Science in China Series A: Mathematics

, Volume 41, Issue 5, pp 527–533

# Modelling and bifurcation analysis of internal cantilever beam system on a steadily rotating ring

• Xiao Shifu
• Chen Bin
Article

## Abstract

Using Hamilton variation principle, a nonlinear dynamic model of the system with a finite deforming Rayleigh beam clamped radially to the interior of a rotating rigid ring, under the assumption that the constitutive relation of the beam is linearly elastic, is discussed. The bifurcation behavior of the simple system with the Euler-Bernoulli beam is also discussed. It is revealed that these two models have no influence on the critical bifurcation value and buckling solution in the steady state. Then we use the assumption model method to analyse the bifurcation behavior of the steadily rotating Euler-Bernoulli beam and get two different types of bifurcation behavior which physically exist. Finite element method and shooting method are used to verify the analytical results. The numerical results confirm our research conclusion.

## Keywords

Rayleigh beam model Euler-Bernoulli beam model bifurcation finite element method shooting method

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© Science in China Press 1998

## Authors and Affiliations

• Xiao Shifu
• 1
• Chen Bin
• 1
1. 1.Department of Mechanics & Engineering SciencePeking UniversityBeijingChina