Prediction of the elastic film effect on sound attenuation of custom molded solid earplugs using transfer matrices

In this paper, an analytical model of the air-conducted sound propagation in an earplug equipped with a film filter is proposed to explain and predict its acoustic attenuation. The model is developed using the transfer matrix (TM) method under the plane wave assumption, with the elastic film modeled as a prestressed circular plate based on the Kirchhoff-Love theory. This film is coupled with multiple interconnected air cavities to form the TM model of the earplug. The validity and limitations of the model are assessed through comparisons with numerical simulations using the finite element (FE) method. The predicted resonant frequencies deviate by less than 2% within the audible frequency band. The TM model is therefore considered useful to conduct parametric studies in order to provide a physical understanding of the predicted sound attenuation of film filters, as well as their optimization. The influence of the film parameters, such as mass, surface tension, and cavity geometrical parameters on the earplugs' sound attenuation is analyzed both qualitatively and quantitatively, with a focus on amplitude and characteristic frequencies.