Finite element boundary element numerical simulation study on acoustic vibration coupling problems

Excessive structural resonance response in the acoustic vibration coupling environment can cause adverse consequences such as structural damage, local instability, and component failure. Accurately predicting the vibration response of instruments under external sound fields helps to avoid structural performance degradation or damage caused by vibration, and ensures the reliability and safety of the system, which is of great significance for the effective load of instrument equipment. This paper constructs a finite element boundary element equation for the acoustic vibration coupling problem, and adopts a series of optimization measures for it. In response to the low computational efficiency of finite element boundary element equations and their inability to meet the computational requirements of complex models, this paper introduces the acoustic vibration reciprocity theorem and the fast directional boundary element method to compensate for the aforementioned shortcomings. In addition, the study used the weighted residual method to construct a data exchange algorithm to ensure energy conservation during the transfer process. The research focuses on typical structures of spacecraft and conducts simulation analysis and application research on acoustic vibration coupling problems. The simulation showcases that the introduction of the reciprocity theorem markedly reduces the calculation time and memory occupied by the equation, with a required calculation time of 1.23h and a data file size of approximately 299.56MB generated by the calculation; The overall error of the data exchange process is below 10−4. Scanning frequency analysis is conducted on the surface and local openings of the model structure, and it is found that the displacement of the selected excitation point is in good agreement with the analytical solution. This study effectively reduces simulation time and memory requirements through the proposed strategy, ensures energy conservation data exchange algorithms, improves the reliability and safety of structural design, and has important practical value for evaluating the structural performance of key equipment such as spacecraft.