On the accuracy and optimization application of an axisymmetric simplified model for underwater sound absorption of anechoic coatings

The finite element method (FEM) is commonly used to analyze the underwater acoustic performances of rubbery coatings due to its flexibility to model scatterers of complex geometric dimensions. However, its calculation efficiency is always denounced as a drawback for its application on optimization design where a large number of repeated calculations should be fulfilled. In this paper, the accuracy of an axisymmetric simplified model, to model the unit cell as circular cross section, is systematically discussed by respectively comparing the absorption coefficients with those calculated by the square and hexagonal models under different punching rates of the cavities. Results show that the axisymmetric model can better describe the sound absorption of the coating with a hexagonal arrangement; however, it may cause comparative large deviations to describe the results of the coating with a square arrangement under not only large punching rates but also small punching rates. This phenomenon can be related to the different boundary differences between two arrangements of cavities and can be relieved when the rubber material possesses a large loss factor. Then, a shape optimization of the embedded cavity using the axisymmetric simplified model and a genetic algorithm has been done to achieve optimal sound absorption in 1-20 kHz. Compared with the coating with isochoric cylindrical cavities, the optimized coating can achieve better sound absorption in low frequencies due to the larger pore-aperture radius of the optimized cavity than that of the isochoric cylindrical cavity. The frequency-dependent parameters of the rubber material play an important role for the broadband high absorption of the optimized coating.