Synchronous patterns in two pendula suspended on multi degrees of freedom support

IF 4.3 2区工程技术 Q1 ACOUSTICS

Journal of Sound and Vibration Pub Date : 2025-05-09 DOI:10.1016/j.jsv.2025.119159

Dawid Dudkowski, Barbara Błażejczyk–Okolewska, Tomasz Kapitaniak

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引用次数: 0

Abstract

We investigate the dynamics and possible synchronization scenarios of two pendula suspended on 3 DOF (three degrees of freedom) beam. The base has been equipped with supporting springs, allowing it to perform both translational and rotary oscillations (full plane motion). Depending on the parameters of the model, we have determined different regions of classical synchronous patterns, as well as uncovered more complex scenarios, including irregular motion and quasiperiodic synchronization. As we have observed, in particular cases the beam can begin to imitate an additional pendulum, performing oscillations with the amplitude comparable to the nodes. The co-existence of possible states has been studied and visualized using basins of attraction, and the properties of synchronous solutions have been discussed. Using the energy balance method, we have followed the energy flows within the system when the dynamics changes. The results presented in this paper have been collected using classical bifurcation tools and modern sample-based methods, showing that both approaches are complementary and can be applied in the analysis of complex nonlinear problems. Enhancing the freedom of motion of the supporting base, we can investigate more practical scenarios of coupled pendula and pendula-like systems, developing the synchronization theory and its use in solving modern engineering problems.

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同步模式在两个钟摆上悬挂在多自由度的支撑上

研究了悬挂在三自由度梁上的两个摆的动力学和可能的同步情况。底座配备了支撑弹簧，允许它执行平移和旋转振荡（全平面运动）。根据模型的参数，我们确定了经典同步模式的不同区域，并揭示了更复杂的场景，包括不规则运动和准周期同步。正如我们所观察到的，在特殊情况下，梁可以开始模仿一个额外的摆，以与节点相当的振幅进行振荡。利用引力盆对可能态的共存进行了研究和可视化，并讨论了同步解的性质。利用能量平衡法，跟踪了系统动态变化时的能量流动情况。本文采用经典分岔工具和现代基于样本的方法收集了结果，表明这两种方法是互补的，可以应用于复杂非线性问题的分析。提高支撑基座的运动自由度，我们可以研究耦合摆和类摆系统的更多实际场景，发展同步理论及其在解决现代工程问题中的应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Sound and Vibration 工程技术-工程：机械

CiteScore

9.10

自引率

10.60%

发文量

551

审稿时长

69 days

期刊介绍： The Journal of Sound and Vibration (JSV) is an independent journal devoted to the prompt publication of original papers, both theoretical and experimental, that provide new information on any aspect of sound or vibration. There is an emphasis on fundamental work that has potential for practical application. JSV was founded and operates on the premise that the subject of sound and vibration requires a journal that publishes papers of a high technical standard across the various subdisciplines, thus facilitating awareness of techniques and discoveries in one area that may be applicable in others.