Research on Acoustic Boundary Conditions under Micro-amplitude Vibration of Object Surface

Abstract When calculating the radiation of sound from a solid to a surrounding fluid medium, the governing equation of the sound field is generally expressed using the Euler method; When describing the acoustic boundary conditions of solids, it is assumed that the solid surface continuously vibrates, thereby radiating sound to distant areas through the surrounding fluid medium. This is described using the Lagrangian method. In existing literature, the motion of the interface is generally not considered and a given vibration velocity condition is directly applied at the equilibrium position. This can cause some confusion: since the interface is also in motion, although it may be small, should this small motion also have an impact on the results. In the article, the conventional approach of not considering interface motion was used to solve for the radiation sound of pulsating spheres. Then, with the small displacement of the boundary as the small parameter, the results were obtained using the regular perturbation method. The two results were very close, which proves the rationality of using linear boundary conditions. The solving process in this article is quite complicated and only applies to objects with regular shapes. However, the results under nonlinear boundary conditions are provided, indicating that micro motion boundaries can indeed bring certain errors. If the boundary is a large amplitude motion, the formulation of the equation and the solution method still need further research.