周期多孔板的面内振动衰减域及其优化

针对Bragg散射型周期多孔板难以实现较低起始频率并维持较宽衰减域的问题,优化设计了一种含菱形孔的周期多孔板。采用有限元法结合周期边界条件,并运用COMSOL对周期多孔板的面内弹性波频散关系进行计算,通过ANSYS模拟有限尺寸周期多孔板的频率响应,将周期多孔板悬吊进行了正弦波激励的振动试验。研究结果表明,含菱形孔的周期多孔板相比于含圆形和六边形孔的周期多孔板具有更宽的衰减域;材料属性对衰减域影响较大,丁晴橡胶和硅橡胶易于获得低频衰减域;孔隙率的增大有利于获得低频宽带的衰减域;增大菱形孔水平夹角能获得较宽的衰减域。对衰减域的形成机理分析发现,含菱形孔的周期多孔板同时具有Bragg散射型和局域共振型声子晶体的特性,表明两种衰减域机理具有内在的联系。优化设计的周期多孔板存在一条5281.76 Hz至8824.30 Hz的完全衰减域,经过至少2个周期,振动即得到较明显衰减。数值和试验得到的衰减区具有较高的一致性。该研究为减振降噪板的开发提供了新的思路,且由于制作过程便捷,在改善建筑声环境中具有潜在的应用前景。 

In-plane attenuation zone and its optimization of periodic porous plates

The periodic porous plate with Bragg scattering mechanism is difficult to obtain low bound frequency and wide attenuation zones.One type of periodic porous plates with rhombus holes is optimized and designed.Based on the finite element method with periodic boundary conditions,the in-plane dispersion curves of periodic porous plates are calculated via COMSOL.The frequency responses of periodic porous plates are investigated by ANSYS simulation.The periodic porous plates are suspended and dynamically tested under sinusoidal excitations.The results show that periodic porous plate with rhombus holes has wider attenuation zones than those with circular and hexagonal holes.The material properties have a great influence on the attenuation zones.Nitrile-butadiene rubber and silicon rubber are easy to obtain low-frequency attenuation zones.Increasing porosity results in lower and wider attenuation zones.The width of attenuation zone increases as the horizontal angle of rhombus holes increases.The analysis on the generation mechanism of attenuation zones shows that the periodic porous plate has both characteristics of Bragg scattering and local resonant phononic crystals,which indicates the inherent relation between two types of mechanisms.The optimized periodic porous plate has a complete attenuation zone ranging from 5281.76 Hz to 8824.30 Hz.The vibrations are significantly reduced when the number of periods is not less than two.The attenuation range obtained by the numerical method is generally consistent with that of experiment.The research does shed light on the noise insulation plate,and has the potential application in improving sound environment due to the simple manufacture.