Nonlinear dynamics of a system of rigid bodies with controlled electromagnetic dampers

Abstract

A nonlinear mathematical model of a system of n rigid bodies undergoing translational vibrations under inertial loading is constructed. The system includes ball supports as a seismic-isolation mechanism and electromagnetic dampers controlled via an inertial feedback channel. A system of differential dynamic equations in normal form describing accelerative damping is derived. The frequencies of small undamped vibrations are calculated. A method for analyzing the dynamic coefficients of rigid bodies subject to accelerative damping is developed. The double phase-frequency resonance of a two-mass system is studied Keywords: mathematical model, system of rigid bodies, electromagnetic damper, seismic-isolation mechanism, feedback, translational acceleration, double phase-frequency resonanceIntroduction. Since the second half of the last century, seismic-isolation mechanisms (SIMs) have been developed and used to mitigate the adverse consequences of major earthquakes [3-7, 16, 17, 21-24]. These mechanisms are designed to weaken the constraint between the structure and the buried portion of its foundation and to intensify the dissipation of seismic energy. Recent developments are models and designs of controlled damping devices with liquid electro-and magneto-rheological materials (suspensions) for SIMs [13][14][15][16][17]. A possible way to improve the dissipative properties of seismic-protection devices is to use frictional electromagnetic dampers without magnetorheological suspensions. Such a damping mechanism for a one-mass system is described in [8,11].In this paper, we model a multimass system of bodies with such a damper in the seismic-isolation mechanism. The SIM includes ball supports and built-in electromagnetic frictional elements, which generate a force resisting the motion of the SIM platform depending on the magnet current. The current in the winding of dampers is controlled by the signal supplied by the feedback loop from the transducers measuring the acceleration of the individual bodies of the system. Acceleration measurement is technically convenient (there is no need for a fixed foundation). By integrating the accelerometer signal, it is possible to control the damping devices by displacement or speed.Feedback control of mechanical systems is an efficient method to improve their dynamic properties [18,19]. Figure 1 shows a system of n rigid bodies with a SIM. This mechanism consists of a lower massive body of mass m 0 with hard flat ferromagnetic surface over which no less than three non-aligned ball supports K s , s = 1 2 , ,…, of radius r can roll. The AS is a system that measures, integrates, and amplifies the signals of the accelerometers mounted on the supported rigid bodies. Design Model of Tandem Rigid Bodies with Ball-Shaped Seismic-Isolation Mechanism and Controlled Electromagnetic Dampers.The upper part of the mechanism includes a body of mass m 1 with semispherical depressions of radius R r >> . The ball

Dynamics of vibration isolation system with a quasi-isochronous roller shock absorber

“…This kinematic constraint shows that the parameters R and r are limited only by the trivial condition R r , > 0. This distinguishes the brachistochrone-shaped surface from that considered in [18,[33][34][35].…”

“…(4), (5) will remain structurally invariant. A similar problem with a braked roller and spherical working surfaces was addressed in [18,[33][34][35].…”