It can be a difficult problem to precisely predict the acoustic field radiated from a finite elastic structure in shallow water channel because of its strong coupling with up-down boundaries and the fluid medium, whose acoustic field cannot be calculated directly by existing methods, such as Ray theory, normal mode theory and other different methods, which are adaptable to sound fields from idealized point sources in waveguide. So, there is no reliable research method of predicting the acoustic radiation of elastic structure in shallow water at present. Based on the finite element method (FEM) coupled with the parabolic equation (PE), the theoretical model for structure acoustic radiation in shallow water at low frequency is established in this paper. This model mainly consists of three sections. First, obtaining the near-field vibro-acoustic characteristics of the elastic structure in shallow water by the multi-physics coupling model established by FEM, whose FEM model includes the up-down boundaries and the completely absorbent sound boundaries in the horizontal direction. Second, getting the acoustic information in the depth, which is set as the acoustic input condition i.e. starting field for the PE. Third, the acoustic information in the far-field quickly calculated by the PE and the finite difference method (FDM). The accuracy, efficiency and fast convergence of FEM-PE method are validated by numerical simulation and theoretical analysis through using a monopole source and structural source in the Pekeris waveguide, respectively. The vibro-acoustic characteristics of elastic cylinder influenced by upper and lower fluid boundaries of the Pekeris waveguide are calculated and analyzed. The cylindrical shell material is steel, and it is 1 m in radius and 10 m in length. The shallow water channel is a Pekeris waveguide with 30 m in depth, at the upper boundary, i.e., the free surface, the lower boundary is the semi-infinite liquid boundary. The analyzed frequencies range from 50 Hz to 200 Hz. The study shows that when the cylindrical shell approaches to the sea surface or bottom, the coupled frequency is higher or lower respectively than that of the shell immersed in the free field. When the diving depth reaches a certain distance range, the coupled frequency tends to be the same as that in free field. The acoustic field radiated from an elastic shell in Pekeris waveguide is similar to that from a point source at low frequency, but there exists a significant difference in high frequency between them, so the structural source can be equivalent to a point source conditionally. The sound radiation attenuation of the structure happens in sequence according to the near-field acoustic shadow zone, the spherical wave attenuation zone, the region between spherical wave and the cylindrical wave attenuation zone, and the cylindrical wave attenuation zone.
Owing to the decomposition of organic material and other reasons, the actual marine sediment contains gas bubbles, and the existence of gas bubbles will significantly affect the low-frequency acoustic characteristics of sediment. Therefore, it is significant to investigate the effect of gas bubbles on the low-frequency sound velocity in the sediment. Considering the uncontrollable environmental factors of field experiment, an experiment platform for obtaining acoustic characteristics of a large-scale gas-bearing unsaturated sandy sediment is constructed in the indoor water tank. Considering the long wavelength of low-frequency acoustic wave and the multipath interference in water tank, the transmitted acoustic signals are received by hydrophones which are buried in the unsaturated sediment. The sound velocity data (79-142 m/s) in the gas-bearing unsaturated sediment are acquired by using a multi-hydrophone inversion method in the bounded space for the first time in a 300-3000 Hz range, and the sound velocity data (112-121 m/s) are also acquired by using a double-hydrophone method in the same frequency range. The refraction experiments at different horizontal distances between the source and the hydrophones are conducted, which verifies the reliability of sound velocity data acquired by using the multi-hydrophone inversion method and the double-hydrophone method. At the acoustic frequency well below the resonance frequency of the largest bubble in the sediment, the pore water and the gas bubbles are regarded as an effective uniform fluid based on effective medium theory. On this basis, the density and the bulk elastic modulus of pore water in the effective density fluid model are replaced by the effective density and the effective bulk modulus of the effective uniform fluid, then a corrected effective density fluid model is proposed in gas-bearing unsaturated sediment. The numerical analysis indicates that when the gas bubble volume fraction is small (1%), a small increase in the gas bubble will cause a significant decrease in the effective bulk elastic modulus of sediment, but the density of pore water is much greater than the density of gas bubbles, the presence of a small number of gas bubbles hardly changes the density of pore fluid and certainly does not change the density of sediment, which results in a significant decrease at a low-frequency sound velocity in the gas-bearing unsaturated sediment. Furthermore, with the increase of gas bubble volume fraction, the sound velocity predicted by the corrected model gradually decreases, and the decreasing trend gradually becomes gentle. The corrected model reveals the effect of gas bubbles on the low-frequency acoustic characteristic of sediment. By analyzing the sensitivity of the predicted sound velocity to parameters of the model, the gas bubble volume fractions (1.07%-2.81%) of different areas are acquired by inversion according to the measured sound velocity distribution and the corrected model. In the future, it will provide a new method of obtaining the volume fraction and the distribution of gas bubbles in the sediment.
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