segments of the column as well as the natural boundary condition and the natural continuity conditions were determined. On the basis of so-defined mathematical model, the computation algorithms enabling numerical examination of the transverse vibration of the column were developed. Within the scope of the carried-out calculations, the range of the changes in the frequency of the free vibration as a function of the external load was determined. An influence of the variable geometric parameters of the column on the value of the natural frequency and the type of the system was discussed, including the parameters describing the shape of the column as well as the geometry of the loading structure.
2
Content available Free vibrations of non-prismatic slender system subjected to the follower force directed towards the positive pole
Szmidla J., Jurczyńska A.
Vibrations in Physical Systems
|
2016
|
Vol. 27
365--368
EN
The paper contains the results of theoretical and numerical studies within the scope of kinetic criterion of stability loss of slender non-prismatic column subjected to the follower force directed towards the positive pole (the case of specific load). Shape of the system approximation by a linear function and polynomial of degree 2 was considered. On the basis of the Bernoulli – Euler’s theory, the mechanical energy was defined. The differential equations of motion and natural boundary conditions were determined according to the Hamilton’s principle. The issue of free vibrations was solved using the small parameter method. Within the range of numerical calculations, the changes in the eigenvalues were presented as a function of external load with variable geometrical parameters of the system, including parameters resulting from the shape approximation and parameters of loading structure.
3
Content available Free vibrations of geometrically nonlinear column locally resting on the winkler elastic foundation under the specific load
Szmidla J., Cieślińska-Gąsior I.
Vibrations in Physical Systems
|
2016
|
Vol. 27
355--362
EN
The results of theoretical and numerical studies concerning continuous system subjected to the follower force directed towards the positive pole, locally resting on Winkler elastic foundation are presented in this paper. The load by follower force directed towards the positive pole is guaranteed by loading structure built of loading and receiving heads made of elements of circular outlines. Abovementioned heads are real constructions, used in experimental research of continuous systems. Taking into account total mechanical energy of the system, the Hamilton’s principle and the small parameter method, the differential equations of motion and boundary conditions of the considered column were determined. On the basis of a solution of the issue of dynamics of the system, an appropriate formulas were formulated and then the trajectory of curves on the plane frequency of free vibrations – the value of external load were calculated taking into considerations physical and geometrical parameters of the structure, including parameter of loading head and parameters describing Winkler elastic foundation.
4
Content available remote Local and Global Instability of the Slender Geometrically Nonlinear SystemWith Non-Prismatic Element Subjected to the Euler’s Load
Szmidla J., Skrzypczak T., Jurczyńska A.
Machine Dynamics Research
|
2016
|
Vol. 40, No. 4
79--88
EN
A theoretical considerations and numerical calculations concerning the issue of the stability of the geometrically nonlinear system with non-prismatic element are presented in this work. The analysed columns were subjected to the Euler’s load. On the basis of the minimum potential energy principle as well as the small parameter method, the differential equations of displacements were formulated and its solutions were obtained. The assumption that the approximation of the non-prismatic rod satisfies the condition of constant total volume resulting from the value of the coefficient of flexural stiffness distribution has been made. The results of the carried out numerical simulations refer to the local and global stability loss. It has been proved that taking into consideration in the geometrically nonlinear system appropriate shaped rod of variable cross-section causes an increase in the value of bifurcation load and in a consequence an „exit” from the area of the local instability (loss of rectilinear form of static equilibrium).
5
Content available remote Free Vibrations of the Slender Non-Prismatic Column Under the Specific Load Regarding the Joint Flexibility
Szmidla J., Jurczyńska A.
Machine Dynamics Research
|
2016
|
Vol. 40, No. 3
79--89
EN
The issue of the free vibrations of the non-prismatic rod subjected to the selected case of the specific load has been studied. In the carried out simulations, a flexibility of a constructional joints modelled by the translational and rotational springs at the point of mounting or on the free end of analysed system was taken into account. The shape of rod was approximated by linear function and by polynomial of degree 2, under the condition of constant volume of the column. After prior definition of total mechanical energy, a differential equations of motion as well as a boundary conditions were formulated on the basis of the Hamilton’s principle. The results of the numerical calculations refer to an influence of variable cross-section of the rod, joint flexibility and a geometry of a loading structure on the value of the frequency of free vibrations due to the external load (a characteristic curves) and on the critical load.
6
Content available Numerical studies on stability of slender supporting structures
Sokół K., Uzny S.
Journal of Applied Mathematics and Computational Mechanics
|
2016
|
Vol. 15, nr 2
157--165
EN
In this paper the results of studies on stability of the geometrically non-linear column (slender system) composed of two rods have been presented. The supporting structure has a defect in the form of cracks which are present in each of rods. The cracks are simulated by means of rotational springs. On the basis of the total potential energy principle, the boundary problem is being formulated. The results show an influence of the crack size on the stability of the column in particular on bifurcation load magnitude.
7
Content available An influence of the geometrical nonlinearity of a frame column of flat frame type Γ subjected to the follower force directed towards the positive pole on its stability
Szmidla J., Wiktorowicz J.
Journal of Applied Mathematics and Computational Mechanics
|
2016
|
Vol. 15, nr 3
155--165
EN
The results of the theoretical and numerical research for the purpose of designation of local and global instability areas of a rectangular frame with a geometrically nonlinear frame column subjected to the follower force directed towards the positive pole are presented in this work. Taking into consideration the total potential energy of an analysed system, the equations describing transverse and longitudinal movements and the boundary conditions necessary for the problem solution are formulated. On the basis of the static criterion of the loss of stability, the influences of the variable flexural stiffness of the system and the geometrical and physical parameters of the flat frame on the value of the bifurcation load are obtained. The results of numerical computations are compared with appropriate values of critical load of the comparative system.
8
Content available remote An Influence of Cracks Location on Instability of a Multi-Member Cantilever Slender Supporting System
Sokół K., Uzny S.
Machine Dynamics Research
|
2015
|
Vol. 39, No. 3
59-68
EN
In this publication the nonlinear slender cantilever column composed of two rods in which the cracks are present is investigated. The cracks are simulated by means of rotational springs with linear characteristic. Additionally the external compressive load is located at the free end to the structure. In order to predict the static behaviour of the column the boundary problem is being formulated by means of the principle of total potential energy. The results of numerical simulations are concern on influence of the locations of cracks on loading capacity. On the basis of the analysis of the results the most dangerous (lowest loading capacity) regions are found.
9
Stabilizacja położenia ładunku w warunkach falowania morskiego
Adamiec-Wójcik I., Drąg Ł.
Logistyka
|
2015
|
nr 4
2216--2224, CD2
PL
Artykuł przedstawia rozwiązanie problemu realizacji zadanej trajektorii masy skupionej zawieszonej na linie i zanurzonej w wodzie niezależnie od ruchów poziomych i pionowych statku wywołanych falowaniem morza. Lina jest przykładem układu wiotkiego. Do dyskretyzacji zastosowano zmodyfikowaną metodę sztywnych elementów skończonych. W tym podejściu współrzędne uogólnione elementów skończonych opisują pozycję środka ciężkości oraz kąt nachylenia osi elementu względem układu inercjalnego. Wzajemne położenie elementów opisują równania więzów geometrycznych. Uwzględniono podatność giętną liny oraz oddziaływanie środowiska wodnego. Uzyskano efektywny numerycznie model pozwalający na rozwiązanie zadania optymalizacji dynamicznej. Zmiennymi decyzyjnymi były wartości przemieszczenia liny nawijanej na bęben wciągarki. Pokazano wpływ liczby punktów, na które dzielono przedział czasu symulacji na realizowaną trajektorię oraz na czas i błąd obliczeń. Analizowano również wpływ prędkości ruchu poziomego statku oraz wartości masy skupionej zawieszonej na linie na wyniki obliczeń.
EN
The paper presents a solution to the problem of trajectory realisation by the payload suspended on a rope submerged in water despite vertical motion of a vessel caused by the wavy sea. The rope is an example of a slender system. It is discretised by means of a modified rigid finite element method. In this approach the coordinates of the center of the mass and the angle of inclination of the element axis with respect to the inertial coordinate system are generalised coordinates of the element. Reciprocal position of elements is defined by means of geometrical constraint equations. Bending flexibility and hydrodynamic forces are taken into account. Due to the numerical effectiveness of the method it can be used for the solution of dynamic optimization problems. The optimization problem presented in the paper is the stabilization of a payload (realization of a given trajectory) despite the motion caused by sea waves and movement of a vessel. Hydrodynamic forces cause the deviation of the payload from its trajectory due to the large deflections and the constant length of the rope. It is shown that the number of points into which the time interval is divided has a significant influence of time and error of calculations. The influence of the velocity of the vessel and the lumped mass at the end of the rope on the displacement of the end of the rope is also discussed.
10
Content available An influence of the Winkler elastic foundation of a geometrically nonlinear column loaded by force directed towards the positive pole on a type of system
Jurczyńska A., Szmidla J.
Journal of Applied Mathematics and Computational Mechanics
|
2015
|
Vol. 14, nr 4
79--91
EN
Depending on the mutual relation between external load, tendon’s length parameter resulting from the direction of loading force and the free vibration frequency parameter, the slope of characteristic curves of a considered column subjected to force directed towards the positive pole can take the negative, zero and positive value. The purpose of this paper is to determine the criterion that allows for classification of an analysed structure to divergent or divergent pseudo-fluttering type of system. On the basis of obtained formulas, the ranges of parameters describing the Winkler elastic foundation for which the considered system may be classified as one of the abovementioned types were determined.
first rewind previous Strona / 1 next fast forward last
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.