Structurally coupled characteristics of rotor blade using new rigid-flexible dynamic model based on geometrically exact formulation

In rotor dynamics, blades are normally modelled as a slender beam, in which elastic deformations are coupled with each other. To identify these coupling effects, new rigid-flexible structural model for helicopter rotor system is proposed in this paper. Finite rotations of the whole blade (on flapwise, lagwise, and torsional) are described as three global rigid degrees of freedom. The nonlinear deformation geometrics of the beam is built on geometrically exact beam theory. New expressions for blade strain energy, kinetic energy, and virtual work of various kinds of external forces are derived as functions of finite rotations and elastic deformations. To quantify the coupling characteristics, following the definition of coupling factor in electromagnetics, a new coupling factor between two modal components on each mode is introduced in modal analysis. Simulations show that the new structural model is highly capable of solving static and dynamic problems in rotor system and the maximum deformation that moderate deformation beam theory can predict might be 15% of beam length. After the new coupling factor is applied to study structurally coupled characteristics of rotor blade, it can be concluded that closeness of natural frequencies likely indicates considerable coupling between corresponding DOFs in structure.