穿孔管消声器横截面模态及消声特性的有限元分析

Finite element analysis for cross-sectional modes and acoustic attenuation characteristics of a perforated tube silencer

将有限元法应用于计算穿孔管消声器的横截面模态频率,推导了相应的有限元公式并编写了计算程序。对于圆形同轴结构的模态频率,有限元法计算结果与解析法计算结果吻合良好,表明了有限元法预测穿孔管消声器横截面模态的准确性。之后将有限元法应用于计算和分析孔径、穿孔率和穿孔管偏移对直通穿孔管消声器横截面模态和消声特性的影响。结果表明,穿孔率低于40%时,孔径减小或穿孔率增大均能使(0,1)阶模态频率升高,消声器中频消声效果变好;穿孔率高于40%后,孔径和穿孔率对(0,1)阶模态频率影响较小。对于非同轴结构,平面波截止频率为第2阶模态频率,对于给定的孔径和穿孔率,穿孔管偏移对第2阶模态频率影响较小。

Finite element method was used to calculate cross-sectional modes of a perforated tube silencer, the corresponding finite element formulation was derived and the computational code was programmed. For the radial modal frequencies of a circular concentric configuration, the finite element predictions agreed well with the analytical results, it was shown that the finite element method can predict cross-sectional modes of a perforated tube silencer accurately. The finite element method was then used to investigate the effects of hole diameter, porosity and perforated tube offset on the cross-sectional modes and acoustic attenuation characteristics of a straight-through perforated tube silencer. The results showed that smaller hole diameter or higher porosity leads to higher frequencies for the （ 0, 1 ） order modes when the porosity is lower than 40%, and then better acoustic attenuation exists in the middle frequency range; the hole diameter and porosity have negligible effect on the （0, 1 ） order modal frequencies when the porosity is higher than 40% ; for non-coaxial silencers, the plane wave cut-off frequency is the second order modal frequency ; the effect of perforated tube offset on the second order modal frequency is not remarkable for certain values of hole diameter and porosity.