Sound-absorbing coatings with nonlinear elastic modulus

This study proposes a nonlinear model for cavity-type underwater anechoic coatings by using a complex Young's modulus that depends on acoustic frequency and incident sound pressure. The nonlinear modulus is represented by the Kraus model, whose parameters are obtained by fitting frequency-extended Dynamic Mechanical Analysis data of rubber from the literature. The absorption results of the nonlinear model are obtained iteratively using the Newton-Raphson method. At low incident sound pressures, the numerical model approaches the linear limit, and its results agree well with the analytical solutions obtained from the transfer matrix method. Acoustic frequency and incident sound pressure affect the frequency and intensity of cavity resonance through the nonlinear modulus. Consequently, compared with the linear model, the resonance-induced peaks of the absorption coefficient predicted by the nonlinear model are enhanced and shifted to lower frequencies with increasing incident sound pressure and also enhanced and shifted to higher frequencies with frequency dependence. Compared with experimental sound absorption data from the literature, the nonlinear model captures all experimentally observed absorption peaks, reducing the average error in predicting the peak frequencies by 33.0% to 55.9% over linear models across the three configurations. Overall, the introduction of material nonlinearity improves the prediction accuracy.