Dynamics of hub-variable section beam systems

The dynamics of a hub-variable section beam system which is rotating in a plane is investigated，where the beam is a flexible one. Both the transversal deformation and the longitudinal deformation of the flexible beam are considered. And in the total longitudinal deformation the non-linear coupling term, also known as the longitudinal shortening caused by transversal deformation, is considered here. The approach of assumed modes is used to describe the deformation of the flexible beam. The rigid-flexible coupling dynamic equations of the system are established via employing the second kind of Lagrange’s equation. Then dynamic characteristics of both of the hub-tapered beam system and the hub-trapezium beam system undergoing large overall motions are investigated in details by using numerical simulation. The results obtained in the investigation indicate that: The ratio in width, the ratio in height, the variable section position of the trapezium beam will have a larger impact to the dynamic response and the chord-wise bending natural frequencies.