含双耦合非线性振子的双梁系统动力学行为研究

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振动与冲击 ›› 2025, Vol. 44 ›› Issue (6) : 1-12.

振动理论与交叉研究

含双耦合非线性振子的双梁系统动力学行为研究

李生1，赵雨皓*2，杜敬涛3，崔海健4

作者信息 +

Dynamic behaviors of a double-beam system with double-coupling nonlinear oscillators

LI Sheng1，ZHAO Yuhao*2，DU Jingtao3，CUI Haijian4

Author information +

文章历史 +

摘要

弹性梁系统作为一种基本工程单元，被广泛应用于建筑、航天航空、海洋工程等领域，控制弹性梁系统的振动水平具有重要工程意义。为揭示双耦合非线性振子（double coupling nonlinear oscillator, DCNO）在双梁系统振动控制中的潜在应用，建立了含 DCNO的双梁系统动力学行为预报分析模型，并采用拉格朗日法预报双梁系统的动力学行为。在确保数值结果正确的基础上，研究了 DCNO的典型工作模式，探讨了 DCNO参数对双梁系统动力学行为的影响规律。研究结果表明， DCNO的引入能够有效实现双梁系统各子结构的同步振动控制。一方面，当 DCNO处于多频线性/非线性振动控制模式时，双梁系统各子梁主共振区处的振动均得到了有效抑制，且多频非线性振动控制模式激发了双梁系统的复杂振动响应，使得弹性梁与DCNO之间出现振动能量时域单向传递现象；另一方面，根据振动控制的需求，DCNO的工作模式及振动控制效果可通过调控其核心控制参数实现，设定合适的DCNO核心控制参数有利于增强DCNO对双梁系统主共振区的振动控制效果。

Abstract

As one of the basic engineering units, elastic beam systems are widely used in various fields, including architecture, aerospace, ocean engineering, and others.It is of great engineering significance to control the vibration level of elastic beam systems.To reveal the potential application of double-coupling nonlinear oscillators(DCNO) in the vibration control of double-beam systems, a dynamic behavior prediction model of double-beam systems with DCNOs was established, where the Lagrange method was used to predict the dynamic behavior of the double-beam system.On the basis of ensuring the correctness of the numerical results, the typical operating mode of the DCNO was studied, and the influence of the DCNO parameters on the dynamic behavior of the double-beam system was discussed.The results show that the introduction of the DCNOs can effectively realize the synchronous vibration control of each substructure of the double-beam system.On the one hand, when the DCNO is in the multi-frequency linear/nonlinear vibration control mode, the vibration of each sub-beam in the main resonance region of the double-beam system is effectively suppressed.Additionally, the multi-frequency nonlinear vibration control mode excites the complicated vibration responses of the double-beam system, resulting in the unidirectional transmission of vibration energy in time domain between elastic beams and DCNOs.On the other hand, according to the vibration control requirements, the working mode and vibration control effect of DCNOs can be realized by adjusting its core control parameters.Setting appropriate core control parameters for DCNOs is conducive to enhancing the vibration control effect of the DCNOs on the main resonance region of the double-beam system.

导出引用

李生1, 赵雨皓2, 杜敬涛3, 崔海健4. 含双耦合非线性振子的双梁系统动力学行为研究[J]. 振动与冲击, 2025, 44(6): 1-12

LI Sheng1, ZHAO Yuhao2, DU Jingtao3, CUI Haijian4. Dynamic behaviors of a double-beam system with double-coupling nonlinear oscillators[J]. Journal of Vibration and Shock, 2025, 44(6): 1-12

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