Research On Acoustic Radiation In Exterior Domains With The Boundary Knot Method

Prediction and control of the structural vibration and noise is an important subject for both civil and naval ships. It is of great engineering value to study the influence of the fluid boundary conditions on the vibration of underwater structures and the acoustic radiation from them. This thesis addresses a detailed numerical analysis on the acoustic radiation of underwater structures under three different fluid boundary conditions.Many meshless methods have been successfully proposed to solve a wide range of problems defined in a closed domain. However, exterior problems are commonly encountered in engineering practices. Based on radial basis functions (RBFs), nonsingular general solutions, and the dual reciprocity method (DRM), this thesis proposes a meshless solution to the Helmholtz equation posed in an infinite region. An exterior problem is reformulated into an equivalent interior problem via a coordinate transformation. The RBFs are employed to approximate the inhomogeneous terms using the DRM, while the nonsingular general solutions lead to a boundary-only approximation of the homogenous solution.Example acoustic radiation models are established in the 2D and 3D free spaces, the 3D half space, and a perfect shallow water waveguide. Numerical results obtained by the proposed method are compared with the corresponding analytical solutions. Good agreements are observed in all the models, which validates the accuracy and efficiency of the present method. Numerical experiments indicate that the number and the distribution of the source and the collocation points have crucial effects on the accuracy of the solutions. A rule of thumb is that using more source and collocation points well distributed in the solution domain usually results in a smaller error until a limit is reached.