随机激励下非线性能量阱系统减振性能优化研究  

Optimization of damping performance of a nonlinear energy sink system under random excitation

作　　者：胡宏祥 陈林聪[1,2] HU Hongxiang;CHEN Lincong(College of Civil Engineering,Huaqiao University,Xiamen 361021,China;Key Laboratory for Intelligent Infrastructure and Monitoring of Fujian Province,Huaqiao University,Xiamen 361021,China)

机构地区：[1]华侨大学土木工程学院,福建厦门361021 [2]华侨大学福建省智慧基础设施与监测重点实验室,福建厦门361021

出　　处：《振动与冲击》2022年第24期27-32,59,共7页Journal of Vibration and Shock

基　　金：国家自然科学基金(12072118);福建省自然科学基金(2021J06024);厦门市青年创新基金(3502Z20206005)。

摘　　要：作为一类具有非线性刚度的典型非线性被动控制装置,非线性能量阱(nonlinear energy sinks,NESs)以其质量轻、频率鲁棒性强等优势引起了工程领域的广泛关注。目前,针对耦合NES的结构系统动力学研究主要是确定性载荷情形,仅少数涉及随机激励情形的研究。该文章研究了随机激励下耦合NES的单自由度(single-degree-of-freedom,SDOF)结构随机振动的参数优化问题。首先应用加权残值法,将原系统等效为具有精确平稳解的随机动力学系统,理论解和蒙特卡洛解模拟(Monte Carlo solution,MCS)在误差允许范围内吻合,显示所提的数值方法有效;然后利用原系统的平稳响应概率密度函数(probability density function,PDF)的近似解析表达式来构造目标函数,提出了一种以主结构位移与速度响应量均方(mean-square,MS)最小为目标的NES参数优化设计策略,讨论了非线性能量阱的阻尼系数、非线性刚度系数、质量比等参数对减振性能的影响。结果表明,增加NES的质量比与阻尼系数,可以实现较强的减振性能,非线性刚度值对NES的减振性能的影响规律与质量比取值相关。相关工作可为NES的设计与应用提供参考。As a typical nonlinear passive control device with nonlinear stiffness,nonlinear energy sinks(NES)have attracted the attention from various engineering fields for their light weight and strong frequency robustness.At present,the studies dealing with the dynamics of structural systems containing NES were almost limited to deterministic load cases in literature.There were only very few investigations available for the random excitation.In this paper,the parameter optimization of random vibration of single-degree-of-freedom(SDOF)structure coupled with NES excited by Gaussian white noise was investigated.First,the original system was equivalent to stochastic dynamic systems with exact stationary solutions by using the method of weighted residual.The theoretical solution and Monte Carlo solution(MSC)agree within the allowable error range,which shows the effectiveness of the proposed numerical method.Subsequently,the approximate analytic expression of probability density function(PDF)of the stationary response of the original system was utilized to construct the objective function.A parameter optimization strategy of NES with the target of minimizing the mean-square(MS)of displacement and velocity response of main structure was proposed.The effects of parameters such as damping,nonlinear stiffness and mass ratio of nonlinear energy sink on damping performance were discussed.The results show that the increase of mass ratio and damping of NES can achieve strong damping performance.The influence law of nonlinear stiffness on the damping performance of NES is related to the value of mass ratio.It can provide a feasible reference for the design and application of NES.

关 键 词：随机振动 非线性能量阱(NES) 参数优化 加权残值法 

分 类 号：TH212[机械工程—机械制造及自动化] TH213.3