Transverse vibration and dynamic stability analysis of slender projects under thrust

The paper discusses dynamic stability and frequency/mode characteristics of lateral vibration of slender projects under a thrust force. The slender project is idealized as a non-uniform beam, with the end rocket thrust defined as a follower force. Then the mathematic model for the vibration of a non-uniform beam with a follower force is built based on the extended Hamilton's principle for a non-conservative system. Finite element method is introduced in the simulation of the model; then the stability analyses of a uniform beam model and a simplified model of generic slender projects are carried out to obtain the vibration characteristics and dynamic stability of the two models, meanwhile, whose variation with the thrust force is analyzed. The results show that the follower thrust may cause the dynamic instability of slender projects; the thrust affects transverse vibration modes and frequencies; the thrust causes the moving of the trough along the body of the project, as well as the changing of mode amplitude.