spinning beam

critical speed

warping

coupled flexural-torsional vibration

The structural modeling and dynamic properties of a spinning beam with an unsymmetrical cross section are studied. Due to the eccentricity and spinning, transverse deflections along the two principal directions and the torsional motion about the longitudinal axis are coupled. The structural model of the beam is established based on the Hamilton principle and by incorporating the torsional inertia. Moreover, because of its significant influence on characteristics for the non-circular cross-sectional beam, the warping effect is considered in the formulation. The proposed model is effectively validated in two cases: the spinning beam with a symmetric cross section and the cantilevered beam with an unsymmetrical cross section. Then the effects of the spinning speed on natural frequencies and mode shapes are investigated. Numerical results reveal that the critical speed is altered with respect to noncoincidence of the centroid and the shear center. For the beams with strong warping rigidities, the warping effect cannot be neglected due to significant influence on natural frequencies.