Aeroelastic eigenvalue analysis of a variable speed rotor blade with an applied compressive load

Abstract

Variable speed rotors are one possible way to meet the industry's increasing demands on noise emissions, flight envelopes and power requirements. The use of this technology is largely prohibited due to the presence of dynamic interactions at various rotor speeds that would lead to excessive vibratory loads. One concept being considered to overcome this is modal tuning by means of an applied compressive load. Herein, the impact of the combined effects of compressive loading, aerodynamic loading in hover and reduced rotor speeds on rotor blade's aeroelastic properties are investigated. A structurally nonlinear blade model directly coupled with an unsteady aerodynamic blade element model is formulated and verified. The model is used to show that moderate static deformations due to aerodynamic loads can introduce stiffening as well as softening effects. Compressive loading is then applied and it is shown that even at large compressive loads the blade's internal tension remains dominated by centrifugal loading. Finally, a study of the change in natural frequencies and damping ratios at various rotor speeds and compressive loadings is performed. It shows that natural frequencies and damping ratios are both affected by changing rotor speed and compressive load and that the sensitivity to the compressive load is greatest at lower rotor speeds.

Free vibration and stability analysis of a cantilever beam axially loaded by an intermittently attached tendon

“…The use of a tendon as the tunable vibration absorber in the helicopter tail boom was studied in [23] while the longitudinal tensile loads were proposed as a means for resonance avoidance in the spinning shafts operating at the supercritical speeds [24]. The idea to incorporate a tendon in the rotorcraft blade to introduce a means of controlling its dynamics was originally proposed in [25]. Since then, it was shown that the blade-tendon system with a free tendon can be used as a means of resonance avoidance [26][27][28].…”

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

“…The present paper was motivated by the future application of an active tendon concept in rotorcraft as investigated within the SABRE project [1,3]. It was already shown [2,38] that the axial force alone has potential to allow rotorcraft to operate with variable rotor speed. This paper indicates that the tendon can be used to induce this axial force which consequently reduces the natural frequencies of the blade.…”

Theoretical and experimental free vibration analysis of a beam-tendon system with an eccentrically placed tendon

“…For the axial force applied through the elastic axis, and neglecting the effect of warping and the cross-sectional parameter β y , Eqs. (1a)-(1c) augmented by the effect of centrifugal forces and beam pre-twist were used in [28,29] to demonstrate a possibility of using the axial force for resonance avoidance in rotorcraft. The full set of EoM in Eq.…”

“…The underlined terms in these two equations capture the contribution of tendon-induced forces in the shear directions. These terms are invariant to the position of the tendon (they do not depend on e y or e z ) and were also used in [21,22,26,27] for the beam-tendon systems and approximated in [28,29] for a compressively loaded blade. Equations (3b) and (3d) represent the bending moments acting on the beam.…”

“…Equations (3e) and (3f) prescribe the torque and warping at the tip of the beam, respectively. The latter condition was not included in the previous studies [21,22,[26][27][28][29] as the effect of warping was assumed to be negligible. In the former equation, the underlined terms relate to the additional moments that are introduced by the shear forces of the eccentrically placed tendon.…”