A Non-linear Model of Rubber Shear Springs Validated by Experiments

Vibrating flip-flow screens provide an effective solution for screening highly viscous or fine materials. However, only linear theory has been applied to their design. Yet, to understand deficiencies and to improve performance an accurate model especially of the rubber shear springs equipped in screen frames is critical for its dynamics to predict, e.g. frequency- and amplitude-dependent behaviour. In this chapter, the amplitude dependency of the rubber shear spring is represented by employing a friction model in which parameters are fitted to an affine function rather constant values used for the classic Berg’s friction model; the fractional derivative model is used to describe its frequency dependency and compared to conventional dashpot and Maxwell models with its elasticity being represented by a non-linear spring. The experimentally validated results indicate that the proposed model with a non-linear spring, friction and fractional derivative model is able to more accurately describe the dynamic characteristics of a rubber shear spring compared with other models

Fractional calculus: application in modelling and control

This contribution introduces the fractional calculus (FC) fundamental mathematical aspects and discuses some of their consequences. Based on the FC concepts, the chapter reviews the main approaches for implementing fractional operators and discusses the adoption of FC in control systems. Finally are presented some applications in the areas of modeling and control, namely fractional PID, heat diffusion systems, electromagnetism, fractional electrical impedances, evolutionary algorithms, robotics, and nonlinear system control