Wyniki wyszukiwania - BazTech

1

Wybrane aspekty analizy danych pomiarowych złożonego systemu energetycznego pod kątem zachowań chaotycznych

Jankowski P.

Zeszyty Naukowe Akademii Morskiej w Gdyni

|

2018

|

nr 103

107--119

PL

W artykule przedstawiono przykład zachowania chaotycznego w wybranym fragmencie sieci elektroenergetycznej zamodelowanej nieliniowym układem równań różniczkowych. Artykuł omawia najistotniejsze aspekty identyfikacji zachowań chaotycznych w systemie na podstawie zarejestrowanego przebiegu czasowego tylko jednej zmiennej stanu bez znajomości wymiaru rzeczywistej przestrzeni fazowej.

EN

The article presents an example of chaotic behavior in a selected piece of the power network modeled by nonlinear system of differential equations. This article also discusses the most important aspects of identifying chaotic behavior in a system, based on only the recorded time course of one state variable without knowing the real dimension of the phase space.

2

MATHEMATICA i mapy Poincaré

Szcześniak W., Ataman M.

Autobusy : technika, eksploatacja, systemy transportowe

|

2016

|

R. 17, nr 6

696--699

PL

W pracy przedstawiono zastosowanie pakietu Wolframa MATHEMATICA do interpretacji graficznej wyników rozwiązań nieliniowych równań ruchu. Analizowano drgania nieliniowe wahadła eliptycznego (rys. 1) oraz drgania nieliniowe wahadła Moone’a (rys. 9). Na podstawie rozwiązań numerycznych równań ruchu obu wahadeł wykonano portrety fazowe oraz mapy Poincaré. Mapy Poincaré (atraktory) wykonano stosując instrukcję „Reap...NDSolve…WhenEvent…Sow”, która jest dostępna w pakiecie MATHEMATICA, począwszy od wersji 9.

EN

The paper presents application of Wolfram MATHEMATICA 10forgraphical interpretation of results of solutions of nonlinear equations of motion. Nonlinear vibrations of elliptic pendulum (Fig.1) and nonlinear vibrations of Moone's pendulum (Fig.9) are analysed in the paper. On the basis of numerical solutions of equations of motion of both pendulums, phase portraits and Poincaré maps (attractors) were made. Poincaré maps were performed using the instructions „Reap...NDSolve…WhenEvent…Sow”. The instruction is available in MATHEMATICA 9 and later versions.

3

Dynamice of three unidirectionally coupled Duffing oscillators

Borkowski Ł.

Mechanics and Mechanical Engineering

|

2011

|

Vol. 15, nr 2

125-132

EN

This article presents a system of three unidirectionally coupled Duffing oscillators. On the basic of numerical study we show the mechanism of translation from steady state to chaotic and hyperchaotic behavior. Additionally, the impact of parameter changes on the behavior of the system will be presented. Confirmation of our results are bifurcation diagrams, timelines, phase portraits, Poincare maps and largest Lyapunov exponent diagrams.

4

Nonlinear dynamic behaviors of high speed rotor supported by rolling element bearings

Harsha S. P., Prakash R., Sandeep K.

International Journal of Applied Mechanics and Engineering

|

2003

|

Vol. 8, no 4

705-720

EN

The paper presents a model for investigating structural vibrations in rolling element bearings. The mathematical formulation accounted for tangential motions of rolling elements as well as inner and outer races with the sources of nonlinearity such as the Hertzian contact force, surface waviness and internal radial clearance transition resulting from no contact to contact state between rolling elements and the races. The contacts between the rollers and races are treated as nonlinear springs and the springs act only in compression to simulate the contact deformation and resulting force. The nonlinear stiffness is obtained by using the equations for the Hertzian elastic contact deformation theory. As the nonlinear bearing forces act on the system, a new reduction method and corresponding integration technique is proposed to increase the numerical stability and decrease computer time for system analysis. The effects of various defects of a rotor bearing system in which the rolling element bearings show the periodic, quasi-periodic and chaotic behavior are analyzed. Poincare maps and Fourier spectra are used to elucidate and to illustrate the diversity of the system behavior. It is shown that due to defects such as surface waviness and internal radial clearance the system exhibits an undesirable jump phenomenon with quasi-periodic, subharmonic and chaotic motions.