耦合分段线性刚度NES系统能量传递和耗散研究  

Energy transfer and dissipation studies of coupled piecewise linear stiffness NES system

作　　者：张云浩 王军 申永军[1,2] 张建超 ZHANG Yunhao;WANG Jun;SHEN Yongjun;ZHANG Jianchao(School of Mechanical Engineering,Shijiazhuang Tiedao University,Shijiazhuang 050043,China;State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures,Shijiazhuang Tiedao University,Shijiazhuang 050043,China)

机构地区：[1]石家庄铁道大学机械工程学院,河北石家庄050043 [2]石家庄铁道大学省部共建交通工程结构力学行为与系统安全国家重点实验室,河北石家庄050043

出　　处：《振动工程学报》2025年第3期480-489,共10页Journal of Vibration Engineering

基　　金：国家自然科学基金资助项目(U1934201,12272242)。

摘　　要：针对耦合分段线性刚度NES的能量传递效率及系统能量耗散进行了研究。采用复变量-平均法得到了1∶1内共振下耦合分段线性刚度能量阱的二自由度系统慢变方程。应用多项式近似法得到了系统慢不变流形两极值点的近似表达式,以此得到了耦合分段线性刚度能量阱系统的能量传递效率方程以及能量耗散方程,并分析了分段间隙和分段线性刚度对能量传递效率的影响以及阻尼比与耗散时间的关系。研究结果表明,系统的能量传递效率随着耦合分段线性刚度能量阱分段间隙的增大而降低,随着分段刚度的增大而提高;能量耗散时间随着主结构阻尼系数的增大而缩短。通过调节结构参数,分段线性刚度能量阱能够高效抑制主结构的振动。The energy transfer efficiency and energy dissipation of coupled piecewise linear stiffness energy sink are studied.The equation of systematic slow-varying equations of the two-degree-of-freedom system coupled with the piecewise linear stiffness energy is derived by the complex variable-averaging method under 1∶1 internal resonance.The approximate expression of two extreme points of the slow-invariant manifold is obtained by using the polynomial approximation method,and the energy transfer efficiency equation and energy dissipation equation of the coupled piecewise linear stiffness energy sink system are obtained.The effects of piecewise gap and piecewise linear stiffness on energy transfer efficiency and the relationship between damping coefficient of the main structure and dissipation time are analyzed.The results indicate that the energy transfer efficiency of the system decreases as the piecewise gap of the coupled piecewise linear stiffness energy sink increases,while it increases with an increase of piecewise stiffness.Additionally,it decreases with an increase of the damping system of the main structure.Therefore,adjusting structural parameters,the piecewise linear stiffness energy sink can effectively mitigate vibrations within the main structure.

关 键 词：非线性振动 非线性能量阱 复变量-平均法 分段线性刚度 

分 类 号：O322[理学—一般力学与力学基础]