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1

Vibration Control of Autoparametric System Using MR Dampers in the Pendula Joints

Sado D., Pietrzakowski M.

Machine Dynamics Research

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2013

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Vol. 37, No. 4

97-107

EN

In this paper a three-degree of freedom autoparametric system with a double pendulum including the magnetorheological (MR) dampers in the pendula joints is investigated numerically. The system consists of the two coupled pendula hangs down from the oscillator. Near the resonance regions except multiperiodic and quasiperiodic vibration, also chaotic motion may appear. For characterising a chaotic response the bifurcation diagrams, Poincaré maps and maximal exponent of Lyapunov for different magnetorheological damping parameters are constructed. The influence of damping moment in the pendula joins (described by Bingham’s model) on the phenomenon of energy transfer can be modified by magnetic field. Results show that MR dampers can be used to change the dynamic behavior of the autoparametric system giving semiactive control possibilities.

2

On the analytical solution for the slewing flexible beam-like system: analysis of the linear part of the perturbed problem

Fenili A., Balthazar J. M.

Journal of Theoretical and Applied Mechanics

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2008

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Vol. 46 nr 1

51-68

EN

The dynamical system investigated in this work is a nonlinear flexible beam-like structure in slewing motion. Non-dimensional and perturbed governing equations of motion are presented. The analytical solution for the linear part of these perturbed equations for ideal and for non-ideal cases are obtained. This solution is necessary for the investigation of the complete weak nonlinear problem where all nonlinearities are small perturbations around a linear known solution. This investigation shall help the analyst in the modelling of dynamical systems with structure-actuator interactions.

PL

Układem dynamicznym badanym w pracy jest podzespół zawierający podatną belkę poruszającą się ruchem obrotowym w płaszczyźnie poziomej. Zaprezentowano bezwymiarowe i perturbowane równania ruchu. Rozwiązania analityczne części zlinearyzowanej tych równań uzyskano dla przypadku idealnego i nieidealnego. Taka postać rozwiązania jest niezbędna do analizy zupełnego i słabo nieliniowego problemu, w którym nieliniowości stanowią niewielkie perturbacje wokół rozwiązania liniowego. Prezentowane wyniki badań mogą okazać się pomocą dla analityków zajmujących się modelowaniem układów dynamicznych uwzględniających interakcje zachodzące pomiędzy daną konstrukcją bazową, a zamocowanymi na niej aktywnymi elementami wykonawczymi (aktuatorami).

3

Influence of an Energy Source on Regular and Chaotic Vibrations of Coupled Nonlinear Oscillators

Warmiński J.

Machine Dynamics Problems

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2007

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Vol. 31, No. 1

101-119

EN

Regular and chaotic vibrations of the system composed of two parametrically and self-excited oscillators are analysed in the paper. The considered system is excited by a non-ideal energy source represented by DC motor with limited power supply. Interactions between different vibration types, bifurcation and the synchronisation regions are found by analytical and numerical methods. Influence of the most important parameters on transition through resonance areas is presented. Possible chaotic motions are determined by Lyapunov exponent criterion.