黏弹性能量阱系统振动抑制响应分析OA
Analysis of Vibration Suppression Response in Viscoelastic Energy Trap Systems
黏弹性材料因其优良的减振特性,被广泛运用于土木、航空等领域.本文将非线性刚度 Zener 模型替代传统非线性能量阱中的能量传递元件,提出一种新型黏弹性能量阱装置,并探讨了简谐激励下模型的分岔行为.首先,基于非线性刚度 Zener 模型建立了耦合主结构-能量阱系统的非线性动力学控制方程,采用复变量平均法解析推导了1∶1 共振条件下的慢变系统方程.基于此,系统揭示了慢变条件下关键参数对系统黏弹性能量阱分岔行为的影响规律,并结合数值模拟方法,以主结构减振效率和能量传递效率为指标,进一步探讨了不同分岔区域黏弹性能量阱的振动抑制效能.研究结果表明:新型黏弹性能量阱通过参数调控可有效调控系统的鞍结分岔和 Hopf 分岔等分岔行为,显著提升了系统的减振效率与能量传递效率,并有效抑制了主结构的位移响应.本研究为新型黏弹性能量阱的工程设计与参数优化提供了一定的理论依据.
Viscoelastic materials are extensively utilized in civil engineering,aviation,and other domains owing to their superior vibration damping characteristics.The nonlinear stiffness Zener model was employed to replace the energy transfer elements in the conventional nonlinear energy trap,thereby making a novel viscoelastic en-ergy trap device.Furthermore,the bifurcation behavior of the model under simple harmonic excitation was in-vestigated.Initially,the nonlinear dynamic control equation for the coupled main structure-energy trap system was formulated based on the nonlinear stiffness Zener model.Subsequently,the slow-varying system's equation under the 1:1 resonance condition was analytical derived with the complex variable averaging method.On this basis,the effects of key parameters on the bifurcation behavior of the system's viscoelastic energy trap under slow-changing conditions were elucidated.Through integration of the numerical simulation approach and in view of the vibration reduction efficiency and energy transfer efficiency of the main structure as evaluation indi-cators,the vibration suppression effectiveness of the viscoelastic energy trap across different bifurcation re-gions was further explored.The results indicate that,the newly developed viscoelastic energy trap can effective-ly modulate saddle-node bifurcations and Hopf bifurcations through parameter adjustments,thereby significant-ly enhancing the system's vibration damping efficiency and energy transfer efficiency while effectively restrai-ning the displacement response of the main structure.This research provides a robust theoretical foundation for the engineering design and parameter optimization of the innovative viscoelastic energy trap.
王道航;周紫怡;刘春霞;孙博;兰树伟
昆明理工大学 公共安全与应急管理学院,昆明 650000昆明理工大学 公共安全与应急管理学院,昆明 650000云南财经大学 统计与数学学院,昆明 650000昆明理工大学 公共安全与应急管理学院,昆明 650000昆明学院 建筑工程学院,昆明 650214
数理科学
非线性能量阱Zener模型复变量平均法分岔研究振动控制
nonlinear energy trapZener modelcomplex variable averaging methodbifurcation studyvibra-tion control
《应用数学和力学》 2026 (4)
454-467,14
云南省科技厅基础研究计划专项(面上项目)(202501AT070448)云南省科技厅基础研究专项(面上项目)(202401AT070031)昆明理工大学自然科学研究基金(人培项目)(241120230015)
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