Modeling study of a flexible hub–beam system with large motion and with considering the effect of shear deformation

For a flexible hub–beam system with large motion, the first-order approximation coupling (FOAC) model is developed currently, which is verified numerically and experimentally to be valid for dynamic description of the system. In the FOAC model, the assumption of Euler–Bernoulli beam is adopted with neglecting the effect of shear deformation of flexible beam. So this model is only available for the case of slender beam. When the beam is short in length direction, shear deformation is a factor that may have biggish effect on system dynamics.In this paper, dynamic modeling of flexible hub–beam system with considering the effect of shear deformation is investigated. Firstly, based on the assumption of Timoshenko beam and using Hamilton's principle, a coupling dynamic model with considering shear deformation is established, in which geometric stiffness term and axial foreshortening effect caused by the transverse deformation of beam are considered in the modeling. Subsequently, the dynamic model is discretized using finite element method (FEM). Finally numerical simulations are carried out to demonstrate the effectiveness of proposed dynamic model. Simulation results indicate that, dynamics characteristics of the hub–beam system using the Timshenko beam hypothesis and the Euler–Bernoulli beam hypothesis are almost identical when the beam is a slender one. For this case, shear deformation has little effect on system dynamics. But when the beam is short in length direction, shear deformation may have biggish effect on system dynamics. This effect becomes larger as the width to length ratio increases.