| With the development of the numerical techniques and the computer performance, engineers can predict the acoustic performance of industrial products and proposes schemes to improve the acoustic performance by using some numerical methods. Some acoustic engineering problems which can not be predicted previously can be simulated currently by using the numerical methods, and the computational acoustics has become a key technology of forecasting and controlling of noise. In the past decades, there has been an increasing interest in the simulation of noise, either to satisfy more and more stringent national and international standards or to improve end-user’s comfort. The numerical simulation of the elastic and acoustic wave propagation, addressed by the Helmholtz equation, is a field of intense developments. The search for simple, efficient and accurate numerical methods applicable to acoustic problem, has been receiving much interest.It is well-known that one key issue of solving the Helmholtz equation using numerical method is the accuracy deterioration in the solution with increasing wave number due to the "numerical dispersion error". In order to improve the accuracy of numerical solution, this dissertation makes an intensive and systemic study of the acoustic smoothed finite element method, the cell-based smoothed radial point interpolation method, the finite element-least square point interpolation method and the finite element-radial point interpolation method. These methods are applied to solve some engineering problems, including the acoustic simulation of "Zhongqi Specific Projects" car and the coupled analysis of mirco-car structural-acoustic models.The main research work and innovative achievements in this dissertation are:(1) The "overly-stiff" property of acoustic finite element method leads to biggish numerical dispersion error, and the accuracy is easily affected by the mesh quality and the wave number. Aim at this problem, the cell-based smoothed theory is extended to the field of acoustic numerical simulation and the acoustic gradient cell-based smoothing operation is proposed, and then the basic formulation of the acoustic smoothed finite element method (SFEM) is induced. Numerical examples, such as the two-dimensional acoustic square domain model and the cavity model of "Zhongqi Specific Projects" car, are analyzed intensively. The relationship, between the accuracy and the factors, such as the mesh quality and the wave number, is obtained. The results show that, compared to the corresponding FEM, the error of the acoustic SFEM model is smaller, and the numerical solution is more insusceptible to the mesh quality and the wave number. Hence, the acoustic SFEM model is more suitable than FEM model to analyze engineering problem with severe element distortion and high wave number.(2) The results of structural-acoustic problems using the FEM are susceptible to the element size and the analytical frequency because of the numerical dispersion error. Aim at this problem, the smoothed finite element method is extended to the coupled analysis of structural-acoustic problems, and then the SFEM/FEM and SFEM/BEM are further derived for the analysis of structural-acoustic problems. The basic formulations of SFEM/FEM and SFEM/BEM are induced, respectively. The investigation of numerical examples and engineering applications show that, the accuracy and efficiency of the SFEM/BEM and SFEM/FEM is higher than that of the corresponding SFEM/BEM and SFEM/FEM, respectively. Hence, the SFEM/BEM and SFEM/FEM have great potential in the practical analysis of engineering problems.(3) In order to reduce the numerical dispersion error of meshless methods, a cell-based smoothed radial point interpolation method (CS-RPIM) is extended to the field of acoustic numerical simulation by incorporating the cell-based acoustic gradient smoothing operation into the radial point interpolation method, and then the basic formulation of cell-based smoothed radial point interpolation method for acoustic problems is induced. At the same time, the great advantage of the method in demand of mesh quality, calculation precision and wave number are proved.(4) The FEM model is in general overly-stiff; the meshless methods are complex and suffer from numerical instability. In order to overcome these problems, the strategy, which is presented by incorporating the meshless method and FEM, is extended to the field of acoustic numerical simulation, and the finite element-least square point interpolation method is investigated as well as the basic formulations are induced. The results of numerical examples show that, the error of acoustic FE-LSPIM model is smaller and the approximate solution is more insusceptible to the mesh quality and the wave number as compared to the FEM and EFGM. Hence, the acoustic FE-LSPIM model is more suitable than the corresponding FEM and EFGM model to analyze engineering problems with low quality mesh.(5) According to the basic ideas of FE-LSPIM, the finite element-the radial point interpolation method (FE-RPIM) is proposed and extended to the field of acoustic numerical simulation. The shape functions of the FE-RPIM inherit the compatibility properties of finite element method and the Kronecker-delta property of the radial point interpolation method (RPIM). Unlike the FE-LSPIM, the local approximation in FE-RPIM doesn’t use the least-square point interpolation method but uses the radial point interpolation method. Numerical tests demonstrate that the accuracy and convergence property of the acoustic FE-RPIM are more excellent than the FEM and FE-LSPIM.(6) This dissertation analyzes some engineering problems, such as the "Zhongqi Specific Projects" car’s cavity model and the mirco-car structural-acoustic coupled model. The analysis results show the effectiveness and superiority of proposed methods.A detail study for the acoustic numerical computation method is implemented in this dissertation. Some acoustic numerical methods such as the smoothed finite element method, the cell-based smoothed radial point interpolation method, the finite element-the least square point interpolation method and the finite element-the radial point interpolation method, are proposed to the acoustic problems. The Research findings can be applied to solving the acoustic problems and has more engineering application foreground.The research of this dissertation is supported by the national major projects called "Yueshen program"-the high level of automotive innovation capacity building (referred to as "Zhongqi Specific Projects") and the program for Changjiang Scholar and Innovative Research Team in University (5311050050037). |
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