Coupled Finite Element Method and Boundary Integral Equation for Axisymmetric!Acoustic Problems

• Main Authors: Lian, Sy-Huei, 連思惠
• Other Authors: Shu-Wei Wu
• Format: Others
• Language: zh-TW
• Published: 1996
• Online Access: http://ndltd.ncl.edu.tw/handle/89604099038184078402

碩士 === 國立中央大學 === 機械工程學系 === 84 === This study presents the application of the coupled Finite Element Method and Boundary Integral Equation for the determination of the acoustic potential fields induced in a full space by totally submerged axisymmetric bodies of arbitrary cross section with known vibrating boundary conditions. A Galerkin based isoparametric finite element formulation is developed to solve these acoustic problems. By taking advantage of a body's axisymmetric properties, the volumn integral is reduced to the surface integral. In this study, eight-noded quadratic, isoparametric quadrilateral elements are mainly used to discretise the acoustic domain under consideration. They are three- noded curvilinear elements in the boundary, which allow the qeometry and variables to vary quadratically over the boundary, thus offering good modelling capabilities. For exterior acoustic fields, where the fluid occupies an unbounded domain, the vast amount of data to be handled makes it difficult to apply the FEM in these problems. Adding the Helmholtz integral equations on the governing equation of the FEM is the main concept in this study. The nonuniqueness in the Helmholtz integral equation, which occurs at the internal eigenfrequencies of the geometry under consideration will be solved by using the boundary integral formulation of Burton and Miller. Applying the coupled Finite Element Method and Boundary Integral Equation in some foundamental acoustic radiation and scattering problems, the results we got are shown to be very accurate compared with the actual acoustic potential values. This numerical method not only eliminates the difficulties when the FEM handles the exterior acoustics, but it also cancels the singular kernel integral which is the most troubled problem in the Boundary Element Method. It is proved that this method is a practical and efficient numerical method in handling the acoustic problems.