A new dynamic model of a planar rotating hub–beam system based on a description using the slope angle and stretch strain of the beam

A new dynamic model of a planar rotating hub–beam system is developed, where the beam is of an Euler–Bernoulli type and the deformation of the beam is described by the slope angle and stretch strain of the centroid line of the beam. The nonlinear partial differential equations of the system and associated boundary conditions are derived using Hamilton׳s principle. Four corresponding spatially discretized models are obtained based on the new modeling method: (1) the spatially discretized exact slope angle (ESA) model that considers stretch of the beam by using the finite element method (FEM); (2) the spatially discretized fourth-order slope angle (FOSA) model by neglecting the fifth- and higher-order nonlinear terms from a quadratic Taylor expansion of the slope angle by using Galerkin׳s method; (3) the second-order slope angle (SOSA) model by neglecting the third- and higher-order nonlinear terms in the FOSA model; and (4) the simplified second-order slope angle (SSOSA) model without considering stretch of the beam. Dynamic responses of the rotating hub–beam system are studied using the new models for two cases: (I) the angular velocity of the hub is given, and (II) an external torque is applied on the hub. Dynamic responses from the four slope angle models are compared with those from previous models in the literature. Results show that when the angular velocity of the hub is small, dynamic responses from the four models and previous models are close to each other. The ESA model has lower computational efficiency compared with the other three slope angle models. Compared with the ESA and FOSA models, the SOSA model is sufficiently accurate for engineering applications. By linearizing the SOSA model, natural frequencies and mode shapes of the rotating hub–beam system with a constant angular velocity with and without the chordwise bending and stretching coupling effect are calculated and compared. Curve veering and mode shift phenomena occur when the bending and stretching coupling effect is included. Natural frequencies calculated from the new model are in excellent agreement with those from previous models. The FOSA and SOSA models can have better computational accuracy and efficiency than previous models.