非等比例惯容及其反共振隔振器

Non proportional Inerter and Its Application inAnti-resonant Vibration Isolators

具有双端点性质的惯性元件被定义为“惯容”。对惯容概念进行梳理,从反共振隔振的实现途径出发指出其定义隐含双端点等比例运动的狭义性。以一个机械式和一个液压式双端点惯性元件示例,说明双端点惯性元件还包括非等比例运动的情形,据此提出“非等比例惯容”概念,拓展了惯容内涵。以非等比例惯容和弹性元件组合3型不同结构的反共振隔振器,推导阻抗矩阵,根据阻抗等效原则,建立非等比例惯容三元件型反共振隔振器的等效模型。结果表明,对于含非等比例惯容的反共振隔振器,其输入端和输出端的反共振频率并不相同,输入端惯质的放大倍率都等于输入端运动耦合系数的平方。

The inertial element with two terminals is defined as the"inerter".However,when analyzing the definition of the inerter from the viewpoint of the realization way of anti-resonant vibration isolation,this definition is incomplete because it takes account of the equally proportional motion of the two terminals only.Taking a mechanical type inertial device and a hydraulic type inertial device with two terminals as examples,their commonality is that the motion of the two terminals is non-proportional,i.e.the inertial device with two terminals also include the non-proportional type motion.Based on the two types of inertial devices,the concept of non-proportional inerter is proposed,and the content of inerter is expanded.With different combinations of a single non-proportional inerter element and a spring element,three types of anti-resonant vibration isolators are synthesized,and the impedance matrixes are deduced.According to the principle of impedance equivalence,the equivalent model for anti-resonant vibration isolator with three non-proportional inerter elements is established.The results show that the anti-resonant frequencies of anti-resonant vibration isolator with single non-proportional inerter element at the input and output terminals are different,and the amplification multiple of the inertance at the input terminal is equal to the square of the input motion coupling coefficient.