Applied Mathematics and Mechanics

, Volume 20, Issue 10, pp 1167–1174

# Modeling and analysis of a coupled rigid-flexible system

• Hu Zhendong
• Hong Jiazhen
Article

## Abstract

Correct predictions of the behavior of flexible bodies undergoing large rigid-body motions and small elastic vibrations is a subject of major concern in the field of flexible multibody system dynamics. Because of failing to account for the effects of dynamic stiffening, conventional methods based on the linear theories can lead to erroneous results in many practical applications. In this paper, the idea of “centrifugal potential field”, which induced by large overall rotation is introduced, and the motion equation of a coupled rigid-flexible system by employing Hamilton's principle is established. Based on this equation, first it is proved that the elastic motion of the system has periodic property, then by using Frobenius' method its exact solution is obtained. The influences of large overall rigid motion on the elastic vibration mode shape and frequency are analysed through the numerical examples.

## Key words

coupled rigid-flexible system dynamic stiffening rigid-body motion elastic vibration periodic property

O313.7

## References

1. [1]
Kane T R, Ryan R R, Banerjee A K. Dynamics of a cantilever beam attached to a moving base[J].J Guid Control and Dynamics, 1987,10(2):139–151.Google Scholar
2. [2]
Bloch A M. Stability analysis of a rotating flexible system [J].Acta Applicandae Mathematicae, 1989,17(1):211–234.
3. [3]
Zhang D J, Huston R L. On dynamic stiffening of flexible bodies having high angular velocity[J].Mech Struct & Mach, 1996,24(3):313–329.Google Scholar
4. [4]
Simo J C, Vu-Quoc L. The role of non-linear theory in transient dynamic analysis of flexible structures[J].J Sound and Vibration, 1987,119:487–508.
5. [5]
Simo J C, Vu-Quoc L. On the dynamics of flexible bodies under large overall motion—the plane case, Parts I and II [J].J Appl Mech, 1986,53:849–869.
6. [6]
Haering W J, Ryan R R, Scott R A. New formulation for flexible beams undergoing large overall plane motion[J].J Guid Control and Dynamics, 1994,17:76–83.

© Editorial Committee of Applied Mathematics and Mechanics 1999

## Authors and Affiliations

• Hu Zhendong
• 1
• Hong Jiazhen
• 1
1. 1.Department of Engineering MechanicsShanghai Jiaotong UniversityShanghaiP R China