High-accuracy Boundary Element Method Of Acoustic-structural Analysis For Thin-walled Structures

During the launching phase, spacecrafts will endure not only the ascending mechanical vibration generated by the rocket, but also the exhaust noise and aerodynamic noise coming through the fairings. Therefore, the coupling acoustic-structural problem is a critical part of mechanical environment prediction for spacecrafts, which plays an important role in guiding the spacecraft design. The frequency range of noise excitation is very broad, from 10 Hz to 10000 Hz. Due to highly random characteristics of the noise excitation of mid-frequency and high-frequency bands, can the statistical energy analysis method becomes the unique method. When the noise excitation is of low-frequency band, the coupling acoustic-structural characteristic is deterministic and obvious. Therefore, the boundary element method is an optional method and pertinent research is of important theoretical significance. In this thesis, a high-accuracy boundary element method frame is established to solve coupling acoustic-structural problem for thin-walled structures and some innovative achievements have been obtained in the following four aspects.Firstly, a new high-accuracy boundary element method is presented for solving acoustic problems. This new method is based on the acoustical Burton-Miller boundary integral equation, and including the following contents: adopting continuous acoustical elements which can keep the real boundary geometry, ensuring the integral precision of the production of kernel functions and interpolation functions over each element, obtaining the initial solution base on the original mesh, using the relative value of discontinuity of sound pressure gradient as an indicator to judge the convergence of the initial results and to guide mesh refined, computing again and judging whether another mesh refined needed up to obtaining a convergent result. In this thesis, spherical boundary is taken as an example and four types of spherical elements are constructed. The acoustical scattering benchmark is adopted to verify the discretization error indicator which is used to solve complex multi-sphere scattering problems.Secondly, calculating methods of singular integrals on spherical surfaces are developed. The final formulas of all the singular integrals on spherical elements are obtained. The methods proposed by Guiggiani and his coauthors are developed to evaluate hypersingular integrals on spherical elements. High accuracy of numerical results verifies the correctness of calculation of hypersingular integrals. For the first time, we applied the radial integral method proposed by Xiaowei Gao to evaluate hypersingular integrals in acoustic problems. And the two methods were compared.Thirdly, in order to establish a high-accuracy boundary element method for solving elastodynamics problems in frequency domain, effective methods are developed to ensure the integral precision of the production of kernel functions and interpolation functions, including: obtaining the final expressions of free term coefficients and calculating them directly, fulfilling the direct calculation of Cauchy principal value integrals on spherical elements and eight-node isoparametric elements.Fourthly, a high-accuracy boundary element method, that couples the integral equations of acoustic problem and elastodynamics problem in frequency domain directly, is established, which provides a new idea for solving acoustic-structural problems for thin-walled structures. The coupled equation is a full coupled boundary integral equation, therefore, all the fast algorithms in boundary element methods can be easily employed to accelerate computing, which provides the base for the establishment of high-performance boundary element method, i.e. the high-accuracy boundary element method with fast algorithms.