Magnetorheological damping and semi-active control of an autoparametric vibration absorber

Meccanica, Aug 2014

A numerical study of an application of magnetorheological (MR) damper for semi-active control is presented in this paper. The damper is mounted in the suspension of a Duffing oscillator with an attached pendulum. The MR damper with properties modelled by a hysteretic loop, is applied in order to control of the system response. Two methods for the dynamics control in the closed-loop algorithm based on the amplitude and velocity of the pendulum and the impulse on–off activation of MR damper are proposed. These concepts allow the system maintaining on a desirable attractor or, if necessary, to change a position from one attractor to another. Additionally, the detailed bifurcation analysis of the influence of MR damping on the number of periodic solutions and their stability is shown by continuation method. The influence of MR damping on the chaotic behavior is studied, as well.

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Magnetorheological damping and semi-active control of an autoparametric vibration absorber

Krzysztof Kecik 0 1 Andrzej Mitura 0 1 Danuta Sado 0 1 Jerzy Warminski 0 1 0 D. Sado Institute of Machine Design Fundamentals, Warsaw University of Technology , Warsaw, Poland 1 K. Kecik (&) A. Mitura J. Warminski Department of Applied Mechanics, Lublin University of Technology , Lublin, Poland A numerical study of an application of magnetorheological (MR) damper for semi-active control is presented in this paper. The damper is mounted in the suspension of a Duffing oscillator with an attached pendulum. The MR damper with properties modelled by a hysteretic loop, is applied in order to control of the system response. Two methods for the dynamics control in the closed-loop algorithm based on the amplitude and velocity of the pendulum and the impulse on-off activation of MR damper are proposed. These concepts allow the system maintaining on a desirable attractor or, if necessary, to change a position from one attractor to another. Additionally, the detailed bifurcation analysis of the influence of MR damping on the number of periodic solutions and their stability is shown by continuation method. The influence of MR damping on the chaotic behavior is studied, as well. 1 Introduction Pendulum-like systems are commonly used in many practical applications, including special dynamical dampers or energy harvesters [1]. Dynamics of such systems can exhibit extremely complex behaviour. Especially, if the system is nonlinear and includes the inertial coupling, among strange attractors, multiple regular attractors may co-exist for some values of system parameters [2]. The presence of the coupling terms can lead to a certain type of instability which is referred to as autoparametric resonance. This kind of phenomenon takes place when the external resonance and the internal resonance meet themselves, due to the coupling terms. The multiple solutions, evolution of the solution due to variations in parameters or initial conditions play a very important role in system dynamics. The small perturbation of initial conditions or systems parameters may transit the response to dangerous motion, like a full rotation of the pendulum or chaotic motion [3]. This problem is essential if the pendulum plays role of a dynamical vibration absorber or the energy harvesting device [4]. An autoparametric system has been intensively analysed for three last decades. The different responses in the autoparametric pendulum vibration absorber for a linear mass-spring damper system have been studied by the harmonic balance method in Hatwal et al. [5]. A nonlinear frequency analysis using the multiple scales method has been presented in Cartmell et al. [6, 7]. The two mode autoparametric interaction and robustness, against variations on the excitation frequency, are improved on the overall system by direct application of an onoff servomechanism, controlling the effective pendulum length and validating also the theoretical results in an experimental setup. A similar pendulum dynamic vibration absorber, with time delay in the internal feedback force, is used to illustrate the realtime application of a dynamic substructuring technique in Kyrichko et al. [8] and in paper [9]. In this paper authors propose application of the MR damper, installed between the oscillator and the ground to provide controllable damping for the system. The model of a damper takes into account the hysteretic effect. The closed-loop control algorithms offer possibility to move the system between selected stable solutions. Moreover, we show, that MR damping practically does not reduce the vibration suppression effect and MR damping can cause a shift of chaotic regions. 2 An autoparametric pendulum system 2.1 Model of magnetorheological damper (MRD) The magnetorheological devices provide modern and elegant solutions for semi-active control in a variety of applications, offering several advantages: simplicity of a structure, small number of mobile components, noise-free fast operation and low power demands. The MRD is a nonlinear component with dissipative capability used in the control of semi-active suspensions, where the damping coefficient varies according to the applied electric current. MR damper is usually characterized by the displacement and/or velocity of the piston, the electric current applied to the coil as inputs and the force generated on the piston as output. The relationship between damping force and velocity shows hysteresis loops whose shapes vary according to the applied current. Hysteresis in dampers is due to the difference between the accelerating and decelerating paths of the force-velocity curve [10], thus imposing a delay in the changes of internal pressures and ultimately forces. Therefore, we propose the nonlinear MR damping force (FMR) approximated by a hyperbolic tangential function of the velocity and the displacement of the oscillator based on the papers [11, 12]. In terms of mathematical expressions, the model makes use of a hyperbolic tange (...truncated)


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Krzysztof Kecik, Andrzej Mitura, Danuta Sado, Jerzy Warminski. Magnetorheological damping and semi-active control of an autoparametric vibration absorber, Meccanica, 2014, pp. 1887-1900, Volume 49, Issue 8, DOI: 10.1007/s11012-014-9892-2