Novel bursting dynamics and the mechanism analysis in a mechanical oscillator

Novel bursting dynamics and the mechanism analysis in a mechanical oscillator
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DOI：
10.1007/s11071-022-07520-5
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发表时间：
2022-05
期刊：
Nonlinear Dynamics
影响因子：
5.6
通讯作者：
Xindong Ma;Heqi Zhao;Qinsheng Bi
Xindong Ma;Heqi Zhao;Qinsheng Bi
中科院分区：
工程技术2区
文献类型：
--
作者：
Xindong Ma;Heqi Zhao;Qinsheng Bi

文献摘要

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研究了机械振子在参数激励和外部强迫激励下的复杂爆发动力学。当强迫项的频率远小于振子的固有频率时，激励可表示为慢变变量，振子可视为光滑自治系统。一个新的路线，称为脉冲状爆炸（PSE）的突发动力学，然后提出。PSE由与系统参数的变换相对应的脉冲形状信号的数量的急剧变化来表示。基于慢-快分析方法，分析了4种PSE型突发动力学：通过PSE/PSE迟滞环的“supHopf/supHopf”型突发动力学、通过PSE/PSE迟滞环的“supHopf/supHopf-PSE/supHopf”型突发动力学、通过PSE/PSE迟滞环的“supHopf/supHopf-PSE/PSE”型突发动力学和通过PSE/PSE迟滞环的“PSE/PSE-PSE/PSE”型突发动力学。此外，还研究了两种非PSE型的爆发动力学：“supHopf/supHopf”型的爆发动力学和“supHopf/supHopf-supHopf/supHopf”型的爆发动力学.我们的结果加强了对PSE型爆发振荡的理解，丰富了复杂爆发行为的可能途径。
The complex bursting dynamics of a mechanical oscillator under parametric and external forced excitations are investigated. When the frequencies of the forcing terms are much smaller than the natural frequency of the oscillator, excitations can be expressed as slow-varying variables and the oscillator is regarded as a smooth autonomous system. A new route to bursting dynamics called the pulse-shaped explosion (PSE) is then proposed. PSE is represented by a sharp change in the number of pulse-shaped signals corresponding to the transformation of system parameters. Four PSE-type bursting dynamics are analyzed based on the slow-fast analysis method: bursting dynamics of “supHopf/supHopf” form via “PSE/PSE” hysteresis loop, bursting dynamics of “supHopf/supHopf-PSE/supHopf” form via “PSE/PSE” hysteresis loop, bursting dynamics of “supHopf/supHopf-PSE/PSE” form via “PSE/PSE” hysteresis loop and bursting dynamics of “PSE/PSE-PSE/PSE” form via “PSE/PSE” hysteresis loop. In addition, two non-PSE-type bursting dynamics are also investigated: bursting dynamics of “supHopf/supHopf” form and bursting dynamics of “supHopf/supHopf-supHopf/supHopf” form. Our results strengthen the understanding of the PSE-type bursting oscillations and enrich the possible routes to complex bursting behaviors.