Abstract
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.
Highlights
The transfer matrix method (TMM) is a simple and powerful method to model acoustical systems
It has proven to be a popular technique in order to model multilayered porous materials [5], parallel assemblies of porous materials [6] and sound absorbing acoustic metamaterials consisting of waveguide structures side-loaded by Helmholtz resonators [7,8]
The methodology developed in this paper can be applied to derive effective properties of a waveguide side loaded with Helmholtz resonators
Summary
The transfer matrix method (TMM) is a simple and powerful method to model acoustical systems. In the acoustics of porous materials, sound propagation in rigid tortuous pores is modelled with the linear superposition of the macroscopic pressure gradient and the averaged velocity within pore segments of constant cross-section This approach of discretising pores into segments was used in the Champoux and Stinson model [9] to determine the effective density and compressibility and enables the building of simple acoustical models. A general methodology is proposed to obtain simple analytical expressions for the effective material properties for systems that can be modelled with the TMM. Simple general expressions for the effective dynamic density and complex compressibility are obtained for a waveguide side-loaded by an arbitrary number of Helmholtz resonators These expressions are validated against results obtained using the traditional TMM and numerically.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
