圆柱空腔橡胶层局域共振声子晶体双层板减振特性分析

Analysis of Vibration Reduction Characteristics of Double-layer Phononic Crystals with Local Resonance of Rubber Layer in Cylindrical Cavity

针对机械设备中的低频减振问题,提出一种圆柱空腔橡胶层局域共振声子晶体双层板结构,即在双层板间周期性排列具有圆柱空腔的橡胶层和实心散射体振子。首先结合弹性波理论和BLOCH定理,采用有限元方法计算带隙范围并分析弯曲波带隙形成的原理,其次通过单变量和组合变量的方式分析单元参数对带隙的影响规律并依此对单元参数进行调整,使其弯曲波带隙范围为48.52~206.21 Hz,最后通过振动传输特性仿真验证其对弯曲波振动的减振效果。研究表明,圆柱空腔橡胶层双层板式声子晶体可以产生200 Hz以下的弯曲波带隙,且可以通过调整单元参数来使其匹配目标减振频段。声子晶体板的振动传输特性分析和振动位移图验证了其对带隙范围内弯曲波传输的抑制作用,可为基于声子晶体减振的工程应用提供一定的参考。

Aiming at the problem of low-frequency vibration reduction in mechanical equipment,a local resonance phonon crystal double-layer plate structure of cylindrical cavity rubber layer is proposed.In this structure,the rubber layer with cylindrical cavity and solid scatterer oscillation vibrator are periodically arranged in the double-layer plates.Firstly,combined with the elastic wave theory and BLOCH theorem,the finite element method is used to calculate the band gap range and analyze the principle of flexural wave band gap formation.Secondly,the influence of the element parameters on the band gap is analyzed by means of uni-variable and hybrid variable methods.On this basis,the element parameters are adjusted accordingly to cause the flexural wave band gap to be ranged from 48.52 to 206.21 Hz.Finally,the vibration reduction effect of flexural waves is verified by the simulation of vibration transmission characteristics.The research shows that the cylindrical cavity rubber layer double-layer plate phononic crystal can generate a flexural wave bandgap below 200 Hz.In addition,the structure and material parameters of the unit can be adjusted to make it more suitable to the target vibration reduction frequency band.The vibration transmission characteristics analysis and vibration displacement diagram of phonon crystal plate verify its inhibitory effect on the transmission of bending waves in the corresponding band gap range.This research provides a certain reference for the engineering vibration reduction application of phononic crystals.