Investigation of the effects of frequency veering phenomenon in a pre-twisted and double-tapered rotating Timoshenko beam

Abstract

The natural frequency curve veering phenomena have been significant and used in several structural dynamic problems. By formulating a pre-twisted and double-tapered rotating Timoshenko beam as a structural problem, variations in mode interactions among coupled axial, chordwise, and flapwise motions were presented. Rotordynamic effects such as gyroscopic couple, centrifugal stiffening, and spin softening effects were taken into account while establishing the equations of motion. Hamilton’s principle was used in deriving the equations of motion and is discretized based on Galerkin finite element method. Using dimensionless parameters, the model was verified with the existing literature for rotation, pre-twist, and double-taper configurations. A comparison of the frequency veering regions among the Euler–Bernoulli beam and Timoshenko beam theories is presented. Two-dimensional mode shape plots were used to show the coupled motions between axial displacement, chordwise bending, and flapwise bending. The effects of pre-twist and double-taper in the non-rotating Timoshenko beam on the modal properties of the rotating beam were examined. Natural frequency maps were drawn to locate the frequency veering curves. Mode interactions around different veering regions were shown with variations in mode shapes. An investigation on 60° pre-twisted and 0.5 ratio double-tapered rotating Timoshenko beam is presented.