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Modelling and bifurcation analysis of internal cantilever beam system on a steadily rotating ring. (English) Zbl 0908.73035
Summary: Using Hamilton’s variation principle, we examine a nonlinear dynamic model of the system with a finitely 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. 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 a model method to analyse the bifurcation behavior of the steadily rotating Euler-Bernoulli beam, and obtain two different types of bifurcation behavior which physically exist. Finite element method and shooting method are used to verify the analytical results.

##### MSC:
 74H55 Stability of dynamical problems in solid mechanics 74H45 Vibrations in dynamical problems in solid mechanics 74K10 Rods (beams, columns, shafts, arches, rings, etc.) 74S05 Finite element methods applied to problems in solid mechanics
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