A mathematical model to describe the seismic vibrator and ground coupling is proposed based on dynamic analyses of the vibrator baseplate structure and properties of soil. This mathematical model is solved using Newmark’s method. It produces reasonable results and the trend of amplitude envelope follows the experimental data. With this model, characterization of the vibrator-ground coupling is performed. Modal analysis study shows that the motions between the vibrator reaction mass and baseplate experience a combination of a first-order vibration mode and a second-order vibration mode. The corresponding frequencies of two vibration modes are located at 2.77 Hz and 488.7 Hz, respectively. As the frequency goes up, the motion behavior of the reaction mass and baseplate is dominated by the second-order vibration mode. It is realized that the second-order vibration mode is responsible for the phase difference between the input sweep signal and the output force signal. Furthermore, the impact of the coupling system parameters on the vibrator output force is also investigated. It is observed that the vibrator output force decreases as the sweep frequency increases. The weight ratio of the reaction mass and the baseplate has an impact on the vibrator output force.
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