Modelling and bifurcation analysis of internal cantilever beam system on a steadily rotating ring |
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Authors: | Shifu Xiao Bin Chen |
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Institution: | (1) Department of Mechanics & Engineering Science, Peking University, 100871 Beijing, China |
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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.
Project supported by the National Natural Science Foundation of China (Grant No. 19332022) and Space High Technology Foundation
of China. |
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Keywords: | Rayleigh beam model Euler-Bernoulli beam model bifurcation finite element method shooting method |
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