The saddle case of a nonsmooth Rayleigh–Duffing oscillator

Release time:2020-12-16

DOI number:10.1016/j.ijnonlinmec.2020.103657

Journal:International Journal of Non-Linear Mechanics

Abstract:We consider a single degree freedom oscillator in order to accurately represent some modeling with ship roll damping. The proposed oscillator is a nonsmooth Rayleigh–Duffing equation 𝑥̈ + 𝑎𝑥̇ + 𝑏𝑥̇ |𝑥̇ | + 𝑐𝑥 + 𝑑𝑥3 = 0. The main goal of this paper is to study the global dynamics of the nonsmooth Rayleigh–Duffing oscillator in the case 𝑑 < 0, i.e., the saddle case. The nonsmooth Rayleigh–Duffing oscillator is only 𝐶1 so that many classical theory cannot be applied directly. In order to see the tendency of evolutions in a large range, we study not only its finite equilibria but also the equilibria at infinity. We find necessary and sufficient conditions for existence of limit cycles and heteroclinic loops respectively. Finally, we give the complete global bifurcation diagram and classify all global phase portraits in the Poincaré disc in global parameters.

First Author:Wang Zhaoxia

Indexed by:Journal paper

Correspondence Author:Chen Hebai*

Document Code:103657

Discipline:Engineering

First-Level Discipline:Mechanics

Document Type:J

Volume:129

Translation or Not:no

Date of Publication:2020-12-01

Included Journals:SCI