基于耦合声场建模的膨胀腔消声器声学性能分析及试验

针对圆柱形膨胀腔消声器三维建模及声学性能分析问题, 提出一种基于切比雪夫变分原理的耦合声场建模方法, 建立三维圆柱形膨胀腔消声器理论模型并搭建试验台架, 传递损失试验结果验证了理论模型的准确性. 将膨胀腔消声器内部声场分解为多个子声场, 基于子声场间压力与质点振速连续性条件, 推导声场耦合变分公式, 构建子声场拉格朗日泛函. 将子声场声压函数展开为切比雪夫-傅里叶级数形式, 通过瑞利-里兹法求解膨胀腔消声器频率、声压响应及传递损失. 计算并对比分析扩张比、扩张腔长度、进出口管偏置对膨胀腔消声器消声性能的影响. 结果表明: 扩张比增大会有效提高消声器在低频段的消声性能, 进出口管的偏置对消声器消声性能影响很小.

Acoustic analysis and experiment of expansion chamber muffler based on coupled sound field modeling method

Aiming at the three-dimensional modeling and acoustic performance analysis of the muffler of cylindrical expansion chamber, a coupled sound field modeling method based on Chebyshev’s variational principle is proposed to establish a three-dimensional theoretical model of the cylindrical expansion chamber muffler. The accuracy of the theoretical model is verified on the test bench and by the transmission loss test results. The internal sound field of the expansion chamber muffler is decomposed into several sub-acoustic fields. Upon the continuous conditions of pressure and particle velocity of vibration between sub-acoustic fields, the variational formula of sound field coupling is constructed to complete the Lagrangian energy function of sub-acoustic field. The sound pressure function in each sub-acoustic field is generalized to the form of Chebyshev-Fourier series, and the Lagrangian function of the expansion chamber muffler’s is solved using Rayleigh Ritz method. As a result, the natural frequency, the sound pressure response and transmission loss of the expansion chamber muffler are predicted. By calculating and comparing the effects of expansion ratio, expansion cavity length, inlet and outlet offset on the performance of expansion cavity mufflers, some useful findings can be drawn, providing helpful references for the design of complex mufflers.