Nonlinear Vibration Analysis of Discontinuous Coupled, spinning Timoshenko Beams
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The 8th IFToMM International Conference on Rotor Dynamics
This paper deals with coupled rotating Timoshenko beams. In order to reduce calculation time and increase the accuracy it is adjuvant to use semi - analytical methods instead of numerical Finite Element (FE) ? approaches. During the run up and down of such devices, the entire speed range of the rotors is passed trough, therefore it is necessary to take the coupling of torsional- and bending vibrations in a nonlinear simulation model into account. The equations of motion are derived using the Projection equation in subsystem representation, leading to partial differential equations. Employing the Transfer ? Matrix ? Method (TMM) to the linearized system delivers adequate ansatz functions for the implemented Galerkin ? Method. Applying the TMM facilitates a solution for the partial differential equations of the discontinuous beam system. Minor changes are required for coupling several beams with discrete or distributed springs. These springs are realized by linear or nonlinear forces acting on the beams causing nonlinear interactions. Coupling of beams is essential for the vibration analysis of structures. Calculated results are presented and compared to a FE solution.