非线性能量阱系统受基底简谐激励的参数优化分析

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振动与冲击 ›› 2019, Vol. 38 ›› Issue (22) : 36-43.

论文

刘良坤1，谭平2，潘兆东1，闫维明3，周福霖2,3

作者信息 +

Parameter optimization analysis of a nonlinear energy sink system under base harmonic excitation

LIU Liangkun1,PAN Zhaodong1,TAN Ping2,YAN Weiming3,ZHOU Fulin2,3

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文章历史 +

摘要

为得到非线性能量阱系统（NES）基底简谐激励下的最优刚度，利用复变量平均法推导了1:1共振的慢变系统方程，经多尺度分析后得到了强调制反应（SMR）的必要条件以及吸引点解析方程；然后利用SMR的特点获取最优刚度下限值，并结合吸引点方程求得最优刚度上限值。经数值分析表明，吸引点方程所得计算值与Runge-Kutta的数值解一致，且吸引点数值与原系统的稳态解相近；此外，慢变系统方程计算简便，结果合理；随着NES阻尼参数的提高，最优刚度区域有增大趋势；与TMD相比，NES具有较宽减振频带，但在主频附近减振效率更低，且易受激励幅值影响。

Abstract

In order to obtain the optimal stiffness parameter of a nonlinear energy sink (NES) system under base excitation, the complex-averaging method was employed to derive the equation of a corresponding slow dynamics system with 1∶1 resonance. The corresponding necessary condition of the strongly modulate response (SMR) and analytical equation of the fixed point were also obtained. Sequently, the lower limit and upper limit were solved based on the characteristics and analytical equation of the fixed point respectively. The numerical simulation results indicate that the fixed point solved by the analytical equation of the fixed point is in agreement with the counterpart directly calculated using Runge-Kutta method. Moreover, the former is also approximate to the stable response of the original dynamic system. Additionally, the slow dynamics system is convenient for computation and has rational results. The optimal stiffness areas for NES system trend to be larger with the increase of damping parameters. Compared with TMD system, NES system has broader frequency band for vibration attenuation but it is of lower efficiency at frequencies close to the inherent frequency and is also easily affected by the excitation magnitude.

导出引用

刘良坤1，谭平2，潘兆东1，闫维明3，周福霖2,3. 非线性能量阱系统受基底简谐激励的参数优化分析[J]. 振动与冲击, 2019, 38(22): 36-43

LIU Liangkun1,PAN Zhaodong1,TAN Ping2,YAN Weiming3,ZHOU Fulin2,3. Parameter optimization analysis of a nonlinear energy sink system under base harmonic excitation[J]. Journal of Vibration and Shock, 2019, 38(22): 36-43

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