Theory and numerical method for the effects of hydrostatic pressure on sound absorption of underwater acoustic coatings with air cavities

A rubber layer embedded with air-filled cavities is often used as a coating of underwater structures for acoustic absorption. Previous studies have reported experimental results of the significant effect of hydrostatic pressure on acoustic properties of the acoustic coatings, but theoretical methods and physical mechanisms of the hydrostatic pressure effect have not been studied sufficiently. In this work, a linearization theory is proposed for representation of the acoustic scattering process of the coating with a large static predeformation caused by the hydrostatic pressure. A constitutive model with hyperelasticity and viscoelasticity is employed for characterizing the dynamic behavior of the rubber with a static predeformation. The corresponding numerical method is established by the procedure of finite element analysis and validated by experimental results from acoustic tests with a water-filled pressure tube system. The fields of deformation and incremental constitutive tensor are analyzed in detail for providing a comprehensive understanding of the physical mechanisms of the effects of hydrostatic pressure. As a consequence, the results indicate that not only the deformation of the cavities but also the prestress and predeformation induced change of the value of incremental constitutive tensor affect the acoustic absorption of the coating.