Effects of damping on the dynamics of an electromechanical system consisting of mechanical network of discontinuous coupled system oscillators with irrational nonlinearities: Application to sand sieves

Abstract

The electromechanical system consisting of an electrical part which is the forced Vander Pol oscillator coupled magnetically to a mechanical part is investigated. The mechanical part is the network consisting of discontinuous elastically coupled system oscillators with strong irrational nonlinearities in which the damping is introduced. This coupled electromechanical system is connected at the output to movable sieve for the industrial applications, it can be used for the filtering of different types of building materials. By using then the Newton’s second law and Kirchhoff’s law, the set of model damped equations governing the dynamics of the system are established. These set of equations have strong irrational nonlinearities, with smooth or discontinuous characteristics depending just to the inclination angles of strings. Then the resonance phenomenon showing the appearing of hysteresis as the frequency shift increases is found and is more and more complex as the cell number increases. By solving numerically the set of equations of the system, one obtains the oscillatory bursting in the electrical part, and impulse bursting in the mechanical part, with their widths which decrease as the excitation frequency increases. It is also found that chaotic bursting appears in the mechanical part when the electric part exhibits periodic bursting oscillations.