Designing Sound Packages with the Transfer Matrix Method

This post on Innovation Intelligence is written by Luc Jaouen, an expert in the vibration and acoustics field and owner of MATELYS Research Lab. MATELYS is a member of the Altair Partner Alliance.

In the context of global competition and a desired reduction of our environmental footprint, sound packages used for the transport of goods, inside buildings, and within household appliances need to become more efficient. Many efforts have thus been made to increase our knowledge of porous media, like polymer foams or mineral fibers materials, which are key components of passive sound control treatments.

Porous media were first studied in our modern world for musical acoustics purposes. In the early 20th century, the petroleum industry addressed the wave propagation in soils (which are examples of porous media) to prospect for oil.

Since the 1980’s, specific theoretical and experimental developments related to acoustics have been conducted on porous media for the transportation and building industries. These efforts led to the creation of models which finely predict the vibro-acoustics performance of conventional porous media. Current development efforts focus on:

  1. Experimental characterization techniques, especially concerning the orthotropy of foams or fibrous materials
    • Models have reached a higher level of maturity than the experimental methods.
  2. Non-conventional porous media such as arrays of Helmholtz resonators or porous composites
    • Compared to common foams or fibrous materials, non-conventional materials add new physical phenomena, such as internal resonances, to dissipate more sound energy or to exhibit transmission band gaps.

When it comes to designing sound packages for industrial applications like a vehicle, a partition between two rooms of a building, or a vacuum cleaner, numerical implementations for acoustical porous media have been developed. These include the finite element method (FEM), the boundary element method (BEM), the ray tracing method, statistical energy analysis (SEA), and the transfer matrix method (TMM). FEM, while versatile, suffers from the large amount of numerical resources required to obtain a fine description of the physical phenomena occurring inside an acoustical porous medium. Indeed, four to six degrees of freedom per node are required, depending upon the implementation used. In contrast, TMM assumes plane layers of materials and is numerically inexpensive. Thus, interest in this method increased and was eventually found to be more adaptable than FEM to conduct preliminary design studies on sound packages.

In recent years, TMM has been further extended to account for things like connections between non successive layers or finite lateral dimensions of material layers. Today, this method may be considered to be a “pocket calculator” of sorts for modern acousticians. TMM is usually the first approach considered when implementing new models related to non-conventional porous media or to study their efficiencies.

AlphaCell is a TMM-based implementation, and provides a handy and efficient tool to design vibro-acoustics solutions. AlphaCell is a software product brought to HyperWorks® users by Matelys Research Lab, a French company and member of the Altair Partner Alliance. In 2012, Matelys was awarded the Industry Prize of SFA (French Acoustical Society), and in 2011 the Research Gold Decibel of CNB (National Council against Noise). Matelys is accredited by the French Ministry of Research.

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