Numerical Vibration Displacement Solutions of Fractional Drawing Self‐Excited Vibration Model Based on Fractional Legendre Functions

Abstract

In practice, due to the fact that the phenomenon of drawing self-excited vibration can be deemed as one of the hunting phenomena of the mechanical system, this study focuses on investigating the drawing self-excited vibration process through proposing the fractional differential equation model of hunting phenomenon of the mechanical system. The fractional Legendre functions together with their fractional differential operational matrices are used to numerically solve the model. In this way, the numerical solutions of vibration displacement of the model are obtained. At the end, the proposed model and algorithm are proved to be effective via analyzing the numerical results and phase position.

Further results on advanced robust iterative learning control and modeling of robotic systems

“…We will now introduce the fractional generalization of these components of friction, and derive the corresponding generalized dissipative force. Even though this contribution can be implicitly connected with the previous results in the literature describing dissipative forces of fractional order [34][35][36] to the best of the authors' knowledge, there is no model of friction in robotic joints similar to the one proposed here. Hence, in this paper we propose the following modification for F…”

A Dynamic Behavior Analysis of a Rolling Mill’s Main Drive System with Fractional Derivative and Stochastic Disturbance

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