Research On Principle And Numericle Method Of Sound Radiation For Structure

In this dissertation, based on the discussed history of numerical method of structure-born sound radiation, the boundary element integral equation is deduced, and then the numerical method of sound radiation, the theory of radiation modal and the sound radiation sensitivity analysis is discussed in details. The two key problems of BEM, namely singular integral and multi-frequency calculation, are studied in details based on the BEM method, and two valid numerical methods is posted, and sound radiation mode and sensitivity analysis of complex structure is also studied, the theory of sound radiation mode explain the principle of structural sound radiation, last, the validity of those methods is tested by experiments. The history and development of numerical method of sound radiation, modal theory and sensitivity analysis is reviewed, and the key problems about those theories are presented, last, the main studied works of this dissertation are summarized. Then the boundary element integral equation of interior and exterior form is deduced in detail, also the form with corner coefficient. The significance for numerical calculation and principle of the singular integral is analyzed, and a non-isoparametric transformation method is presented to calculate weak singular integral and Cauchy integral, the method presented provides us a very simple way to computer the two kinds of singular integral of Helmholtz boundary integral equation, and it is easy to program in computer. After the difficulty of the calculation for multi-frequency of Helmholtz boundary element is explained, a method named SECHIEF (Series Expansion Combined Helmholtz Integral Equation Formulation), which is focused on the computational efficiency, is presented. The method can not only provide uniqueness of solution and reduce the computational time but also give accurate results under the coarse elements. The essential of this method is to enhance the computational efficiency by increasing the use of disc space. For the problems of non-uniqueness, the CHIEF method is used to overcome it, and the CHIEF equation is also expanded by series. Based on the previous results, the principle of structral sound radiation is studied by the theory of structrural sound radiation mode. According to the studied results at present, the studied objects are mainly thin plate and beam about sound radiation mode, a method computed sound radiation mode of complex structure is presented in this dissertation, according to the results of the previous two chapter, a theoretical method to solve acoustical radiation mode and acoustical radiation efficiency of complex structure by boundary element method and acoustical radiation theory is posed, the acoustical radiation power is expressed as a Hermitian quadratic form, while the radiation modes is determined by general eigenvalue decomposing, and then the radiation efficiency is computed via the orthodoxy of radiation modes with regard to impedance matrix and average velocity matrix; lastly, the validity of the method is proved by pulsating sphere and radiating cube with analytical results. According to results of the form three chapter, the structure sound radiation sensitivity is studied in detail, the sound radiation power of structure can be expressed as positive Hermitian quadratic form, the sound radiation sensitivity can be expressed as two parts by partial differential with respect to design variable, which are sensitivity of boundary velocity and impedance matrix, combined with the theory of FEM and BEM, the structure sound radiation can be translated to the analysis of structure dynamic sensitivity and impedance matrix sensitivity. The theory posted in this dissertation is tested by the FEM software ANSYS and the software AAS(Advanced Acoustic Simulation) programmed by author. Lastly, the summarization and expectation are given.