Based on the Timoshenko beam theory,a novel mathematical model of a rotating shaft with centrifugal terms is developed by using Hamilton^principle and Euler angles.The associated conventional model is provided for com...Based on the Timoshenko beam theory,a novel mathematical model of a rotating shaft with centrifugal terms is developed by using Hamilton^principle and Euler angles.The associated conventional model is provided for comparison purpose.The features of the proposed mathematical model are discussed based on some selected coordinate systems.The frequencies and modes are investigated to show the influences of centrifugal terms on the stability of the gyroscopic systems.The results show that the novel model proposed may lose stability due to the centrifugal terms.It is also found that the backward precession mode can be changed into a forward one beyond the critical rotating velocity.展开更多
基金the National Natural Science Foundation of China(Project Nos.11972050,11672007,11832002)Beijing Natural Science Foundation(Project No.3172003).
文摘Based on the Timoshenko beam theory,a novel mathematical model of a rotating shaft with centrifugal terms is developed by using Hamilton^principle and Euler angles.The associated conventional model is provided for comparison purpose.The features of the proposed mathematical model are discussed based on some selected coordinate systems.The frequencies and modes are investigated to show the influences of centrifugal terms on the stability of the gyroscopic systems.The results show that the novel model proposed may lose stability due to the centrifugal terms.It is also found that the backward precession mode can be changed into a forward one beyond the critical rotating velocity.
