On the rotating beam: Some theoretical and numerical results
The authors study in this clearly written paper the nonlinear plane buckling problem of a beam rotating about its axis, which is clamped at one end and free at the other. By means of Lyapunov Schmidt reduction and singularity theory in the spirit of \textit{M. Golubitsky} and \textit{D. Schaeffer} [e.g. Lect. Notes Pure Appl. Math. 54, 229-254 (1980; Zbl 0438.73044) and Commun. Pure Appl. Math. 32, 21-98 (1979; Zbl 0409.58007)] the complete set of all local solutions of the imperfect problem is given. Finally by means of finite difference methods numerical solutions of the nonlinear boundary value problem are compared with local bifurcation solutions.
Golubitsky-Schaeffer theory of singularities
rotation velocity as bifurcation parameter
constants describing position of beam are considered as small perturbation parameters
compared with local bifurcation solutions
scientific article; zbMATH DE number 3915750