Investigation of underwater sound scattering on a cylindrical shell coated with anechoic coatings by the finite element method based on an equivalent parameter inversion

Abstract

Anechoic coating attached to the surface of an underwater object is used for absorbing sound wave thereby reducing the reflection. The anechoic coating is often made of viscoelastic materials embedded with designed acoustic substructures, such as air cavities. The prediction of sound scattering on underwater object coated with such materials can be challenging due to the complex geometry of the anechoic coating, and it has been a research subject of interest in underwater acoustics. In this paper, we study the sound scattering on an infinite cylindrical shell coated with anechoic coating. Two types of coatings are considered: one is a layer of homogeneous isotropic material, and the other is a layer of homogeneous isotropic material with periodically embedded cylindrical air cavities. We use an equivalent method, in which the anechoic coating with air-filled cavities is regarded as a homogeneous isotropic material with equivalent material properties. The key point of the equivalent method is to ignore the internal structure of the anechoic coating, and the anechoic coating is considered as a homogeneous isotropic layer with the same complex reflection coefficient. These equivalent material properties are acquired based on the data of complex reflection coefficient obtained from either the physical experiment using water-filled impedance tube or the numerical experiment using the finite element method with COMSOL Mutiphysics software. Then a genetic algorithm is developed to inversely calculate the equivalent Young's modulus, Poisson's ratio, and damping loss factor of the coating which has the same reflection coefficient as the original coating. The results of the equivalent material properties show that 1) the three properties are all frequency dependent; 2) in general, equivalent Young's modulus increases with the increase of frequency, meanwhile the equivalent damping loss factor tends to decrease; 3) there is a wide variation in the results of equivalent Poisson's ratio. Despite that, the reflection coefficient of the equivalent homogeneous isotropic coating accords well with that of the original coating.Based on the above, the sound scattering on the infinite cylindrical shell coated with the equivalent coating is calculated by using the finite element method based on COMSOL Mutiphysics software. In order to verify the accuracy of the equivalent model, we use COMSOL Mutiphysics software to build up the full geometrical model of the coated shell to calculate the sound scattering. This can be considered as the benchmark. The results of morphic function show that the scattering calculated using equivalent material properties accords well with that obtained from the full finite element model with a mean error of about 1 dB in all frequency spectrum range.