Free vibration analysis of a rotating pre-twisted beam subjected to tendon-induced axial loading

The main objective of this paper is to investigate free vibration of a rotating pre-twisted beam with bending-bending-torsion coupling that is axially loaded by a tendon. The tendon is connected to the tip of the beam, passes through its body, and is fixed and loaded at the axis of rotation. Due to their connection, the motion of the beam influences the motion of the tendon and vice versa. The equations of motion of the beam-tendon system are introduced and solved numerically by a combination of a boundary value problem solver and differential quadrature method to obtain the natural frequencies and mode shapes of the system. The numerical implementation is firstly validated against literature for a non-rotating beam-tendon system and a rotating pre-twisted blade. Then, the effect of the tendon on the free vibration of the system is studied for a wide range of loading cases and rotation speeds. From the computed modal characteristics, it is found that the presence of a tendon leads to the frequency shift of beam's natural frequencies as well as frequency loci veering between the beam-dominated and tendon-dominated modes. Both of these effects strongly depend on the beam-tendon rotation speed.