Vibration control of a rotating Timoshenko beam-tendon system via internal guiding inerter-dampers

Abstract A guided active tendon concept is proposed to modify the dynamics of the main rotor blades to enable the rotorcraft to operate at the wider range of working conditions. Because some blade modes are not sensitive to the applied axial force, in this paper, a new vibration suppression method for a rotating Timoshenko beam axially loaded by a tendon with the inerter-damper guiding elements is proposed and studied. The equations of motion are derived by means of the Lagrange's equation with the use of the energy expressions, and the modal and harmonic analyses are carried out. The analytical model is verified and compared with an independently formulated finite element model. It is found that inerter-dampers introduce non-local modes. To tune the chosen beam-dominated modes using inerter-dampers without introducing the additional resonances, the new optimal tuning strategy is used. When one inerter-damper is used, the inertance and damping coefficient for the optimal tuning of the higher modes are lower than those for the lower modes. When the inerter-damper is used to tune a single mode optimally, its function is analogous to a viscous damper for the lower modes, but it is similar to a rigid attachment for the higher modes. The maximum attainable damping ratio tends to decrease with the reduction of the applied axial force and increase of the rotational speed. The optimal performance of the single inerter-damper at different locations varies. For example, it is found that the damping ratio of the second beam-dominated mode reaches the maximum value with the inerter-damper located between 0.5-0.6L from the fixed end, where the required inertance and damping coefficient for the optimal tuning reach the minimum. More inerter-dampers can be used to tune a larger number of the beam-dominated modes optimally and simultaneously. The inerter-dampers are shown to effectively suppress the beam-dominated modes in wide axial force and speed ranges. In addition, inerter-dampers can be used to support the same function as the rigid tendon-guiding attachments of increasing the frequencies of the tendon-dominated modes. However, they cannot alter the critical compressive force. By integrating inerter-dampers into the tendon-loaded blades internally, the modes insensitive to the applied axial force can be suppressed to mitigate resonant vibrations.