Finite element method for analyzing environmental vibration without apparent sources and its application in Beijing High-Energy Photon Source

The environmental vibration without apparent sources refers to the vibration with very small amplitude in the field where there are no apparent excitation sources. It may significantly affect the normal operation of high-precision scientific apparatuses, and therefore appropriate methods are needed to analyze such environmental vibration precisely. A dynamic finite element method is introduced to analyze the environmental vibration without apparent sources in this study. Firstly, the time histories of vibration at the soil surface are obtained through the field measurements. Then, the transfer-matrix method is utilized to calculate the dispersion curve of the Rayleigh waves and the vibration attenuation factors with depth for each frequency. With the measured time histories on the ground and the attenuation factors, the time histories at different depths can be calculated. The calculated time history at each node is applied to the corresponding node on the finite element model boundary, which ensures the similarity of vibration conditions in the model and the reality. Finally, the proposed method is adopted to analyze the environmental vibration of the raft foundation of High-Energy Photon Source (HEPS). The results indicate that the proposed method can successfully capture the characteristics of vibration without apparent sources and provide useful reference for similar projects.