Analysis of bending-torsional-axial vibration of multi-stage variable-section shaft system

Abstract

To examine the geometric relationships and mechanical characteristics of a variable-section beam, a Timoshenko beam model was selected. The finite element method (FEM) was applied to derive each coefficient matrix of the bending-torsional axial vibrations of a variable-section shaft system and the geometric matrix constructed by the axial load. The differential equations of motion of the variable-section shaft system were constructed by combining the bearing characteristics. The frequencies of single-stage and multi-stage beams under different boundary conditions were investigated separately, verifying the correctness of the simulations. Furthermore, the analysis methodology of the rotating shaft system was proposed, the vibration characteristics of the rotating variable-section shaft system and the rotating stepped-shaft system were analyzed and compared, the vibration mode shapes of the shaft system under different axial loads were studied, and the unbalanced response characteristics of the rotating shaft system were obtained. This work provides guidelines for improving the stability of shaft system operation. The results of this study provide a dynamic description of shaft systems.

Keywords

• Finite element method (FEM)
• Axial load
• Rotating shaft system
• Vibration mode
• Unbalanced response