PASSIVE VIBRATION REDUCTION OF SPACE TRUSS STRUCTURES BASED ON NES
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摘要: 该文利用等效方法将由众多杆件构成的、离散的空间直线式桁架等效为连续梁，对等效梁附加NES(非线性能量阱)的桁架结构进行瞬态减振研究。通过等效方法将梁式桁架结构建模为等效线性连续系统(有限长度梁)，并用有限元模型对其进行了验证。建立了含NES附件的等效悬臂梁的振动控制方程，并采用伽辽金法进行离散，分别分析了附加和不附加NES附件的梁在外激励下的横向振动位移响应。通过计算NES附件附着在结构的不同位置条件下的外激励响应，研究了NES对结构的振动抑制作用。此外，还研究了不同质量的NES附件在不同位置时结构的外激励响应，得到了NES附加质量对减振效果的影响。从结果可以看到，NES附件可以减弱X型桁架在瞬态激励作用下的响应，且当NES附件的质量增加时，系统的振动振幅下降更快，NES附件的能源消耗效率更高。同时还对比了NES被动减振和线性刚度阻尼减振器(TMD)的减振效果。结果表明，在附加NES的结构中，在激励发生后的5 s左右时，结构振幅的衰减就达到了可观的程度，振幅下降的趋势更为陡峭，体现了NES优于线性刚度阻尼减振的良好减振效果。并通过实验验证了不同质量的NES附件的衰减效果，在梁的自由端施加相同的位移激励幅值(15 mm)，在此情况下，NES附件的质量越大，悬臂梁结构的瞬态响应衰减效率越高。实验结果与理论计算结果吻合较好。Abstract: The discrete linear spatial truss structure composed of many bar members is taken as a continuous beam by using an equivalent method. The transient vibration suppression of the truss structure is studied by adding nonlinear energy sinks (NES) to the equivalent beam. The lattice structure of the beam is modeled as an equivalent linear continuous system (finite length beam) by an equivalent method, which is verified by a finite element model. The vibration control equations of an equivalent cantilever beam with a NES attachment are established. The Galerkin method is adopted for discretization. The displacement responses of beams with and without a NES attachment under external excitation are analyzed. The vibration suppression effect of NES on the structure is studied by calculating the external excitation response of NES attachments at different positions in the structure. In addition, the external excitation response of NES attachments with different masses at different positions are also investigated. The effect of NES additional mass on the vibration reduction is obtained. The results show that the NES attachments can reduce the response efficiency of the x-truss under transient excitation When the mass of the NES attachments increases, the vibration amplitude of the system declines more rapidly and the energy consumption efficiency of the NES attachments becomes higher. The NES passive vibration reduction effect is compared with the linear stiffness damping damper (TMD). The results show that, in the structure with additional NES, the attenuation of the structure amplitude is appreciable at about 5 seconds after the excitation occurred, and the decline in the amplitude is steeper. This means that the NES passive reduction effect is much better than that of the linear stiffness damping damper (TMD). Additionally, the attenuation effect of the NES attachments with different qualities is verified through experiments, in which the same displacement excitation amplitude (15 mm) is applied to the free end of a beam. The results show that the greater the mass of the NES attachment is, the higher is the attenuation efficiency of the transient response of the cantilever structure. The experimental results are in good agreement with the theoretical calculation results.
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图 1 桁架结构附加NES附件的示意图
Figure 1. Schematic diagram of truss structure with NES attachment
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图 5 桁架结构有限模型与等效梁模型固有频率的相对误差
Figure 5. Relative error of natural frequency between finite model of truss structure and equivalent beam model
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图 10 当NES附件选取不同质量时，结构的振动幅值衰减效果
Figure 10. Vibration amplitude attenuation effect of structure with NES’s of different masses
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图 11 选取不同的质量系数，系统振动幅值衰减为初始幅值25%时所用时间
Figure 11. With different mass coefficient, time taken by system when response amplitude is reduced to 25% of initial amplitude
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图 13 悬臂梁结构耦合NES附件振动实验简图
Figure 13. Experiment diagram of cantilever beam coupling NES attachment
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图 16 不同NES附件质量时悬臂梁振动幅值的时域响应
Figure 16. Time-domain curve of transient response attenuation of structures with NES’s of different masses
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图 17 不同NES附件质量时悬臂梁振动幅值的时域响应包络线
Figure 17. Envelope of time-domain curves of transient response attenuation of structures with different masses
表 1 桁架的几何属性
Table 1 Geometric properties of truss
杆件 长/m 截面外径/m 截面内径/m 数量 横杆 1.00 0.009 0.008 20 竖杆 1.00 0.009 0.008 11 斜杆 1.41 0.009 0.008 20 
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表 2 桁架的前两阶弯曲频率
Table 2 First two bending frequencies of truss
模态 FEM模型 等效模型 一阶弯曲 /Hz 16.14 15.49 二阶弯曲 /Hz 91.27 97.57
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