非线性能量阱的曲梁设计研究  

Design method of Euler curved beams in nonlinear energy sinks

作　　者：郑智伟 黄修长[1,2] 华宏星 袁志豪[3] 杨咏 ZHENG Zhiwei;HUANG Xiuchang;HUA Hongxing;YUAN Zhihao;YANG Yong(State Key Laboratory of Mechanical System and Vibration,Shanghai Jiao Tong University,Shanghai 200240,China;National Engineering Research Center of Special Equipment and Power System for Ship and Marine Engineering,Shanghai Marine Equipment Research Institute,Shanghai 200031,China;Key Laboratory of Nuclear Reactor System Design Technology,China Nuclear Power Research and Design Institute,Chengdu 610213,China)

机构地区：[1]上海交通大学机械系统与振动全国重点实验室,上海200240 [2]上海船舶设备研究所船舶与海洋工程特种装备和动力系统国家工程研究中心,上海200031 [3]中国核动力研究设计院核反应堆系统设计技术重点实验室,成都610213

出　　处：《振动与冲击》2024年第22期53-61,共9页Journal of Vibration and Shock

基　　金：中核集团“领创科研”项目(CNNC-LC-2021-中核科发[2021]155号);上海航天先进技术联合研究基金(USCAST2021-13);上海高等学校特聘教授(东方学者)项目(SHDP2022)。

摘　　要：非线性能量阱(nonlinear energy sink,NES)在减振和能量采集领域具有重要价值。尽管立方刚度NES及含立方刚度的双稳态NES已受广泛研究,但精确实现指定立方刚度的方法鲜有讨论。为此针对基于欧拉曲梁实现的NES开展研究,通过减小曲梁回复力与一个特定的理想非线性回复力之间的相对偏差,来实现NES中精确的立方刚度。基于欧拉梁理论得到圆弧梁和折线梁的初始刚度公式,用于设计曲梁长度。基于有限元方法求解了不同曲梁形状的非线性回复力,确定了能够实现立方刚度的圆弧梁和折线梁形状,并得到了满足相对偏差要求的临界位移拟合公式。基于以上两个公式总结出一套快速设计曲梁的方法,通过合理调节形状和截面尺寸使曲梁的回复力在需要的变形区间内逼近于理想非线性回复力。与有限元仿真进行对比,推导的解析公式可以对大初始挠度曲梁的初始刚度进行精确计算,设计出的NES回复力与目标之间的相对偏差绝对值小于1%。该设计方法有助于更精准、高效地设计NES,为曲梁实现非线性弹簧提供了新的设计方法。Nonlinear energy sinks(NESs) are important in the realms of vibration mitigation and energy harvesting due to their target energy transfer phenomenon.While extensive research has been conducted on the cubic stiffness NES and the bistable NES incorporating cubic stiffness,there exists a noticeable gap in discussions regarding the precise realization of cubic stiffness,thereby constraining the practical applications of NES.In this study,the methodology was investigated for designing curved beams to approximate its restoring force to a specific ideal nonlinear restoring force,and to ultimately achieve precise cubic stiffness in the NES.Initial stiffness formulas for circular and folded beams were derived based on the Euler beam theory and used to design the beam lengths.Nonlinear restoring forces for various beam shapes were solved using the finite element method,and circular and folded beam shapes capable of achieving cubic stiffness were identified.Critical displacement fitting formulas meeting relative deviation requirements were obtained.A rapid beam design method was summarized based on these formulas,allowing adjustment of shape and cross-sectional dimensions to make the restoring force of the beam approach the ideal nonlinear restoring force within the required deformation range.A comparison with finite element simulations shows that the derived analytical formulas can accurately calculate the initial stiffness of beams with large initial deflections,and the absolute value of relative deviation between the designed NES restoring force and the target is less than 1%.The proposed design method contributes to a more precise and efficient NES design,offering a new approach for implementing required nonlinear springs in curved beams.

关 键 词：欧拉曲梁 非线性能量阱(NES) 立方刚度 非线性回复力 

分 类 号：TH212[机械工程—机械制造及自动化] TH213.3