The transfer matrix method (TMM) is a common method for the modelling of acoustical systems. Traditionally, this method requires each unique layer within a system to be defined by a transfer matrix and then for each matrix to be multiplied together in the sequential order of the system. Whilst the resulting matrix can be used to find the effective material properties of the modelled system, the resulting analytical expressions of these properties are often unwieldy for use. Here, a simplified approach is proposed to obtain simple analytical expressions in the low frequency regime for the effective properties of acoustical systems based on the components of the TMM and inspired by the Champoux and Stinson model. It was shown that the proposed approximation of TMM matches the effective fluid properties of a cylindrical rigid tortuous pore derived with the Champoux and Stinson model. Using this approach, analytical expressions for the effective fluid properties of a waveguide of constant cross section, side-loaded by an arbitrary number of Helmholtz resonators, were derived. These expressions were validated against the traditional transfer matrix method and with numerical computation. The result of this work offers a validated general approach that provides simple analytical low frequency approximations of the acoustical properties of media which consist of complicated networks of pores or side-branches.

传递矩阵法 (TMM) 是声学系统建模的常用方法。传统上，这种方法要求系统内的每个唯一层都由一个传递矩阵定义，然后每个矩阵按照系统的顺序相乘。虽然得到的矩阵可用于找到建模系统的有效材料属性，但这些属性的结果分析表达式通常难以使​​用。在这里，基于 TMM 的组件并受 Champoux 和 Stinson 模型的启发，提出了一种简化的方法，以在低频范围内获得声学系统有效属性的简单解析表达式。结果表明，所提出的 TMM 近似与使用 Champoux 和 Stinson 模型导出的圆柱形刚性曲折孔的有效流体特性相匹配。使用这种方法，导出了恒定截面波导的有效流体特性的解析表达式，由任意数量的亥姆霍兹谐振器侧向加载。这些表达式针对传统的传递矩阵方法和数值计算进行了验证。这项工作的结果提供了一种经过验证的通用方法，该方法提供了由复杂的孔或侧枝网络组成的介质声学特性的简单分析低频近似值。由任意数量的亥姆霍兹谐振器侧向加载。这些表达式针对传统的传递矩阵方法和数值计算进行了验证。这项工作的结果提供了一种经过验证的通用方法，该方法提供了由复杂的孔或侧枝网络组成的介质声学特性的简单分析低频近似值。由任意数量的亥姆霍兹谐振器侧向加载。这些表达式针对传统的传递矩阵方法和数值计算进行了验证。这项工作的结果提供了一种经过验证的通用方法，该方法提供了由复杂的孔或侧枝网络组成的介质声学特性的简单分析低频近似值。