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1
Content available remote Road to chaos in a Duflng oscillator with time delay loop
Borkowski Łukasz
Mechanics and Mechanical Engineering
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2021
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Vol. 25, nr 1
84--87
EN
This article examines a single Duffing oscillator with a time delay loop. The research aims to check the impact of the time delay value on the nature of the solution, in particular the scenario of transition to a chaotic solution. Dynamic tools such as bifurcation diagrams, phase portraits, Poincaré maps, and FFT analysis will be used to evaluate the obtained results.
2
Content available remote A value of damping factor in relation to the dynamic response for a plate structure
Borkowski Łukasz
Mechanics and Mechanical Engineering
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2021
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Vol. 25, nr 1
47--52
EN
The subject of the research is the analysis of the impact of damping value on the dynamic response of plate. The work presents the areas of dynamic stability and instability for the different damping values and compared with the plate without damping. Furthermore, the nature of solution for each analyzed case was presented. Research by using the dynamic tools such as phase portraits, Poincaré maps, FFT analysis, the largest Lyapunov exponents were performed. The compatibility of the selected method of stability analysis with the Volmir criterion was also presented.
3
Content available Vibration and damage detections of composite beams with defects
Manoach E., Mitura A., Samborski S., Warmiński J.
Prace Instytutu Lotnictwa
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2011
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Nr 9 (218)
44-53
EN
In this work, the geometrically nonlinear vibrations of composite beams subjected to harmonic loading and thermal changes are used to study the sensitivity of selected vibration response parameters to the presence of damage (delamination). The damage detection criterion formulated earlier for non-heated plates, based on analysing the points in the Poincaré sections of the damaged and healthy plate, is modified and tested for the case of beams additionally subjected to elevated temperatures. The mportance of the actual temperature in the process of damage detection is shown.
PL
W niniejszej pracy omówiono wykorzystanie drgań nieliniowych belek kompozytowych, poddanych wymuszeniom harmonicznym i obciążeniom cieplnym, do celów wykrywania uszkodzenia (delaminacji). Przestudiowano czułość wybranych parametrów opisujących dynamiczną odpowiedź układu na obecność wady w strukturze. Kryterium uszkodzenia, sformułowane we wcześniejszych pracach autorów dla niepodgrzewanych płyt, oparte na porównywaniu map Poincaré dla płyty zdrowej oraz uszkodzonej, zostało zmodyfikowane i przetestowane na strukturach belkowych. W modelach numerycznych belek zastosowano dodatkowo działanie podwyższonej temperatury. Pokazano w ten sposób istotne znaczenie temperatury na proces wykrywania uszkodzenia. Zaprezentowano także pierwsze wyniki badań doświadczalnych.
4
Content available remote Nonlinear dynamic analysis of a rotor bearing system due to distributed defects using factorial design of experiments
Harsha S. P., Nataraj C.
International Journal of Applied Mechanics and Engineering
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2007
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Vol. 12, no 2
379-399
EN
This paper focuses on accurate performance prediction which is essential to the design of high performance rotor bearing system. It considers distributed defects such as internal radial clearance and surface waviness of the bearing components. In the analytical formulation the contacts between the rolling elements and the races are considered as nonlinear springs, whose stiffnesses are obtained by using Hertzian elastic contact deformation theory. The governing differenlial equations of motion are obtained by using Lagrange's equations. In terms of the feature that the nonlinear bearing forces act on the system, a reduction method and corresponding integration technique is used to increase the numerical stability and decrease computer time for system analysis. Poincare maps are used to elucidate and to iIIustrate the diversity of the system behavior. For investigating the nonlinear behavior of a rotor bearing system, effects of distributed defects are considered simultaneously. lt is shown that the system dynamic behavior is sensitive to small variations of distributed defects.
5
Content available remote Vibrations Induced During a Stability Loss of Periodic Trajectories of the Manipulator
Szumiński P., Kapitaniak T.
Machine Dynamics Problems
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2004
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Vol. 28, No. 2
65-85
EN
We present how to avoid dangerous situations that occur during a robot periodic motion and are caused by different kinds of vibrations. Theoretical analysis of stability regions of nonlinear and linearized system and of the ways of inducing vibrations during a stability loss of periodic trajectories is developed. For practical control of motion a common part of areas of stability received for nonlinear and using linearized Poincare map can be taking into considerations. The areas of stability are identificated by the bifurcation diagrams and Poincare maps. Stability regions of periodic trajectories as a function of varying parameters of the system are investigated . As a practical tool for the control of stability, a spectrum of Lyapunov exponents is proposed. To illustrate our method theoretically and numerically, a model of the RRP-type manipulator has been considered.
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