磁力耦合下双板簧振动模式研究

Study on the vibration modes of twoleaf springs coupled with magnetic interaction

简正模式和简正频率是多自由度振动体系的关键属性.体系的简正模式如何受各自由度之间的耦合作用影响,既是基础的力学问题,也和很多工程应用问题直接相关.我们研究一对完全相同的板簧在磁力耦合作用下的振动.研究表明,磁力耦合导致双板簧系统产生一套与耦合强度有关的相向振动模式,以及一套与耦合强度无关的同向振动模式;并且,低阶模式受磁力影响大,而高阶模式几乎不产生耦合.所以,两板簧不同的初始条件会导致两板簧振动频谱不同.我们也开展了实验研究,观察到的板簧振动现象及简正频率随板簧间距、厚度、长度等关键参量的变化规律均符合理论模型.

Normal modes and eigen frequencies are crucial characteristics of a multi-degree-of-freedom oscillation system.The influence of the coupling interactions between different degrees of freedom on the normal modes is a fundamental mechanical research topic,and is alsOrelevant tOvarious engineering and application problems.Here,we study the vibration of twOidentical leaf springs coupled with magnetic force.We show that the magnetic coupling causes a set of coupling-dependent modes,with the springs moving in opposite directions,and another set of coupling-independent modes,with the springs moving in same directions.In addition,the lower order vibration modes are more strongly affected by the magnetic force,while the higher order modes of the twOsprings are barely coupled.Thus,the twOsprings would have distinct vibration frequency spectrums if their initial conditions are different.We have alsOperformed experiments,tOobserve the vibration phenomena and measure the eigen frequencies with different key variables,including the spacing distance of the springs,spring thickness and length.The experimental results are all in accordance with our theoretical predictions.