均匀弹性杆弯曲振动的机电等效电路

The electromechanical equivalent circuit of the uniform section elastic rod in flexural vibration mode

为简化弯曲振动系统的设计,基于Shear梁和Euler-Bernoulli梁理论与机电类比原理,推导了均匀弹性杆弯曲振动的机电等效电路及其共振频率方程.在此基础上,探讨了杆的前10阶弯曲振动共振频率与其几何尺寸之间的依赖关系,并对其弯曲振动特性进行了数值仿真计算与分析.结果表明:均匀弹性杆两端横向力与振速之间满足互易关系,其弯曲振动亦可用机电类比T型等效电路来描述;杆的弯曲振动共振频率随其振动阶次的增加而增大;相同阶次的弯曲共振频率随其长高比的增加而减小;对于考虑剪切变形影响的Shear梁,在较高的振动阶次及较小的长高比范围内,其弯曲振动共振频率的理论与仿真结果吻合较好.研究结果可为弯曲振动及其耦合振动系统的设计及应用提供一种有效的等效电路分析方法.

In order to simplify the diesign of the flexurel vibartion system,the electro-mechanical equivalent circuit and the resonance frequency equation of the uniform section elastic rod in flexural vibration were derived based on the theory of the Shear beam and the Euler-Bernoulli beam as well as the electro-mechanical analogy.The relationship between the resonant frequency of the rod in the first ten orders flexural vibration mode and its geometrical dimensions were analyzed,and the flexural vibration characteristics of the uniform elastic rod were simulated and invetigated.It was showed that the reciprocal relationship between transverse force and vibration velocity at the both ends of the uniform section elastic rod was satisfied,and the electro-mechanical equivalent circuit of the rod in flexural vibration was also an equivalent T-circuit.The flexural resonance frequency of the rod increased as the vibration order increased.The flexural resonance frequency of the rod decreases as the length-height ratio increased at the same vibration order.Because the Shear deformation was considered in the Shear beam theory,the theoretical resonance frequency of the rod in flexural vibration mode were in good agreement with the simulated results in the range of higher vibration orders and smaller length-height ratios.The relavant findings would provide a designing method of the equivalent circuit analysis for the flexural vibration and the coupling vibration systems.