Simulation For Mid-frequency Acoustic Problems Of Ship Using The Smoothed Point Interpolation Method

With the increasing demand for concealing of military vessels and comfortableness of civil ships,acoustics requirements should be fully considered during the ship design stage.By this way,we can avoid repeated design and manufacturing,reduce construction costs and accelerate construction progress.In this process,accurate and effective numerical simulation of acoustic problems is needed for guiding the structural acoustic design of ships.And the numerical simulation of ship structures' mid-frequency acoustics has always been one of the problems to be solved urgently.It has been found that the original reason for the traditional finite element method(FEM)model's serious dispersion error in the mid-frequency acoustic simulation is the overly-stiff nature.By introducing the generalized gradient smoothing technique(GGST),the cell-based smoothed radial point interpolation methods(CSRPIMs)are applied to solve three-dimensional acoustic problems of ship structures.The author studies the modal stiffness of the existing CSRPIMs and their influences on the results,and proposes an idea to control the modal stiffness effectively.Based on this theory,a novel cell-based smoothed radial point interpolation method with eight virtual nodes,called CSRPIM-T5-Cd8,is presented in this paper.In order to verify the accuracy of the proposed method,harmonic response analysis and eigenvalue calculation are conducted to the examples of a tube,which showed that the accuracy and computational efficiency of the proposed method are of great improvement compared with the FEM using four-node tetrahedron element(FEM-T4).The proposed method's performance even exceeds that of the FEM suing eight-node hexahedron elements with modified integration rules(MIR-H8),especially in the mid-frequency range.Meanwhile,CSRPIM-T5-Cd8 uses tetrahedron elements generated by commercial software automatically as the background meshes and performs insensitively to mesh distortion,which can reduce the preprocessing time and has great potential for engineering application.For further study,the proposed CSRPIM-T5-Cd8 is applied to the acoustic problems,such as the internal noise of ship engine cabin and underwater noise radiated from structures,for verifying the practicality of the method.It can be found that compared to FEM-T4,CSRPIM-T5-Cd8 can effectively reduce the dispersion error for both the internal acoustic problems and the external acoustic problems,which makes it perform well in the mid-frequency range.Therefore,the proposed method has a promising future in engineering numerical simulations for mid-frequency acoustic problems.At last,the structural-acoustic coupling analysis is carried out by combining two-dimensional Mindlin plate element based on edge-based smoothed finite element method(ESFEM)and three-dimensional acoustic element based on CSRPIM-T5-Cd8.The study finds that the ESFEM/CSRPIM-T5-Cd8 coupling method not only provides coupling frequencies close to the reference solutions,but also extends the computable range of frequency response analysis owing to the reasonable construction of structural stiffness and acoustic stiffness.