Turbine blades are modeled as cantilever beams on a disc rotating with a constant angular velocity. A study is conducted to understand the dynamic relationship between a rotating cantilever beam and various factors like pre-twist, hub radius, rotation speed, and slenderness ratio in in-plane and out-of-plane vibrations. Hub is assumed to be rigid in the study. Using Hamilton's principle, governing differential equations for free vibration analysis of Euler-Bernoulli beam, Timoshenko beam, and pre-twisted Timoshenko beam under rotation are derived. The effects of Coriolis are also taken into account in the equation. The equations' weak formulations are shown, and the beam model is further discretized using the Finite element approach. Derived differential equations are transformed into dimensionless quantities in which dimensionless parameters are identified. Numerical results for different rotational speed with and without hub radius are presented and it was observed that hub radius has a direct influence on the natural frequencies of the rotating uniform cantilever beam. A Campbell diagram is drawn to understand how natural frequencies are influenced by an increased rotational speed for all the three variants of the beams. A thorough comparative study on the influence of&nbsp;the slenderness ratio on the rotating uniform beam is&nbsp;discussed in the article.Keywords:&nbsp;Rotating beams, Hamilton’s principle, Natural frequencies, Pre-twisted Timoshenko beam.

Dynamic Modelling and Free Vibration Characteristics Analysis of Rotating Beams

Paper Proceedings: https://asmedigitalcollection.asme.org/GTINDIA/GTINDIA2021/volume/85536

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