An optimal control method of internal resonances for vibration isolation system using an aperiodic isolator  

基于非周期隔振器的一种内共振抑制及优化方法

作　　者：Yujun Liu Jing Liu Guang Pan Qiaogao Huang Baowei Song 刘玉君;刘静;潘光;黄桥高;宋保维

机构地区：[1]School of Marine Science and Technology,Northwestern Polytechnical University,Xi’an 710072,China [2]Key Laboratory of Unmanned Underwater Vehicle,Northwestern Polytechnical University,Xi’an 710072,China

出　　处：《Acta Mechanica Sinica》2025年第1期175-191,共17页力学学报(英文版)

基　　金：supported by the National Key Research and Development Plan of China (Grant No.2023YFB3406302);Guangdong Basic and Applied Basic Research Foundation (Grant No.2024A1515011126);the Key Research and Development Plan of Shanxi (Grant No.2024GH-ZDXM-29)。

摘　　要：Periodic isolator is well known for its wave filtering characteristic.While in middle and high frequencies,the internal resonances of the periodic isolator are evident especially when damping is small.This study proposes a novel aperiodic vibration isolation for improving the internal resonances control of the periodic isolator.The mechanism of the internal resonances control by the aperiodic isolator is firstly explained.For comparing the internal resonances suppression effect of the aperiodic isolator with the periodic isolator,a dynamic model combing the rigid machine,the isolator,and the flexible plate is derived through multi subsystem modeling method and transfer matrix method,whose accuracy is verified through the finite element method.The influences of the aperiodicity and damping of the isolator on the vibration isolation performance and internal resonances suppression effect are investigated by numerical analysis.The numerical results demonstrate that vibration attenuation performances of the periodic isolator and aperiodic isolator are greatly over than that of the continuous isolator in middle and high frequencies.The aperiodic isolator opens the stop bandgaps comparing with the periodic isolator where the pass bandgaps are periodically existed.The damping of the isolator has the stop bandgap widening effect on both the periodic isolator and the aperiodic isolator.In addition,a parameter optimization algorithm of the aperiodic isolator is presented for improving the internal resonances control effect.It is shown that the vibration peaks within the target frequency band of the aperiodic isolator are effectively reduced after the optimization.Finally,the experiments of the three different vibration isolation systems are conducted for verifying the analysis work.隔振器的内共振会明显影响其在中高频段的隔振性能,周期隔振器具有良好的中高频滤波特性,但内共振效应依然存在,尤其是在隔振器阻尼较小的情况下.为了降低周期隔振器的内共振影响,本文提出了一种新型非周期隔振器.首先解释了基于非周期隔振器的内共振控制机理;通过子系统法和传递矩阵法,推导了电机、非周期隔振器和弹性支撑板耦合的动力学模型,采用有限元方法验证了数值模型的准确性,数值分析了隔振器的非周期性和阻尼对内共振的抑制效果.结果表明,在中高频段,周期隔振系统和非周期隔振系统的隔振性能明显优于连续隔振系统.与能带结构中滤波通带周期性存在的周期隔振器相比,非周期隔振器打开了能带结构中的通带带隙.结果表明含阻尼的周期隔振器和非周期隔振器都具有能带结构加宽效应.为了提高内共振的控制效果,提出了一种非周期隔振器参数优化方法,优化后的非周期隔振器在目标频带内的内共振峰值得到了有效的降低.最后,基于实验方法对三种不同的隔振系统的隔振性能进行了测试.

关 键 词：Internal resonances Vibration isolation Periodic structure Vibration wave propagation 

分 类 号：TB123[理学—工程力学]