局域共振型隔振系统的低频振动特性分析

Analysis of Low Frequency Vibration Characteristics of Locally-resonant Vibration Isolation Systems

为有效降低基体低频振动对精密仪器测量精度的影响,提出了周期布置吸振器的减振方式。建立了基体-隔振设备-吸振器系统的动力学模型,利用模态叠加法导出了系统耦合振动方程的解析解,并用有限元法进行了验证。获得了吸振器数量、参数对系统低频振动特性的影响规律,在吸振器总数一定的情况下,将其划分为包含不同数量振子的周期元胞。以低频段设备振幅最大值的0.7倍和平均值的0.3倍之和为目标函数,利用粒子群算法对元胞中振子的参数进行了优化。结果表明,在目标频段,解析解与有限元解之间的相对误差分别为4.39%和2.98%;在目标频段,针对单振子元胞,采用5个吸振器减振性能最优,减振效率为11.34%,吸振器质量比、固有频率比、阻尼比分别在0.16、0.8、0.18附近取值时减振性能最优,减振效率分别为10.46%、8.69%、12.20%;优化后的单振子、双振子、三振子元胞的减振效率可分别达到12.45%、18%、18.3%。

To effectively reduce the impact of low-frequency vibration of the base on measurement accuracy of precision instruments,a vibration attenuation method of periodically arranged absorbers was proposed.The dynamics model of substrate-vibration isolation equipment-vibration absorber system was established,the analytical solution of coupled vibration equation of the systems was derived by modal superposition method and verified by finite element method.The influence laws of number and parameters of vibration absorbers on low frequency vibration performance of the systems were obtained,when the total number of vibration absorbers was fixed,which was divided into several periodic cells with different number of resonators.Taking 0.7 times of the maximum amplitude and 0.3 times of the average amplitude as objective function,the parameters of resonator in cell were optimized by PSO algorithm.Results show that within the target frequency range,the relative errors between the analytical solution and the finite element one are as 4.39%and 2.98%respectively.Within the target frequency range,for the single-resonator cell,the vibration attenuation performance with 5 resonators is the best and the vibration attenuation efficiency is as 11.34%.When the mass ratio,natural frequency ratio and damping ratio of the absorber are around 0.16,0.8 and 0.18 respectively,the vibration attenuation performance is the best,and the damping efficiencies are as 10.46%,8.69%and 12.20%respectively.The vibration attenuation efficiency of optimized single-resonator,double-resonator,and triple-resonator cells may achieve 12.45%,18%and 18.3%respectively.