Dynamic analysis of semi-rigidly connected and partially embedded piles via the method of reverberation-ray matrix

Free vibration and dynamic responses of piles semi-rigidly connected with the superstructures are investigated. Timoshenko beam theory is employed to characterize the pile partially embedded in a two-parameter elastic foundation. The formulations for the method of reverberation-ray matrix (MRRM) are then derived to investigate the dynamics of the pile with surface cracks, which are modeled as massless rotational springs. Comparison with existent numerical and experimental results indicates the proposed method is very effective and accurate for dynamic analysis, especially in the high frequency range. Finally, the effects of some physical parameters on the natural frequencies, frequency responses and transient responses of the piles are studied.