Theoretical Analysis of Low-Frequency Sound Absorption Owing to the Vibration of Lightweight Powder Using a 1D Beam Model

Lightweight powder-based sound-absorbing materials are characterized by sound absorption peaks at lower frequencies compared to other sound absorption materials of the same thickness. This behavior is attributed to the excitation of longitudinal vibration modes in the powder particles by incident sound waves, wherein acoustic energy is converted into kinetic energy and subsequently dissipated through interparticle interactions. These lightweight, fine powders are artificially engineered acoustic materials. Despite their structural simplicity, they exhibit emergent and complex sound absorption behaviors through fundamental vibrational mechanisms. Representing the powder layer with a transfer matrix simplifies model-based development and enhances versatility as an acoustic element. The powder layer was modeled as a longitudinally oscillating 1D beam, and transfer matrix of the powder layer was derived. To verify the obtained transfer matrix, the experimental values were compared with the theoretical values for a single powder layer. In addition, both were compared for the case of other acoustic elements stacked on top of each other, which were close to each other. The theoretical values were compared with the experimental values, which were close to each other.