Dynamic modeling and coupling characteristics of rotating inclined beams with twisted-shape sections

Abstract

In the existing literature, most studies investigated the free vibrations of a rotating pre-twisted cantilever beam; however, few considered the effect of the elasticsupport boundary and the quantification of modal coupling degree among different vibration directions. In addition, Coriolis, spin softening, and centrifugal stiffening effects are not fully included in the derived equations of motion of a rotating beam in most literature, especially the centrifugal stiffening effect in torsional direction. Considering these deficiencies, this study established a coupled flapwise–chordwise–axial–torsional dynamic model of a rotating double-tapered, pre-twisted, and inclined Timoshenko beam with elastic supports based on the semi-analytic method. Then, the proposed model was verified with experiments and ANSYS models using Beam188 and Shell181 elements. Finally, the effects of setting and pretwisted angles on the degree of coupling among flapwise, chordwise, and torsional directions were quantified via modal strain energy ratios. Results showed that 1) the appearance of torsional vibration originates from the combined effect of flapwise–torsional and chordwise–torsional couplings dependent on the Coriolis effect, and that 2) the flapwise–chordwise coupling caused by the pure pre-twisted angle is stronger than that caused by the pure setting angle.