On nonlinear dynamic of a non-ideal Duffing system with fractional damping

J M Balthazar,C Oliveira,G Litak,A Nabarrete,V Piccirillo,A M Tusset,M Belhaq

doi:10.1051/matecconf/20168301002

Abstract

Fractional damping is appearing in different contexts in any systems with memory and hysteresis. Such damping is defined by a fractional derivative term, in contrary to classical viscous damping which takes into account the first order derivative. In this work, we characterize the nonlinear dynamics of a non-ideal Duffing system, with fractional damping using nonlinear dynamical tools. The non-ideal excitation originates from a DC electric motor with limited power supply driving an unbalanced rotating mass. The response of the system is investigated with the voltage as a control parameter. Numerical simulations show the occurrence of regular and non-regular motions, which are investigated via bifurcation diagramoccurrence diagrams and phase plane portraits.

Highlights

The study of problems that involve the coupling of several systems was explored widely in the last years in function of the change of constructive characteristics of the machines and structures
Some phenomena are observed in dynamical systems composed by supporting structures and rotating machines, where the unbalancing of the rotating parts is the main cause of vibrations
The idea in this work is study the nonlinear dynamic of a non-ideal Duffing system with fractional damping

Summary

Introduction

The study of problems that involve the coupling of several systems was explored widely in the last years in function of the change of constructive characteristics of the machines and structures. In this way, some phenomena are observed in dynamical systems composed by supporting structures and rotating machines, where the unbalancing of the rotating parts is the main cause of vibrations. The idea in this work is study the nonlinear dynamic of a non-ideal Duffing system with fractional damping. The vibrating system under consideration consists of a main structure of mass m1 , constrained by a linearly viscous element with damping coefficient μ and a pseudoelastic SMD.

System description and governing equations

Numerical Results

Conclusions