On Dynamic Behavior of a Cantilever Beam with Tip Mass in a Centrifugal Field

Abstract

The phenomenon of dynamic stiffening is a research field of general interest in flexible multi-body systems. In fact,there is dynamic stiffening as well as dynamic softening phenomenon in flexible multi-body systems. In this paper,a nonlinear dynamic model of a cantilever beam with tip mass in a centrifugal field is established by adopting the general Hamilton's Variational Principle. The dynamic behavior of the flexible multi-body system is studied by analytical,numerical,and experimental methods. The research indicates that the dynamic behavior of the flexible component can be affected by the overall motions of the system and the geometrical and physical parameters of the tip mass. The following conclusions are obtained. The overall motions can result in dynamic stiffening as well as dynamic softening of flexible components. The rigid body and the flexible components may bring about the coupling character of the mode. Dynamic softening may make the trivial equilibrium lose its stability through bifurcation and so on. Furthermore,the lower-order critical bifurcation values and the first buckled equilibria are investigated by employing approximately analytical and numerical methods. The result shows that the geometrical and physical parameters of the tip mass affect the critical bifurcation values and buckled equilibria significantly.

Key Words:

• Flexible multi-body system
• Dynamic stiffening
• Dynamic softening
• Stability
• Bifurcation
• Post-buckling

Notes

* Project supported by the National Natural Science Foundation of China (10272002) and the Doctoral Program from the Ministry of Education of China (20020001032).

Communicated by: F. Amirouche.