基于声学模态的椭圆截面扩张腔声学分析

Acoustic Analysis on the Expansion Chambers with Elliptical Cross-section Based on Acoustic Modes

利用马丢函数来求解椭圆双曲柱坐标系下的声波方程,获得声压的解析解,进而求得椭圆柱腔的声学模态,并利用声源激励法分析椭圆截面扩张腔的传递损失。与同截面积圆型扩张腔相比,椭圆截面扩张腔的传递损失在(2,1,n)偶阶模态处产生通过频率。将进、出口偏移至长轴(2,1,0)偶阶模态的波节线处,可消除(2,1,n)偶阶模态的影响;将进、出口偏移至短轴(0,2,0)偶阶模态的波节线处,可消除(0,2,n)偶阶模态的影响。

Mathieu function is used to solve the sound wave equation under elliptic-hyperbolic cylindrical coordinate with the analytical solutions of sound pressure obtained.The acoustic modes of cylindrical chambers with elliptical cross section are further acquired and sound source excitation method is employed to analyze the transmission loss of expansion chamber.Compared with expansion chamber with round cross section of same area,the transmission loss of expansion chamber with elliptical cross section generates passing frequency at even mode（2,1,n）.With its inlet and outlet moving onto the nodal line of even mode（2,1,0） on the major axis of expansion chamber,the effects of even mode（2,1,n） can be eliminated;while with its inlet and oudet moving onto the nodal line of even mode（0,2,0） on the minor axis of expansion chamber,the effects of even mode（0,2,n） can be eliminated.