“…Zhang et al (2020a) studied the frequency and mode of a flexible rotor system using Hamilton's principle and Euler's angle, and discussed the effect of centrifugal forces on the stability of the system. In recent years, researchers have been concerned with vibration of shafts under simultaneous effects of axial movement and rotational motion (Zhu and Chung, 2019;Ebrahimi-Mamaghani et al, 2021;Yang et al, 2021;Li et al, 2018;Katz, 2001). For example, applying the Hamilton principle, Zhu and Chung (2019) derived the governing equation of motion for a simply supported Rayleigh beam with spinning and axial motions.…”