Nonlinear Resonance Response of Suspended Cables Under Multi-Frequency Excitations and Time-Delayed Feedback

IF 2.7 3区工程技术 Q3 MATERIALS SCIENCE, MULTIDISCIPLINARY

Acta Mechanica Solida Sinica Pub Date : 2024-11-29 DOI:10.1007/s10338-024-00555-8

Jian Peng, Hui Xia, Lianhua Wang, Xiaoyu Zhang, Xianzhong Xie

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Abstract

This study investigates the nonlinear resonance responses of suspended cables subjected to multi-frequency excitations and time-delayed feedback. Two specific combinations and simultaneous resonances are selected for detailed examination. Initially, utilizing Hamilton’s variational principle, a nonlinear vibration control model of suspended cables under multi-frequency excitations and longitudinal time-delayed velocity feedback is developed, and the Galerkin method is employed to obtain the discrete model. Subsequently, focusing solely on single-mode discretization, analytical solutions for the two simultaneous resonances are derived using the method of multiple scales. The frequency response equations are derived, and the stability analysis is presented for two simultaneous resonance cases. The results demonstrate that suspended cables exhibit complex nonlinearity under multi-frequency excitations. Multiple solutions under multi-frequency excitation can be distinguished through the frequency–response and the detuning-phase curves. By adjusting the control gain and time delay, the resonance range, response amplitude, and phase of suspended cables can be modified.

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多频激励和时滞反馈下悬索的非线性共振响应

研究了悬索在多频激励和时滞反馈作用下的非线性共振响应。选择两种特定的组合和同时共振进行详细检查。首先，利用Hamilton变分原理，建立了多频激励和纵向时滞速度反馈作用下悬索非线性振动控制模型，并采用伽辽金方法得到离散模型。随后，仅关注单模离散化，采用多尺度方法推导了两个同时共振的解析解。推导了频率响应方程，并对两种同步谐振情况进行了稳定性分析。结果表明，悬索在多频激励下表现出复杂的非线性特性。通过频率响应和失谐相位曲线可以区分多频激励下的多个解。通过调节控制增益和延时，可以改变悬索的谐振范围、响应幅度和相位。

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来源期刊

Acta Mechanica Solida Sinica 物理-材料科学：综合

CiteScore

3.80

自引率

9.10%

发文量

1088

审稿时长

9 months

期刊介绍： Acta Mechanica Solida Sinica aims to become the best journal of solid mechanics in China and a worldwide well-known one in the field of mechanics, by providing original, perspective and even breakthrough theories and methods for the research on solid mechanics. The Journal is devoted to the publication of research papers in English in all fields of solid-state mechanics and its related disciplines in science, technology and engineering, with a balanced coverage on analytical, experimental, numerical and applied investigations. Articles, Short Communications, Discussions on previously published papers, and invitation-based Reviews are published bimonthly. The maximum length of an article is 30 pages, including equations, figures and tables