Sound Absorption and Transmission Loss of Lightweight Powders Under Longitudinal Vibration: Application of a Frequency-Dependent Complex Modulus to a One-Dimensional Beam Model

A powder layer was treated as a one-dimensional beam undergoing longitudinal vibration, and the loss factor was derived from the damping ratio based on Rayleigh damping, thereby introducing frequency dependence into the complex modulus. The transfer matrix of the powder layer was subsequently formulated based on the complex modulus, and the validity and effectiveness of the proposed model were evaluated by comparing the calculated and measured values of transmission loss and sound-absorption coefficient. A loss correction was introduced to account for energy dissipation associated with viscous boundary-layer effects and other dissipative mechanisms. A parametric study of the loss correction was conducted, and the correction was quantitatively incorporated through curve fitting based on the root mean square error (RMSE). Comparison of theoretical and experimental transmission loss values revealed that the increasing trend in transmission loss at high frequencies was captured by the proposed model. In the comparison between the experimental and theoretical sound absorption coefficients, this evaluation approach places greater emphasis on the average degree of agreement across the full measurement frequency range rather than at specific frequency points. Consequently, the loss correction yielding the minimum error across the entire frequency range was selected, which occasionally resulted in differences in peak values near the first-order peak frequency.