Modelling and analysis of coupled flap-lag-torsion vibration characteristics helicopter rotor blades

This paper presents the development of a mathematical approach targeting the modelling and analysis of coupled flap-lag-torsion vibration characteristics of non-uniform continuous rotor blades. The proposed method is based on the deployment of Lagrange's equation of motion to the three-dimensional kinematics of rotor blades. Modal properties derived from classical-beam and torsion theories are utilized as assumed deformation functions. The formulation, which is valid for hingeless, freely hinged and spring-hinged articulated rotor blades, is reduced to a set of closed-form integral expressions. Numerical predictions for mode shapes and natural frequencies are compared with experimental measurements, non-linear finite element analyses and multi-body dynamics analyses for two small-scale hingeless rotor blades. Excellent agreement is observed. The effect of different geometrical parameters on the elastic and inertial coupling is assessed. Additionally, the effect of the inclusion of gyroscopic damping is evaluated. The proposed method, which is able to estimate the first seven coupled modes of vibration in a fraction of a second, exhibits excellent numerical stability. It constitutes a computationally efficient alternative to multi-body dynamics and finite element analysis for the integration of rotor blade flexible modelling into a wider comprehensive rotorcraft tool.