The saddle case of a nonsmooth Rayleigh–Duffing oscillator
发布时间：2020-12-16
点击次数：
DOI码：10.1016/j.ijnonlinmec.2020.103657
发表刊物：International Journal of Non-Linear Mechanics
摘要：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.
第一作者：Wang Zhaoxia
论文类型：期刊论文
通讯作者：Chen Hebai*
论文编号：103657
学科门类：工学
一级学科：力学
文献类型：J
卷号：129
是否译文：否
发表时间：2020-12-01
收录刊物：SCI