Study on bearing force of marine propeller induced by longitudinal vibration of propulsion-shaftingFootnote^*

* This paper was completed under the collaboration of the whole team. The specific contributions were as follows. The first author Donglin Zou developed the theoretical models and MATLAB codes, performed the analyses and wrote the manuscript. Fangrui Lv and Na Ta post-processed the data. They also compared the calculation results with the experimental results. The corresponding author Zhushi Rao made a critical revision.

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